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Orbital mechanics

Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets, satellites, and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal gravitation. Orbital mechanics is a core discipline within space-mission design and control.

Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets. Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbital plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive maneuvers.

General relativity is a more exact theory than Newton's laws for calculating orbits, and it is sometimes necessary to use it for greater accuracy or in high-gravity situations (e.g. orbits near the Sun).

History
Until the rise of space travel in the twentieth century, there was little distinction between orbital and celestial mechanics. At the time of Sputnik, the field was termed 'space dynamics'. The fundamental techniques, such as those used to solve the Keplerian problem (determining position as a function of time), are therefore the same in both fields. Furthermore, the history of the fields is almost entirely shared.

Johannes Kepler was the first to successfully model planetary orbits to a high degree of accuracy, publishing his laws in 1605. Isaac Newton published more general laws of celestial motion in the first edition of Philosophiæ Naturalis Principia Mathematica (1687), which gave a method for finding the orbit of a body following a parabolic path from three observations. This was used by Edmund Halley to establish the orbits of various comets, including that which bears his name. Newton's method of successive approximation was formalised into an analytic method by Leonhard Euler in 1744, whose work was in turn generalised to elliptical and hyperbolic orbits by Johann Lambert in 1761–1777.

Another milestone in orbit determination was Carl Friedrich Gauss's assistance in the "recovery" of the dwarf planet Ceres in 1801. Gauss's method was able to use just three observations (in the form of pairs of right ascension and declination), to find the six orbital elements that completely describe an orbit. The theory of orbit determination has subsequently been developed to the point where today it is applied in GPS receivers as well as the tracking and cataloguing of newly observed minor planets. Modern orbit determination and prediction are used to operate all types of satellites and space probes, as it is necessary to know their future positions to a high degree of accuracy.

Astrodynamics was developed by astronomer Samuel Herrick beginning in the 1930s. He consulted the rocket scientist Robert Goddard and was encouraged to continue his work on space navigation techniques, as Goddard believed they would be needed in the future. Numerical techniques of astrodynamics were coupled with new powerful computers in the 1960s, and humans were ready to travel to the Moon and return.

Rules of thumb
The following rules of thumb are useful for situations approximated by classical mechanics under the standard assumptions of astrodynamics outlined below. The specific example discussed is of a satellite orbiting a planet, but the rules of thumb could also apply to other situations, such as orbits of small bodies around a star such as the Sun.

 * Kepler's laws of planetary motion:
 * Orbits are elliptical, with the heavier body at one focus of the ellipse. A special case of this is a circular orbit (a circle is a special case of ellipse) with the planet at the center.
 * A line drawn from the planet to the satellite sweeps out equal areas in equal times no matter which portion of the orbit is measured.
 * The square of a satellite's orbital period is proportional to the cube of its average distance from the planet.
 * Without applying force (such as firing a rocket engine), the period and shape of the satellite's orbit will not change.
 * A satellite in a low orbit (or a low part of an elliptical orbit) moves more quickly with respect to the surface of the planet than a satellite in a higher orbit (or a high part of an elliptical orbit), due to the stronger gravitational attraction closer to the planet.
 * If thrust is applied at only one point in the satellite's orbit, it will return to that same point on each subsequent orbit, though the rest of its path will change. Thus one cannot move from one circular orbit to another with only one brief application of thrust.
 * From a circular orbit, thrust applied in a direction opposite to the satellite's motion changes the orbit to an elliptical one; the satellite will descend and reach the lowest orbital point (the periapse) at 180 degrees away from the firing point; then it will ascend back. The period of the resultant orbit will be less than that of the original circular orbit. Thrust applied in the direction of the satellite's motion creates an elliptical orbit with its highest point (apoapse) 180 degrees away from the firing point. The period of the resultant orbit will be longer than that of the original circular orbit.

The consequences of the rules of orbital mechanics are sometimes counter-intuitive. For example, if two spacecraft are in the same circular orbit and wish to dock, unless they are very close, the trailing craft cannot simply fire its engines to go faster. This will change the shape of its orbit, causing it to gain altitude and actually slow down relative to the leading craft, missing the target. The space rendezvous before docking normally takes multiple precisely calculated engine firings in multiple orbital periods, requiring hours or even days to complete.

To the extent that the standard assumptions of astrodynamics do not hold, actual trajectories will vary from those calculated. For example, simple atmospheric drag is another complicating factor for objects in low Earth orbit.

These rules of thumb are decidedly inaccurate when describing two or more bodies of similar mass, such as a binary star system (see n-body problem). Celestial mechanics uses more general rules applicable to a wider variety of situations. Kepler's laws of planetary motion, which can be mathematically derived from Newton's laws, hold strictly only in describing the motion of two gravitating bodies in the absence of non-gravitational forces; they also describe parabolic and hyperbolic trajectories. In the close proximity of large objects like stars the differences between classical mechanics and general relativity also become important.

Laws of astrodynamics
The fundamental laws of astrodynamics are Newton's law of universal gravitation and Newton's laws of motion, while the fundamental mathematical tool is differential calculus.

In a Newtonian framework, the laws governing orbits and trajectories are in principle time-symmetric.

Standard assumptions in astrodynamics include non-interference from outside bodies, negligible mass for one of the bodies, and negligible other forces (such as from the solar wind, atmospheric drag, etc.). More accurate calculations can be made without these simplifying assumptions, but they are more complicated. The increased accuracy often does not make enough of a difference in the calculation to be worthwhile.

Kepler's laws of planetary motion may be derived from Newton's laws, when it is assumed that the orbiting body is subject only to the gravitational force of the central attractor. When an engine thrust or propulsive force is present, Newton's laws still apply, but Kepler's laws are invalidated. When the thrust stops, the resulting orbit will be different but will once again be described by Kepler's laws which have been set out above. The three laws are:
 * 1) The orbit of every planet is an ellipse with the Sun at one of the foci.
 * 2) A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.
 * 3) The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axis of the orbits.

Escape velocity
The formula for an escape velocity is derived as follows. The specific energy (energy per unit mass) of any space vehicle is composed of two components, the specific potential energy and the specific kinetic energy. The specific potential energy associated with a planet of mass M is given by
 * $$\epsilon_p = - \frac{G M}{r} \,$$

where G is the gravitational constant and r is the distance between the two bodies;

while the specific kinetic energy of an object is given by
 * $$\epsilon_k = \frac{v^2}{2} \,$$

where v is its Velocity;

and so the total specific orbital energy is
 * $$ \epsilon = \epsilon_k+\epsilon_p = \frac{v^2}{2} - \frac{G M}{r} \,$$

Since energy is conserved, $$ \epsilon$$ cannot depend on the distance, $$r$$, from the center of the central body to the space vehicle in question, i.e. v must vary with r to keep the specific orbital energy constant. Therefore, the object can reach infinite $$r$$ only if this quantity is nonnegative, which implies
 * $$v\geq\sqrt{\frac{2 G M}{r}}.$$

The escape velocity from the Earth's surface is about 11 km/s, but that is insufficient to send the body an infinite distance because of the gravitational pull of the Sun. To escape the Solar System from a location at a distance from the Sun equal to the distance Sun–Earth, but not close to the Earth, requires around 42 km/s velocity, but there will be "partial credit" for the Earth's orbital velocity for spacecraft launched from Earth, if their further acceleration (due to the propulsion system) carries them in the same direction as Earth travels in its orbit.

Formulae for free orbits
Orbits are conic sections, so the formula for the distance of a body for a given angle corresponds to the formula for that curve in polar coordinates, which is:
 * $$r = \frac{ p }{1 + e \cos \theta}$$
 * $$\mu= G(m_1+m_2)\,$$
 * $$p=h^2/\mu\,$$

$$\mu$$ is called the gravitational parameter. $$m_1$$ and $$m_2$$ are the masses of objects 1 and 2, and $$h$$ is the specific angular momentum of object 2 with respect to object 1. The parameter $$\theta$$ is known as the true anomaly, $$p$$ is the semi-latus rectum, while $$e$$ is the orbital eccentricity, all obtainable from the various forms of the six independent orbital elements.

Circular orbits
All bounded orbits where the gravity of a central body dominates are elliptical in nature. A special case of this is the circular orbit, which is an ellipse of zero eccentricity. The formula for the velocity of a body in a circular orbit at distance r from the center of gravity of mass M can be derived as follows:

Centrifugal acceleration matches the acceleration due to gravity.

So, $$\frac{v^2}{r} = \frac{GM}{r^2}$$

Therefore,
 * $$\ v = \sqrt{\frac{GM} {r}\ }$$

where $$G$$ is the gravitational constant, equal to
 * 6.6743 × 10−11 m3/(kg·s2)

To properly use this formula, the units must be consistent; for example, $$M$$ must be in kilograms, and $$r$$ must be in meters. The answer will be in meters per second.

The quantity $$GM$$ is often termed the standard gravitational parameter, which has a different value for every planet or moon in the Solar System.

Once the circular orbital velocity is known, the escape velocity is easily found by multiplying by $$\sqrt{2}$$:
 * $$\ v = \sqrt 2\sqrt{\frac {GM} {r}\ } = \sqrt{\frac {2GM} {r}\ }.$$

To escape from gravity, the kinetic energy must at least match the negative potential energy. Therefore, $$\frac{1}{2}mv^2 = \frac{GMm}{r}$$
 * $$v = \sqrt{\frac {2GM} {r}\ }.$$

Elliptical orbits
If $$0 < e < 1$$, then the denominator of the equation of free orbits varies with the true anomaly $$\theta$$, but remains positive, never becoming zero. Therefore, the relative position vector remains bounded, having its smallest magnitude at periapsis $$r_p$$, which is given by:
 * $$r_p=\frac{p}{1+e}$$

The maximum value $$r$$ is reached when $$\theta = 180^\circ$$. This point is called the apoapsis, and its radial coordinate, denoted $$r_a$$, is
 * $$r_a=\frac{p}{1-e}$$

Let $$2a$$ be the distance measured along the apse line from periapsis $$P$$ to apoapsis $$A$$, as illustrated in the equation below:
 * $$2a=r_p+r_a$$

Substituting the equations above, we get:
 * $$a=\frac{p}{1-e^2}$$

a is the semimajor axis of the ellipse. Solving for $$p$$, and substituting the result in the conic section curve formula above, we get:
 * $$r=\frac{a(1-e^2)}{1+e\cos\theta}$$

Orbital period
Under standard assumptions the orbital period ($$T\,\!$$) of a body traveling along an elliptic orbit can be computed as:
 * $$T=2\pi\sqrt{a^3\over{\mu}}$$

where: Conclusions:
 * $$\mu\,$$ is the standard gravitational parameter,
 * $$a\,\!$$ is the length of the semi-major axis.
 * The orbital period is equal to that for a circular orbit with the orbit radius equal to the semi-major axis ($$a\,\!$$),
 * For a given semi-major axis the orbital period does not depend on the eccentricity (See also: Kepler's third law).

Velocity
Under standard assumptions the orbital speed ($$v\,$$) of a body traveling along an elliptic orbit can be computed from the Vis-viva equation as:
 * $$v=\sqrt{\mu\left({2\over{r}}-{1\over{a}}\right)}$$

where:
 * $$\mu\,$$ is the standard gravitational parameter,
 * $$r\,$$ is the distance between the orbiting bodies.
 * $$a\,\!$$ is the length of the semi-major axis.

The velocity equation for a hyperbolic trajectory is $$v=\sqrt{\mu\left({2\over{r}}+\left\vert {1\over{a}} \right\vert\right)}$$.

Energy
Under standard assumptions, specific orbital energy ($$\epsilon\,$$) of elliptic orbit is negative and the orbital energy conservation equation (the Vis-viva equation) for this orbit can take the form:
 * $${v^2\over{2}}-{\mu\over{r}}=-{\mu\over{2a}}=\epsilon<0$$

where: Conclusions:
 * $$v\,$$ is the speed of the orbiting body,
 * $$r\,$$ is the distance of the orbiting body from the center of mass of the central body,
 * $$a\,$$ is the semi-major axis,
 * $$\mu\,$$ is the standard gravitational parameter.
 * For a given semi-major axis the specific orbital energy is independent of the eccentricity.

Using the virial theorem we find:
 * the time-average of the specific potential energy is equal to $$2\epsilon$$
 * the time-average of $$r^{-1}$$ is $$a^{-1}$$
 * the time-average of the specific kinetic energy is equal to $$-\epsilon$$

Parabolic orbits
If the eccentricity equals 1, then the orbit equation becomes:
 * $$r={{h^2}\over{\mu}}{{1}\over{1+\cos\theta}}$$

where:
 * $$r\,$$ is the radial distance of the orbiting body from the mass center of the central body,
 * $$h\,$$ is specific angular momentum of the orbiting body,
 * $$\theta\,$$ is the true anomaly of the orbiting body,
 * $$\mu\,$$ is the standard gravitational parameter.

As the true anomaly θ approaches 180°, the denominator approaches zero, so that r tends towards infinity. Hence, the energy of the trajectory for which e=1 is zero, and is given by:
 * $$\epsilon={v^2\over2}-{\mu\over{r}}=0$$

where:
 * $$v\,$$ is the speed of the orbiting body.

In other words, the speed anywhere on a parabolic path is:
 * $$v=\sqrt{2\mu\over{r}}$$

Hyperbolic orbits
If $$e>1$$, the orbit formula,
 * $$r={{h^2}\over{\mu}}{{1}\over{1+e\cos\theta}}$$

describes the geometry of the hyperbolic orbit. The system consists of two symmetric curves. The orbiting body occupies one of them; the other one is its empty mathematical image. Clearly, the denominator of the equation above goes to zero when $$\cos\theta = -1/e$$. we denote this value of true anomaly
 * $$\theta_\infty = \cos^{-1} \left( -\frac1e \right)$$

since the radial distance approaches infinity as the true anomaly approaches $$\theta_\infty$$, known as the true anomaly of the asymptote. Observe that $$\theta_\infty$$ lies between 90° and 180°. From the trigonometric identity $$\sin^2\theta+\cos^2\theta=1$$ it follows that:
 * $$\sin\theta_\infty = \frac1e \sqrt{e^2 - 1}$$

Energy
Under standard assumptions, specific orbital energy ($$\epsilon\,$$) of a hyperbolic trajectory is greater than zero and the orbital energy conservation equation for this kind of trajectory takes form:
 * $$\epsilon={v^2\over2}-{\mu\over{r}}={\mu\over{-2a}}$$

where:
 * $$v\,$$ is the orbital velocity of orbiting body,
 * $$r\,$$ is the radial distance of orbiting body from central body,
 * $$a\,$$ is the negative semi-major axis of the orbit's hyperbola,
 * $$\mu\,$$ is standard gravitational parameter.

Hyperbolic excess velocity
Under standard assumptions the body traveling along a hyperbolic trajectory will attain at $$r =$$ infinity an orbital velocity called hyperbolic excess velocity ($$v_\infty\,\!$$) that can be computed as:
 * $$v_\infty=\sqrt{\mu\over{-a}}\,\!$$

where:
 * $$\mu\,\!$$ is standard gravitational parameter,
 * $$a\,\!$$ is the negative semi-major axis of orbit's hyperbola.

The hyperbolic excess velocity is related to the specific orbital energy or characteristic energy by
 * $$2\epsilon=C_3=v_{\infty}^2\,\!$$

Kepler's equation
One approach to calculating orbits (mainly used historically) is to use Kepler's equation:
 * $$ M = E - \epsilon \cdot \sin E $$.

where M is the mean anomaly, E is the eccentric anomaly, and $$ \epsilon $$ is the eccentricity.

With Kepler's formula, finding the time-of-flight to reach an angle (true anomaly) of $$\theta$$ from periapsis is broken into two steps:
 * 1) Compute the eccentric anomaly $$E$$ from true anomaly $$\theta$$
 * 2) Compute the time-of-flight $$t$$ from the eccentric anomaly $$E$$

Finding the eccentric anomaly at a given time (the inverse problem) is more difficult. Kepler's equation is transcendental in $$E$$, meaning it cannot be solved for $$E$$ algebraically. Kepler's equation can be solved for $$E$$ analytically by inversion.

A solution of Kepler's equation, valid for all real values of $$ \textstyle \epsilon $$ is:

$$ E = \begin{cases}

\displaystyle \sum_{n=1}^{\infty} {\frac{M^{\frac{n}{3}}}{n!}} \lim_{\theta \to 0} \left( \frac{\mathrm{d}^{\,n-1}}{\mathrm{d}\theta^{\,n-1}} \left[ \left( \frac{\theta}{ \sqrt[3]{\theta - \sin(\theta)} } \right) ^n \right] \right) , & \epsilon = 1  \\

\displaystyle \sum_{n=1}^{\infty} { \frac{ M^n }{ n! } } \lim_{\theta \to 0} \left( \frac{\mathrm{d}^{\,n-1}}{\mathrm{d}\theta^{\,n-1}} \left[ \left( \frac{ \theta }{ \theta - \epsilon \cdot \sin(\theta)} \right) ^n \right] \right) , & \epsilon \ne  1

\end{cases} $$

Evaluating this yields:

$$ E = \begin{cases} \displaystyle x + \frac{1}{60} x^3 + \frac{1}{1400}x^5 + \frac{1}{25200}x^7 + \frac{43}{17248000}x^9 + \frac{ 1213}{7207200000 }x^{11} + \frac{151439}{12713500800000 }x^{13} \cdots \ | \ x = ( 6 M )^\frac{1}{3} , & \epsilon = 1  \\ \\ \displaystyle \frac{1}{1-\epsilon} M - \frac{\epsilon}{( 1-\epsilon)^4 } \frac{M^3}{3!} + \frac{(9 \epsilon^2 + \epsilon)}{(1-\epsilon)^7 } \frac{M^5}{5!} - \frac{(225 \epsilon^3 + 54 \epsilon^2 + \epsilon ) }{(1-\epsilon)^{10} } \frac{M^7}{7!} + \frac{ (11025\epsilon^4 + 4131 \epsilon^3 + 243 \epsilon^2 + \epsilon ) }{(1-\epsilon)^{13} } \frac{M^9}{9!} \cdots

, & \epsilon \ne  1

\end{cases} $$

Alternatively, Kepler's Equation can be solved numerically. First one must guess a value of $$E$$ and solve for time-of-flight; then adjust $$E$$ as necessary to bring the computed time-of-flight closer to the desired value until the required precision is achieved. Usually, Newton's method is used to achieve relatively fast convergence.

The main difficulty with this approach is that it can take prohibitively long to converge for the extreme elliptical orbits. For near-parabolic orbits, eccentricity $$\epsilon$$ is nearly 1, and substituting $$e = 1$$ into the formula for mean anomaly, $$E - \sin E$$, we find ourselves subtracting two nearly-equal values, and accuracy suffers. For near-circular orbits, it is hard to find the periapsis in the first place (and truly circular orbits have no periapsis at all). Furthermore, the equation was derived on the assumption of an elliptical orbit, and so it does not hold for parabolic or hyperbolic orbits. These difficulties are what led to the development of the universal variable formulation, described below.

Conic orbits
For simple procedures, such as computing the delta-v for coplanar transfer ellipses, traditional approaches are fairly effective. Others, such as time-of-flight are far more complicated, especially for near-circular and hyperbolic orbits.

The patched conic approximation
The Hohmann transfer orbit alone is a poor approximation for interplanetary trajectories because it neglects the planets' own gravity. Planetary gravity dominates the behavior of the spacecraft in the vicinity of a planet and in most cases Hohmann severely overestimates delta-v, and produces highly inaccurate prescriptions for burn timings. A relatively simple way to get a first-order approximation of delta-v is based on the 'Patched Conic Approximation' technique. One must choose the one dominant gravitating body in each region of space through which the trajectory will pass, and to model only that body's effects in that region. For instance, on a trajectory from the Earth to Mars, one would begin by considering only the Earth's gravity until the trajectory reaches a distance where the Earth's gravity no longer dominates that of the Sun. The spacecraft would be given escape velocity to send it on its way to interplanetary space. Next, one would consider only the Sun's gravity until the trajectory reaches the neighborhood of Mars. During this stage, the transfer orbit model is appropriate. Finally, only Mars's gravity is considered during the final portion of the trajectory where Mars's gravity dominates the spacecraft's behavior. The spacecraft would approach Mars on a hyperbolic orbit, and a final retrograde burn would slow the spacecraft enough to be captured by Mars. Friedrich Zander was one of the first to apply the patched-conics approach for astrodynamics purposes, when proposing the use of intermediary bodies' gravity for interplanetary travels, in what is known today as a gravity assist.

The size of the "neighborhoods" (or spheres of influence) vary with radius $$r_{SOI}$$:
 * $$r_{SOI} = a_p\left(\frac{m_p}{m_s}\right)^{2/5}$$

where $$a_p$$ is the semimajor axis of the planet's orbit relative to the Sun; $$m_p$$ and $$m_s$$ are the masses of the planet and Sun, respectively.

This simplification is sufficient to compute rough estimates of fuel requirements, and rough time-of-flight estimates, but it is not generally accurate enough to guide a spacecraft to its destination. For that, numerical methods are required.

The universal variable formulation
To address computational shortcomings of traditional approaches for solving the 2-body problem, the universal variable formulation was developed. It works equally well for the circular, elliptical, parabolic, and hyperbolic cases, the differential equations converging well when integrated for any orbit. It also generalizes well to problems incorporating perturbation theory.

Perturbations
The universal variable formulation works well with the variation of parameters technique, except now, instead of the six Keplerian orbital elements, we use a different set of orbital elements: namely, the satellite's initial position and velocity vectors $$x_0$$ and $$v_0$$ at a given epoch $$t = 0$$. In a two-body simulation, these elements are sufficient to compute the satellite's position and velocity at any time in the future, using the universal variable formulation. Conversely, at any moment in the satellite's orbit, we can measure its position and velocity, and then use the universal variable approach to determine what its initial position and velocity would have been at the epoch. In perfect two-body motion, these orbital elements would be invariant (just like the Keplerian elements would be).

However, perturbations cause the orbital elements to change over time. Hence, the position element is written as $$x_0(t)$$ and the velocity element as $$v_0(t)$$, indicating that they vary with time. The technique to compute the effect of perturbations becomes one of finding expressions, either exact or approximate, for the functions $$x_0(t)$$ and $$v_0(t)$$.

The following are some effects which make real orbits differ from the simple models based on a spherical Earth. Most of them can be handled on short timescales (perhaps less than a few thousand orbits) by perturbation theory because they are small relative to the corresponding two-body effects.
 * Equatorial bulges cause precession of the node and the perigee
 * Tesseral harmonics of the gravity field introduce additional perturbations
 * Lunar and solar gravity perturbations alter the orbits
 * Atmospheric drag reduces the semi-major axis unless make-up thrust is used

Over very long timescales (perhaps millions of orbits), even small perturbations can dominate, and the behavior can become chaotic. On the other hand, the various perturbations can be orchestrated by clever astrodynamicists to assist with orbit maintenance tasks, such as station-keeping, ground track maintenance or adjustment, or phasing of perigee to cover selected targets at low altitude.

Orbital maneuver
In spaceflight, an orbital maneuver is the use of propulsion systems to change the orbit of a spacecraft. For spacecraft far from Earth—for example those in orbits around the Sun—an orbital maneuver is called a deep-space maneuver (DSM).

Orbital transfer
Transfer orbits are usually elliptical orbits that allow spacecraft to move from one (usually substantially circular) orbit to another. Usually they require a burn at the start, a burn at the end, and sometimes one or more burns in the middle.
 * The Hohmann transfer orbit requires a minimal delta-v.
 * A bi-elliptic transfer can require less energy than the Hohmann transfer, if the ratio of orbits is 11.94 or greater, but comes at the cost of increased trip time over the Hohmann transfer.
 * Faster transfers may use any orbit that intersects both the original and destination orbits, at the cost of higher delta-v.
 * Using low thrust engines (such as electrical propulsion), if the initial orbit is supersynchronous to the final desired circular orbit then the optimal transfer orbit is achieved by thrusting continuously in the direction of the velocity at apogee. This method however takes much longer due to the low thrust.

For the case of orbital transfer between non-coplanar orbits, the change-of-plane thrust must be made at the point where the orbital planes intersect (the "node"). As the objective is to change the direction of the velocity vector by an angle equal to the angle between the planes, almost all of this thrust should be made when the spacecraft is at the node near the apoapse, when the magnitude of the velocity vector is at its lowest. However, a small fraction of the orbital inclination change can be made at the node near the periapse, by slightly angling the transfer orbit injection thrust in the direction of the desired inclination change. This works because the cosine of a small angle is very nearly one, resulting in the small plane change being effectively "free" despite the high velocity of the spacecraft near periapse, as the Oberth Effect due to the increased, slightly angled thrust exceeds the cost of the thrust in the orbit-normal axis.

Gravity assist and the Oberth effect
In a gravity assist, a spacecraft swings by a planet and leaves in a different direction, at a different speed. This is useful to speed or slow a spacecraft instead of carrying more fuel.

This maneuver can be approximated by an elastic collision at large distances, though the flyby does not involve any physical contact. Due to Newton's Third Law (equal and opposite reaction), any momentum gained by a spacecraft must be lost by the planet, or vice versa. However, because the planet is much, much more massive than the spacecraft, the effect on the planet's orbit is negligible.

The Oberth effect can be employed, particularly during a gravity assist operation. This effect is that use of a propulsion system works better at high speeds, and hence course changes are best done when close to a gravitating body; this can multiply the effective delta-v.

Interplanetary Transport Network and fuzzy orbits
It is now possible to use computers to search for routes using the nonlinearities in the gravity of the planets and moons of the Solar System. For example, it is possible to plot an orbit from high Earth orbit to Mars, passing close to one of the Earth's Trojan points. Collectively referred to as the Interplanetary Transport Network, these highly perturbative, even chaotic, orbital trajectories in principle need no fuel beyond that needed to reach the Lagrange point (in practice keeping to the trajectory requires some course corrections). The biggest problem with them is they can be exceedingly slow, taking many years. In addition launch windows can be very far apart.

They have, however, been employed on projects such as Genesis. This spacecraft visited the Earth-Sun point and returned using very little propellant.

title: Orbital mechanics


text:
Sidney Darlington

Sidney Darlington (July 18, 1906 – October 31, 1997) was an American electrical engineer and inventor of a transistor configuration in 1953, the Darlington pair. He advanced the state of network theory, developing the insertion-loss synthesis approach, and invented chirp radar, bombsights, and gun and rocket guidance.

Darlington was awarded a B.S. in physics, magna cum laude, from Harvard in 1928, where he was elected to Phi Beta Kappa. He also received a B.S. in E.E. from MIT in 1929, and a Ph.D. in physics from Columbia in 1940.

In 1945, he was awarded the Presidential Medal of Freedom, the United States' highest civilian honor, for his contributions during World War II. He was an elected member of the National Academy of Engineering, which cited his contributions to electrical network theory, radar, and guidance systems. In 1975, he received IEEE's Edison Medal "For basic contributions to network theory and for important inventions in radar systems and electronic circuits" and the IEEE Medal of Honor in 1981 "For fundamental contributions to filtering and signal processing leading to chirp radar".

He died at his home in Exeter, New Hampshire, USA, at the age of 91.

Patents

 * — Wave Transmission Network
 * — Semiconductor signal translating devices.(ed., "Darlington Transistor")
 * — Bombsight Computer
 * — Tracking Device
 * — Fire Control Computer
 * — Pulse Transmission(Chirp)
 * — Rocket Guidance
 * — Two-Port Network Synthesis
 * — Chirp Pulse Equalizer

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Sidney Darlington


text:
1904 Summer Olympics

The 1904 Summer Olympics (officially the Games of the III Olympiad and also known as St. Louis 1904) were an international multi-sport event held in St. Louis, Missouri, United States, from 1 July to 23 November 1904. Many events were conducted at what is now known as Francis Field on the campus of Washington University in St. Louis. This was the first time that the Olympic Games were held outside Europe.

Tensions caused by the Russo–Japanese War and difficulties in traveling to St. Louis resulted in very few top-class athletes from outside the United States and Canada taking part in the 1904 Games. Only 69–74 of the 651 athletes who competed came from outside North America, and only between 12 and 15 nations were represented in all. Some events subsequently combined the U.S. national championship with the Olympic championship. The current three-medal format of gold, silver and bronze for first, second and third place was introduced at the 1904 Olympics.

Background
Chicago, Illinois, initially won the bid to host the 1904 Summer Olympics, but the organizers of the Louisiana Purchase Exposition in St. Louis would not accept another international event in the same timeframe.

The exposition organization began to plan for its own sports activities, informing the Chicago OCOG that its own international sports events intended to eclipse the Olympic Games unless they were moved to St. Louis. Pierre de Coubertin, founder of the modern Olympic movement, then intervened and awarded the Games to St. Louis.

Highlights
Boxing, dumbbells, catch wrestling (which later became freestyle wrestling), and the decathlon made their debuts. The swimming events were held in a temporary pond near Skinker and Wydown Boulevards, where "lifesaving demonstrations" of unsinkable lifeboats for ocean liners took place.

One of the most remarkable athletes was the American gymnast George Eyser, who won six medals even though his left leg was made of wood, and Frank Kugler won four medals in freestyle wrestling, weightlifting and tug of war, making him the only competitor to win a medal in three different sports at the same Olympic Games. Chicago runner James Lightbody won the steeplechase and the 800 m and then set a natural world record in the 1500 m. Harry Hillman won both the 200 m and 400 m hurdles and also the flat 400 m. Sprinter Archie Hahn was champion in the 60 m, 100 m and 200 m. In this last race, he set an Olympic record in 21.6, a natural record that stood for 28 years. In the discus, after American Martin Sheridan had thrown exactly the same distance as his compatriot, Ralph Rose (39.28 m), the judges gave them both an extra throw to decide the winner. Sheridan won the decider and claimed the gold medal. Ray Ewry again won all three standing jumps.

The team representing Great Britain was awarded a total of two medals, both won by Irish athletes. The top non-U.S. athlete was Emil Rausch of Germany, who won three swimming events. Zoltán Halmay of Hungary and Charles Daniels of the United States each won two swimming gold medals. Galt Football Club from Canada won the gold medal in football.

Anthropology Days
The organizers of the World's Fair held "Anthropology Days" on August 12 and 13. Since the 1889 Paris Exposition, human zoos, as a key feature of world's fairs, functioned as demonstrations of anthropological notions of race, progress, and civilization. These goals were followed also at the 1904 World's Fair. Fourteen hundred indigenous people from Southeast Asia, the Pacific Islands, East Asia, Africa, the Middle East, South America and North America were displayed in anthropological exhibits that showed them in their natural habitats. Another 1600 indigenous people displayed their culture in other areas of the Louisiana Purchase Exposition (LPE), including on the fairgrounds and at the Model School, where American Indian boarding schools students demonstrated their successful assimilation. The sporting event itself took place with the participation of about 100 paid indigenous men (no women participated in Anthropology Days, though some, notably the Fort Shaw Indian School girls basketball team, did compete in other athletic events at the LPE). Contests included "baseball throwing, shot put, running, broad jumping, weight lifting, pole climbing, and tugs-of-war before a crowd of approximately ten thousand". According to theorist Susan Brownell, world's fairs – with their inclusion of human zoos – and the Olympics were a logical fit at this time, as they "were both linked to an underlying cultural logic that gave them a natural affinity". Also, one of the original intentions of Anthropology Days was to create publicity for the official Olympic events.

Sports
The 1904 Summer Olympic program featured 16 sports encompassing 95 events in 18 disciplines. Swimming, diving and water polo are considered three disciplines of the same sport, aquatics. In July 2021 the IOC accepted the recommendation of Olympic historian Bill Mallon regarding which sports and events should be considered as Olympic. The number of events in each discipline is noted in parentheses. • Aquatics

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New sports
Boxing made its Olympic debut at the St. Louis Games. The sport has since featured at every Summer Olympics, except for the 1912 Stockholm Games.

While wrestling made a return, it was exclusively the newly-debuted catch wrestling (which later became freestyle wrestling) as opposed to Greco-Roman style of the 1896 Summer Olympics. Five nations were represented, with each of the 42 competitors having resided in the United States. Later editions would have both styles of wrestling in their programs.

Demonstration sports
Basketball, hurling, American football and Gaelic football were featured as unofficial sports. There was a demonstration bout of women's boxing. Baseball is also noted by the World Baseball Softball Confederation to have appeared at the Games, though it does not appear in the list compiled by Olympic historian Bill Mallon and any results are not known.

Venues
Five sports venues were used for the 1904 Summer Olympics. The venues included Glen Echo Country Club, the first golf course constructed west of the Mississippi River, which had opened in 1901. Three Olympic sports were hosted at Forest Park, the site of the Louisiana Purchase Exposition which was being held concurrently with the Olympics: the Life Saving Exhibition Lake at Forest Park was used for the diving, swimming, and water polo events.

Creve Coeur Lake became the first park of St. Louis County in 1945. The Lake has hosted rowing regattas since 1882 and still hosts them as of 2010. Francis Olympic Field and Gymnasium are still in use on the Washington University in St. Louis campus as of 2021. An ornamental gate commemorating the 1904 Games was constructed outside the stadium immediately after the Exposition. A swimming pool was added to the gymnasium in 1985. Forest Park, constructed in 1876, is still in use as of 2021 and attracts over 12 million visitors annually. Glen Echo Country Club remains in use as a golf course today as of 2021.

Participating nations
[[File:1904 Summer Olympic games countries.png|thumb|400px|Participants.

Blue = Participated for the first time

Green = Previously participated

Host city (St Louis) marked by yellow square]]

Athletes from twelve nations competed in St. Louis. Numbers in parentheses indicate the number of known competitors for each nation. Due to the difficulty of getting to St. Louis in 1904, and European tensions caused by the Russo-Japanese War, only 69–74 athletes from outside North America participated in the Olympics.

Disputed
Some sources also list athletes from the following nations as having competed at these Games:
 * [[file:Newfoundland - banner of arms.svg|border|22px]] Newfoundland Colony (1)
 * [[file:Newfoundland - banner of arms.svg|border|22px]] Newfoundland Colony (1)

Medal count
These are the nations that won medals at the 1904 Games.

Notes on medalists
The nationalities of some medalists were disputed, as many American athletes were recent immigrants to the United States who had not yet been granted U.S. citizenship. In July 2021, the IOC accepted the recommendations of Olympic historian Bill Mallon, and adjusted their database with regard to the following cases:

 * In 2009, historians from the International Society of Olympic Historians discovered that cyclist Frank Bizzoni, believed to be an American, was still an Italian citizen when he competed in 1904: he received U.S. citizenship in 1917.
 * Two Norwegian-American wrestlers, Charles Ericksen and Bernhoff Hansen won gold medals. In 2012, Norwegian historians found documentation showing that Ericksen did not receive American citizenship until March 22, 1905, while Hansen probably never received American citizenship. The historians therefore petitioned the IOC to have the athletes registered as Norwegians. In May 2013, it was reported that the Norwegian Olympic Committee had filed a formal application for changing the nationality of the wrestlers in the IOC's medal database, which was done.
 * Swimmer and multi-medalist Francis Gailey competed in 1904 as an Australian. He immigrated to America in 1906, sailing to San Francisco on the SS Sonoma, and worked as a banker in California, living for a time in Ontario, Canada, where he married Mary Adams, and finally settled in southern California in 1918, managing orange-grove plantations.
 * Multi-medalist Frank Kugler of Germany, a member of the St. Louis Southwest Turnverein team, was granted U.S. citizenship in 1913.
 * Gustav Tiefenthaler was born in Switzerland, but the family moved to the United States when he was a child: he represented the South Broadway AC in St. Louis. At the Olympics, Tiefenthaler wrestled one bout and lost, but earned a bronze medal.
 * French-American Albert Corey won silver medals in the marathon, and in the team race as part of a mixed team (together with four undisputed Americans).
 * Austrian-American gymnast Julius Lenhart won gold and silver medals in individual events and gold medal in team competition as a part of the mixed team.

The IOC also counted one gold, one silver, and two bronze medals won by the American fencer Albertson Van Zo Post for Cuba instead of the United States: the IOC also showed Charles Tatham as Cuban for individual fencing events and American for the team event, but he was an American.

title: 1904 Summer Olympics


text:
Doctor Dolittle

Doctor John Dolittle is the central character of a series of children's books by Hugh Lofting starting with the 1920 The Story of Doctor Dolittle. He is a physician who shuns human patients in favour of animals, with whom he can speak in their own languages. He later becomes a naturalist, using his abilities to speak with animals to better understand nature and the history of the world.

Doctor Dolittle first appeared in the author's illustrated letters to his children, written from the trenches during World War I when actual news, he later said, was either too horrible or too dull. The stories are set in early Victorian England, where Doctor John Dolittle lives in the fictional English village of Puddleby-on-the-Marsh in the West Country.

Doctor Dolittle has a few close human friends, including Tommy Stubbins and Matthew Mugg, the Cats'-Meat Man. The animal team includes Polynesia (a parrot), Gub-Gub (a pig), Jip (a dog), Dab-Dab (a duck), Chee-Chee (a monkey), Too-Too (an owl), the Pushmi-pullyu, and a white mouse later named simply "Whitey". Later on, in the 1925 novel Doctor Dolittle's Zoo, Whitey founds (with the doctor's help) the Rat and Mouse Club, whose membership eventually reaches some 5,000 rats and mice.

Inspiration
One inspiration for his character appears to be the Scottish surgeon John Hunter.

Stories
The Story of Doctor Dolittle: Being the History of His Peculiar Life at Home and Astonishing Adventures in Foreign Parts Never Before Printed (1920) begins the series. The sequel The Voyages of Doctor Dolittle (1922) won the prestigious Newbery Medal. The next three, Doctor Dolittle's Post Office (1923), Doctor Dolittle's Circus (1924), and Doctor Dolittle's Caravan (1926) take place during and/or after the events of The Story of Doctor Dolittle. Five more novels followed, and after Lofting's death in 1947, two more volumes of short, previously unpublished pieces appeared.

The stories, in order of publication, are:

 * 1) The Story of Doctor Dolittle (1920)
 * 2) The Voyages of Doctor Dolittle (1922)
 * 3) Doctor Dolittle's Post Office (1923)
 * 4) Doctor Dolittle's Circus (1924)
 * 5) "Doctor Dolittle Meets a Londoner in Paris" (1925)
 * 6) Doctor Dolittle's Zoo (1925)
 * 7) Doctor Dolittle's Caravan (1926)
 * 8) Doctor Dolittle's Garden (1927)
 * 9) Doctor Dolittle in the Moon (1928)
 * 10) Gub Gub's Book: An Encyclopaedia of Food (1932)
 * 11) Doctor Dolittle's Return (1933)
 * 12) Doctor Dolittle's Birthday Book (1936)
 * 13) Doctor Dolittle and the Secret Lake (copyrighted 1923, but not published until 1948)
 * 14) Doctor Dolittle and the Green Canary (1950)
 * 15) Doctor Dolittle's Puddleby Adventures (1952)
 * 16) *"The Sea Dog"
 * 17) *"Dapple"
 * 18) *"The Dog Ambulance"
 * 19) *"The Stunned Man"
 * 20) *"The Crested Screamers"
 * 21) *"The Green Breasted Martins"
 * 22) *"The Story of the Maggot"
 * 23) *"The Lost Boy"

Gub Gub's Book: An Encyclopaedia of Food (1932) is purportedly written by the pig Gub-Gub. It is a series of food-themed animal vignettes. In the text, the pretence of Gub-Gub's authorship is dropped; Tommy Stubbins, Dr. Dolittle's assistant, explains that he is reporting a series of Gub-Gub's discourses to the other animals of the Dolittle household around the evening fire. Stubbins also says that the full version of Gub-Gub's encyclopaedia, which was an immense and poorly-organized collection of scribblings written by the pig in a language for pigs invented by Dr. Dolittle, was too long to translate into English.

Doctor Dolittle's Birthday Book (1936) is a little day-book illustrated with pictures and quotations from the earlier stories. It appeared between Doctor Dolittle's Return and Doctor Dolittle and the Secret Lake.

"Doctor Dolittle Meets a Londoner in Paris" is a short story included in The Flying Carpet, pp. 110–19 (1925), an anthology of children's short stories and poems with illustrations by Cynthia Asquith.

In April 2021, the Japanese biologist Shinichi Fukuoka created a new story Dr. Dolittle Saves Galápagos Islands which appeared in The Asahi Shimbun.

Chronology
The main events of The Story of Doctor Dolittle take place in 1819 or 1820, although the events of the early chapters seem to be spread over several years. The Voyages of Doctor Dolittle begins in 1839.

Dolittle returned from his journey to the moon in Doctor Dolittle's return during a full lunar eclipse that was visible low in the sky one late evening in spring. This was the first full lunar eclipse for a couple of years, and it took place in May 1844 in real life.

Backstory references indicate that Dr. Dolittle travelled to the North Pole in April 1809, and already knew how to speak to some species of animals at that date, suggesting that the early chapters of The Story of Doctor Dolittle take place before that date. However, it is possible that the internal chronology is not consistent.

The internal chronology of the books is somewhat different from the publishing order. The first book is followed by Doctor Dolittle's Circus (1924), Doctor Dolittle's Caravan (1926), and Doctor Dolittle and the Green Canary (1950). Only then follows the second book, The Voyages of Doctor Dolittle (1922), continued by Doctor Dolittle's Zoo (1925). After that, the publishing order is restored; Doctor Dolittle's Garden (1927) is followed by Doctor Dolittle in the Moon (1928) and Doctor Dolittle's Return (1933), ending with Doctor Dolittle and the Secret Lake (1948).

Doctor Dolittle's Post Office (1923) can't be placed anywhere in the internal chronology without creating contradictions. Doctor Dolittle's Circus contains references to events that occurred in Post Office, indicating that Post Office must precede Circus. But the Prologue of Post Office indicates just as definitely that it must happen sometime after Circus. Furthermore, in the narrative sequence that stretches from the end of the first book, through Circus and Caravan, to Green Canary, there's no gap into which Post Office could be inserted. For the sake of a reading order, the most logical options are to place Post Office immediately before Circus, or immediately after Green Canary.

The stories, in order of internal chronology, are:

 * The Story of Doctor Dolittle (1920)
 * "The Green Breasted Martins" (follows Chapter XII in The Story of Doctor Dolittle; collected in Doctor Dolittle's Puddleby Adventures (1952))

 * Doctor Dolittle's Circus (1924)
 * Doctor Dolittle's Caravan (1926)
 * "The Crested Screamers" (takes place within Part One, Chapter 12 of Doctor Dolittle's Caravan; collected in Doctor Dolittle's Puddleby Adventures (1952))
 * "The Lost Boy" (takes place within Part One, Chapter 12 of Doctor Dolittle's Caravan; collected in Doctor Dolittle's Puddleby Adventures (1952))

 * Doctor Dolittle and the Green Canary (1950)
 * "Doctor Dolittle Meets a Londoner in Paris" (1925 – uncollected)

 * Doctor Dolittle's Post Office (1923)
 * The Voyages of Doctor Dolittle (1922)
 * Doctor Dolittle's Zoo (1925)
 * Doctor Dolittle's Garden (1927)
 * "The Sea Dog" (takes place at the beginning of Doctor Dolittle's Garden; collected in Doctor Dolittle's Puddleby Adventures (1952))
 * "Dapple" (takes place at the beginning of Doctor Dolittle's Garden; collected in Doctor Dolittle's Puddleby Adventures (1952))
 * "The Dog Ambulance" (takes place at the beginning of Doctor Dolittle's Garden; collected in Doctor Dolittle's Puddleby Adventures (1952))
 * "The Stunned Man" (takes place at the beginning of Doctor Dolittle's Garden; collected in Doctor Dolittle's Puddleby Adventures (1952))
 * "The Story of the Maggot" (given a greatly reduced summary at the conclusion to early printings of Part Two, Chapter 4 of Doctor Dolittle's Garden; collected in Doctor Dolittle's Puddleby Adventures (1952))

 * Gub Gub's Book: An Encyclopaedia of Food (1932)
 * Doctor Dolittle in the Moon (1928)
 * Doctor Dolittle's Return (1933)
 * Doctor Dolittle's Birthday Book (1936)
 * Doctor Dolittle and the Secret Lake (copyrighted 1923, but not published until 1948)

Adaptations
There have been a number of adaptations of the Doctor Dolittle stories in other media:

Animation: Audio:
 * 1928: Doktor Dolittle und seine Tiere (Doctor Dolittle and his Animals), a silent animated short in German by Lotte Reiniger
 * 1970–1972: Doctor Dolittle animated TV series, produced at DePatie-Freleng Enterprises for 20th Century Fox Television
 * 1984: The Voyages of Doctor Dolittle (ドリトルせんせいものがたり) (U.S.-Japan coproduction, not aired in Japan until 1997)
 * 2011: The Voyages of Young Doctor Dolittle direct-to-video animated film, starring Jane Seymour, Jason Alexander, and Tim Curry
 * 1933–1934: NBC radio series
 * 1995–2001: BBC audio books read by Alan Bennett

Stages
 * 1973: stage adaptation by the Philadelphia Boys Choir & Chorale, which was used during their concert tour to Belgium and Kenya
 * 1998: Doctor Dolittle stage musical by Leslie Bricusse, based on the 1967 film musical
 * 2007: stage musical adaptation by TheatreWorksUSA, written by Randy Courts and Mark St. Germain

Film:
 * 1967: Doctor Dolittle, starring Rex Harrison
 * 1998: Dr. Dolittle and its sequels: Dr. Dolittle 2 (2001), Dr. Dolittle 3 (2006), Dr. Dolittle: Tail to the Chief (2008), and Dr. Dolittle: Million Dollar Mutts (2009). The first two star Eddie Murphy in the title role, whereas all five star Kyla Pratt as his daughter, Maya. Norm Macdonald appears in each film as the voice of their dog, Lucky.
 * 2020: Dolittle, a live action adaptation starring Robert Downey Jr., Michael Sheen, and Antonio Banderas.

Video games:
 * 2006: Dr. Dolittle PS2 video game produced by	Aqua Pacific and distributed by Blast! Entertainment Ltd.

Appearances in other languages
A Russian children's novel Doctor Aybolit (Doctor Oh-it-hurts) by Korney Chukovsky (first published in 1924) was loosely based on the stories of Doctor Dolittle. The original novel credited Lofting's work, as did Chukovsky in his memoirs.

Norwegian playwright, songwriter, and illustrator Thorbjørn Egner made an album called Doktor Dyregod (Doctor good-toward-animals) with songs and story based on Doctor Dolittle.

All the books in the series have been translated into Japanese by Masuji Ibuse and into Lithuanian by Pranas Mašiotas.

title: Doctor Dolittle


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User:Youthinayzhuh/Articles

Here's a complete list of what articles I have worked on.

(M) Minor changes made only. (O) Originator of article.

Most Wanted articles added:
 * (O) - 11 Feb 03 - 1904 Summer Olympics
 * (O) - 10 Feb 03 - Period 6 element
 * (O) - 10 Feb 03 - Period 4 element

Requested articles added:
 * Animals:
 * (O) - 09 Feb 03 - sand dollar
 * (O) - 08 Feb 03 - How to give a dog a bath

Independently added/edited articles:
 * (O) - 10 Feb 03 - Thermite synthesis
 * (O) - 09 Feb 03 - List of NES accessories
 * (O) - 09 Feb 03 - Hashish oil
 * (M) - 08 Feb 03 - Nintendo Entertainment System
 * (M) - 08 Feb 03 - The Doors of Perception

title: User:Youthinayzhuh/Articles


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Gaius Caesar

Gaius Caesar (20 BC – 21 February 4 AD) was a grandson and heir to the throne of Roman emperor Augustus, alongside his younger brother Lucius Caesar. Although he was born to Marcus Vipsanius Agrippa and Julia, Augustus' only daughter, Gaius and Lucius were raised by their grandfather as his adopted sons and joint-heirs. He experienced an accelerated political career befitting a member of the Julio-Claudian dynasty, with the Roman Senate allowing him to advance his career without first holding a quaestorship or praetorship, offices that ordinary senators were required to hold as part of the cursus honorum.

In 1 BC, Gaius was given command of the eastern provinces, after which he concluded a peace treaty with King Phraates V of Parthia on an island in the Euphrates. Shortly afterwards, he was appointed to the office of consul for the following year, 1 AD. The year after Gaius' consulship, Lucius died at Massilia in the month of August. Approximately eighteen months later, Gaius died of an illness in Lycia. He was married to his second cousin Livilla but they did not have children. In 4 AD, following the deaths of Gaius and Lucius, Augustus adopted his stepson, Tiberius, as well as his sole-surviving grandson, Agrippa Postumus.

Background

Marcus Vipsanius Agrippa was an early supporter of Augustus (then "Octavius") during the Final War of the Roman Republic that ensued as a result of the assassination of Julius Caesar in 44 BC. He was a key general in Augustus' armies, commanding troops in pivotal battles against Mark Antony and Sextus Pompeius. From early on, Agrippa was trusted to handle affairs in the eastern provinces and was even given the signet ring of Augustus, who was seemingly on his deathbed in 23 BC, a sign that he would become princeps were Augustus to die. However, as soon as he recovered, Augustus began to show he favored his nephew, Marcus Claudius Marcellus, then just 19. However, Marcellus died of an illness that had spread throughout the city of Rome that year.

With Marcellus gone, Augustus arranged for the marriage of Agrippa to his daughter Julia the Elder, who was previously the wife of Marcellus. Agrippa was given tribunicia potestas ("the tribunician power") in 18 BC, a power that Augustus received in 23 BC, and later on was exercised only by the emperor and shared with some heirs (Agrippa, Tiberius). The tribunician power allowed him to control the Senate. Agrippa acted as tribune in the Senate to pass important legislation and, though he lacked some of the emperor's power and authority, he was approaching the position of co-regent.

Early life and family
Gaius was born in Rome in 20BC to Marcus Vipsanius Agrippa and Julia the Elder. He was a part of the Julio-Claudian dynasty, and was related to all the Julio-Claudian emperors. On his mother's side, he was the oldest grandson of emperor Augustus. He was the stepson of Tiberius by his mother Julia's marriage to him, and brother in law of Claudius by his sister Agrippina the Elder's marriage to Germanicus. He also was the uncle of Caligula, who was the son of his sister Agrippina. The last emperor of the dynasty was Nero, who was Gaius' great-nephew and the grandson of Germanicus. An annual sacrifice on his birthday was granted in a decree.

In 17BC, his brother Lucius was born. Augustus immediately adopted both Gaius and Lucius from their father by a symbolic sale, and named both Gaius and Lucius his (personal) heirs. It is unknown what their father thought of the adoption. Their adoptive father initiated them into administrative life when they were still young, and sent them to the provinces as consuls-elect. Augustus taught Gaius and Lucius how to read, swim, and the other elements of education, taking special pains to train them to imitate his own handwriting, mostly by himself. Shortly after their adoption in the summer, Augustus held the fifth-ever Ludi Saeculares ("Secular Games"). The adoption of the boys coupled with the games served to introduce a new era of peace – the Pax Augusta.

That year his family left for the province of Syria, because Agrippa was given command of the eastern provinces with proconsular imperium maius. Four years later, in 13BC, Gaius took part in the Trojan games with the other patrician youths at the dedication of the Theatre of Marcellus. Also in 13BC, Agrippa and Augustus returned to Rome. Augustus sent Agrippa to Pannonia at the end of 13 to suppress a rebellion. Agrippa arrived there that winter (in 12BC), but the Pannonians gave up their plans. Agrippa returned to Campania in Italy, where he fell ill and died soon after. The death of Gaius' father made succession a pressing issue. The aurei and denarii issued in 13–12BC made clear the Emperor's dynastic plans for Gaius and Lucius.

The luxurious rural villa-estate at Ossaia near Cortona was owned by Gaius and Lucius Caesar.

Their father was no longer available to assume the reins of power if the Emperor were to die, and Augustus had to make it clear who his intended heirs were in case anything should happen. To learn about military affairs, he accompanied Tiberius in his campaign against the Sicambri in 8BC. The year before, Tiberius' brother Drusus the Elder died on his way back from a campaign across the Rhine. Tiberius was given command of Germania, and waged two campaigns across the Rhine in 8BC and 7BC. He marched his army between the Elbe and the Rhine, and met little resistance, except from the Sicambri. Tiberius came close to exterminating the Sicambri, and had those who survived transported to the Roman side of the Rhine, where they could be watched more closely.

Early political career
Gaius was elected consul designatus by the Comitia Centuriata in 6BC with the intention that he should assume the consulship in his twentieth year. The next year, Augustus made him a pontifex, and granted him the right to attend Senate meetings, behold spectacles, and to be present at banquets with senators. Roman support for the young prince soon spread through Italy; statues and inscriptions were set up in every district to commemorate the fact that he had been nominated as a consul at an unprecedented age of fourteen.

The following year (5BC), when he attained military age, he assumed the toga virilis, and was introduced by Augustus to the Senate, who declared him as princeps iuventutis ("leader of the youth") and sevir turmae (commander of a cavalry division). Having been designated consul, he was allowed to give his opinion to the senate. Lucius, three years his junior, was granted the same honours after the appropriate interval had elapsed.

Herodian succession
Following the death of King Herod of Judaea in 4BC, his sons Antipas and Archelaus both came to Rome with their own copy of Herod's will to plead their case as to why they each deserved to inherit their father's kingdom. Augustus, as usual, declined the sole responsibility of the decision. He convened a council of senators, among whom he included Gaius. The council decided to ratify the will brought by Archelaus, which included a large bequest to Augustus and his wife Livia. The cities of Judaea rose in revolt after the procurator, Sabinus, garrisoned Syria Palaestina to guard the tens of millions of sesterces promised to the Emperor. The governor of Syria, Varus, was forced to bring in the legions from Syria to restore order.

At the same time, King Phraates IV of Parthia had seized Armenia with the help of Armenian nationalists, and expelled Tigranes IV, the king installed by Rome. Historian Ferrero speculates that Phraates may have been hoping to use Armenia as a bargaining chip to secure the release of his sons who were held captive by the Romans. Roman supremacy in Asia depended on its possession of Armenia as a protectorate. Before Rome could deal with the Parthians in Armenia, it would first need to make its Syrian legions available, which were still tied down in Palestine. In order to free up the legions there, the Kingdom of Judaea was divided among the sons of Herod the Great. One half remained under Archelaus, while the other half was subdivided between his brothers, Antipas and Philip. This served to restore stability to the region, whilst keeping Judaea from becoming powerful. Having settled matters in Judaea, the Emperor decided to deploy an army to Armenia to re-establish its status as a Roman protectorate and to show the eastern world that Rome held dominion over all land as far as the Euphrates.

Departure

Due to his advanced age, Augustus was unable to travel to the east himself. There were few to whom the Emperor could entrust matters in the east, but he was confident in Gaius. Gaius made a good choice because his presence represented that of the imperial family – all orders, promises, or threats coming from him were as valid as if they came from the Emperor himself. Nonetheless, he was only eighteen, and therefore too young for the conduct of important business.

Before leaving for the east, he and his brother Lucius were given the authority to consecrate buildings, and they did, with their management of the games held to celebrate the dedication of the Temple of Mars Ultor (1 August 2BC). His youngest brother, Postumus, participated in the Trojan game with the rest of the equestrian youth. 260 lions were slaughtered in the Circus Maximus, there was gladiatorial combat, a naval battle between the "Persians" and the "Athenians", and 36 crocodiles were slaughtered in the Circus Flaminius.

Friends of Augustus had hoped that he would abandon his plan of sending Gaius to the east but, faced with increasing troubles there, he persisted with the plan and dispatched Gaius to Syria at the beginning of 1BC. The Emperor entrusted Gaius with proconsular authority and had him marry his second cousin Livilla, the daughter of Drusus the Elder and Antonia Minor.

Due to Gaius' youth and inexperience, the Emperor had advisors go with him. Among his entourage to the east were: Marcus Lollius as adiutor ("helper"), Publius Sulpicius Quirinus as rector ("guide"), the future historian Velleius Paterculus, Lucius Domitius Ahenobarbus (grandfather of Nero), Juba II of Numidia, and future praetorian prefect Sejanus.

On his way to Syria, Gaius met with Tiberius, who had abandoned politics and retired to Rhodes. According to Suetonius, Gaius gave Tiberius a cold reception on the isle of Samos. Tiberius was alienated at the meeting, by the behaviour of both Lollius and Gaius' centurions. Suetonius further wrote that Tiberius wrote to the Emperor that Lollius should be replaced. Lollius' rivalry with Tiberius continued even after Gaius and his entourage reached Syria. Lollius strove to turn Gaius against Tiberius; Gaius, in any case, had no affection for the man who had contributed, directly or indirectly, to the ruin of his mother. On one occasion, Lollius offered to decapitate Tiberius if Gaius gave the word. Suetonius wrote that it was Lollius' growing influence that compelled Tiberius to plead with Augustus for his return to Rome.

Consulship
The next year, on 1 January, he entered the consulship in absentia with his brother-in-law, Lucius Aemilius Paullus, in accordance with the decision of 6BC which named him consul designate. Gaius, who was twenty, had reached Asia, and was probably at Antioch at the time his consulship commenced, where he was organizing an army for the invasion of Armenia and opening negotiations with Phraates in the hopes of securing an agreement. The Emperor did not desire an open war, and the king of Parthia seemed open to peace. Negotiations were probably hastened by the presence of Gaius' army in Syria, which threatened Parthia. From every corner, the young consul was visited by envoys offering requests and paying homage. This year, monuments were raised to him and to his brother as the son of Ares or as Ares himself.

His inexperience meant he was forced to rely on his companions, namely the unruly Lollius, who had taken advantage of the powers he held, and was reportedly holding towns, individuals, and even sovereign princes for ransom. After Gaius opened negotiations with Phraates, Lollius offered the Parthian king certain concessions in return for money.

Preparations for the war continued into the spring and summer of 1AD, at which point there had been a successful breakthrough in negotiations. As Phraates was not willing to go to war, he agreed to evacuate Armenia and abandon his brothers who were still in Roman captivity. In the second half of the year, Gaius had advanced with his army to the Parthian frontier to an unknown spot and brought Phraates to a final agreement on the proposals, in which he renounced all claims to Armenia and all power over his half-brothers.

It was about this time that Augustus passed through Judea and commended Gaius for not offering prayers at Jerusalem, as it would have been provocative to the Jews living there.

Expedition in Arabia
Sometime in the course of his time in the east, Gaius led an expedition into Arabia. Exactly where and for what purpose remains uncertain, though Pliny mentioned it in connection with Aelius Gallus' exploits in South Arabia. The term "Arabia" is never defined, and the term was used loosely by Roman sources. Various reasons, such as an attempt by Rome to control the incense trade, have been suggested but never proven. Juba II, former king of Mauretania, accompanied Gaius to the east. In order to prepare Gaius for his encounter with the Arabs, Juba wrote him a treatise. According to Pliny, the young prince made it as far as the Gulf of Aqaba. It is certain that this expedition happened before his time in Armenia, and, referencing Gaius' cenotaph in Pisa, it is almost certain to have taken place during his consulship.

Author and historian John Grainger places Gaius at the Gulf of Aqaba, or in Nabataea. It is known that the Nabataean Kingdom later became the province of Arabia, and so, it might be that Gaius conducted his "Arabian expedition" to either support or to discipline the King of Nabataea, Aretas IV. This is probably evidenced by the continuation of coinage in the king's name after Gaius' consulship.

Cassius Dio, in a fragmentary notice, mentions trouble in Egypt which was suppressed by a tribune of the Praetorian Guard. It is very likely this man was part of Gaius' entourage, but other than that nothing is known of him.

Supremacy in Armenia
In the year following his consulship, in spring, he had held a meeting with Phraates on the bank of the Euphrates, in which a banquet was held to celebrate a peace treaty. It was here that Phraates, offended by Lollius, disclosed the guardian's secret negotiations to Gaius. It was for the crime of extorting presents from kings (regnum muneribus) that Lollius lost the friendship of Gaius and drank poison. Pliny says he amassed a fortune from his crimes and that, as a result, his granddaughter could afford to wear jewelry worth 40,000,000 sesterces, a considerable amount of money. The death of Lollius was fortunate to Tiberius, after which Gaius consented to his return to Rome and consequent return to Roman politics.

At the same time, the throne of Armenia had become vacant and, with permission from the Emperor, Gaius placed Ariobarzanes II of Atropatene on the throne. The Romans weren't the only ones interested in Armenia: the Parthians stirred up a revolt among nationalists in the nation. A large force of rebels had occupied the fortress in the city of Artagira. Gaius was drawn into the conflict, and invaded Armenia in late August of 2 AD. He encountered no serious opposition as there were only a few revolts he had to suppress as a result of the nationalist party.

On 9 September, Abbadon, the leader of the rebellion, invited Gaius into the fortress to speak with him. It proved to be a trick, and Gaius was wounded in the confrontation. He had to be carried away by his outraged lieutenants. His forces promptly laid siege to the city and captured the fortress after intense fighting. At first the wound did not seem serious and he was able to complete the pacification of Armenia, a relatively easy task.

By the next year (3AD), he was entirely prostrated by the effects of his wound, had resigned his command, and withdrawn to Syria from where he informed Augustus that he had no further desire to take part in public life. The eastern campaign had proven severe: his health was weak and his mental balance unstable. At the age of twenty-three, the young man whom the Emperor considered his heir and sole hope of prosperity had abandoned his prospects of reputation and power in a wild fit of despair and fear. Augustus did his best to cheer him up and convince him to return to Italy. It was in vain: Gaius died in a little Lycian town on 21 February 4AD.

Post mortem
While Gaius was in Armenia, his brother Lucius had been sent by Augustus to complete his military training in Spain. While there, he fell ill and died on 20 August 2AD in Massalia, Gaul. In the span of 18 months, the planned future of Rome was shaken. The deaths of both Gaius and Lucius, the Emperor's two most favoured heirs, led Augustus to adopt his stepson Tiberius and his sole remaining grandson Postumus as his new heirs on 26 June 4AD.

Many honors were heaped upon Gaius by citizens and city officials of the Empire, including Colonia Obsequens Iulia Pisana (Pisa), where it was decreed that proper rites must be observed by matrons to lament his passing. Temples, public baths, and shops shut their doors as women wept inconsolably. To commemorate his brief life, a cenotaph was erected on the Limyrus River at Limyra in Lycia. Posthumously, the Senate voted honours for the young Caesars, and arranged for the golden spears and shields the boys had received on achieving the age of military service to be hung in the Senate House. The caskets containing their ashes were stored in the Mausoleum of Augustus alongside those of their father Agrippa and other members of the imperial family.

Both Tacitus and Cassius Dio suggested foul play may have been involved in the death of Gaius and Lucius and that Gaius's step grandmother Livia may have had a hand in their deaths. Livia's presumed motive may have been to orchestrate the accession of her own son Tiberius as heir to Augustus.

In popular culture

 * Gaius and Lucius both appeared as characters in the 1976 TV series I, Claudius; the series reverses the order of their deaths, with Gaius dying first. Gaius was played by Earl Rhodes.

Ancient sources

 * Cassius Dio, Roman History Book 55, English translation
 * Josephus, Antiquities of the Jews Book 17, English translation
 * Suetonius, Lives of the Twelve Caesars, Life of Augustus, Latin text with English translation
 * Suetonius, Lives of the Twelve Caesars, Life of Nero, Latin text with English translation
 * Suetonius, Lives of the Twelve Caesars, Life of Tiberius, Latin text with English translation
 * Tacitus, Annals, I–IV, English translation
 * Velleius Paterculus, Roman History Book II, Latin text with English translation

title: Gaius Caesar


text:
Grave of the Fireflies

Grave of the Fireflies (火垂るの墓) is a 1988 Japanese animated war drama film written and directed by Isao Takahata, and produced by Studio Ghibli. It is based on the 1967 semi-autobiographical short story Grave of the Fireflies by Akiyuki Nosaka.

The film stars Tsutomu Tatsumi, Ayano Shiraishi, Yoshiko Shinohara (voice actress) and Akemi Yamaguchi. Set in the city of Kobe, Japan, it tells the story of siblings and war orphans Seita and Setsuko, and their desperate struggle to survive during the final months of World War II. Universally acclaimed, Grave of the Fireflies has been ranked as one of the greatest war films of all time and is recognized as a major work of Japanese animation.

Plot
In March 1945, American Boeing B-29 Superfortress bombers destroy most of Kobe during the close of World War II. Military children of an Imperial Japanese Navy captain, Seita and Setsuko Yokokawa, survive, but their mother is severely injured and later dies. Seita conceals their mother's death from Setsuko to keep her happy. The siblings move in with a distant aunt, and Seita retrieves supplies he buried before the bombing and gives everything to his aunt, save for a tin of Sakuma drops. As rations shrink, the aunt convinces Seita to sell his mother's silk kimonos for rice. Seita also uses some of his mother's money in the bank to buy supplies.

Their aunt, brainwashed by the Imperial cause and only concerned for her wellbeing, keeps most of the supplies for herself, her daughter, and her male lodger while becoming verbally abusive towards Seita and Setsuko, accusing them of leeching off her. After she forces them to provide for themselves, Seita and Setsuko leave by July and move into an abandoned bomb shelter. They capture and release fireflies from the marshes into the refuge for light. The next day, the fireflies die; Setsuko buries them and reveals their aunt told her their mother died, then mournfully asks why they died so soon. As they run out of rice, Seita steals from farmers and loots homes during air raids, for which a farmer brutally assaults him. A police officer realizes Seita is stealing due to hunger and makes the farmer back off.

Two months later, Setsuko falls ill, and a doctor explains that she is suffering from malnutrition. Seita desperately withdraws the last of the money from their mother's bank account. After doing so, he becomes distraught when he learns that Japan has surrendered and that his father is most likely dead, as most of Japan's navy has been sunk. Seita returns to Setsuko with food but finds her dying. She later dies as Seita finishes preparing the food. Seita cremates Setsuko's body and her stuffed doll in a straw casket. He carries her ashes in the candy tin along with his father's photograph.

Seita dies of starvation a few weeks later at a Sannomiya train station surrounded by other malnourished people. A janitor is tasked with removing the bodies before the Americans' arrival. As the janitor sorts through Seita's possessions, he finds the candy tin and throws it into a field. Setsuko's ashes spread out, and her spirit springs from the container and is joined by Seita's spirit and a cloud of fireflies. The two board a ghostly train and, throughout the journey, look back at the events leading to Seita's death as silent, passive observers. Their spirits arrive at their destination: a hilltop bench overlooking present-day Kobe, surrounded by fireflies, healthy and content.

Development
Grave of the Fireflies author Akiyuki Nosaka said that many offers had been made to make a live-action film adaptation of his short story. Nosaka argued that "it was impossible to create the barren, scorched earth that's to be the backdrop of the story". He also argued that contemporary children would not be able to convincingly play the characters. Nosaka expressed surprise when an animated version was offered. After seeing the storyboards, Nosaka concluded that it was not possible for such a story to have been made in any method other than animation and expressed surprise in how accurately the rice paddies and townscape were depicted.

Isao Takahata said that he was compelled to film the short story after seeing how the main character, Seita, "was a unique wartime ninth grader". Takahata explained that any wartime story, whether animated or not animated, "tends to be moving and tear-jerking", and that young people develop an "inferiority complex" where they perceive people in wartime eras as being more noble and more able than they are, and therefore the audience believes that the story has nothing to do with them. Takahata argued that he wanted to dispel this mindset. When Nosaka asked if the film characters were "having fun", Takahata answered that he clearly depicted Seita and Setsuko had "substantial" days and that they were "enjoying their days". Takahata said that Setsuko was even more difficult to animate than Seita, and that he had never before depicted a girl younger than five. Takahata said that "In that respect, when you make the book into a movie, Setsuko becomes a tangible person", and that four-year-olds often become more assertive and self-centered, and try to get their own ways during that age. He explained that while one could "have a scene where Seita can't stand that anymore", it is "difficult to incorporate into a story". Takahata explained that the film is from Seita's point of view, "and even objective passages are filtered through his feelings".

Takahata said that he had considered using non-traditional animation methods, but because "the schedule was planned and the movie's release date set, and the staff assembled, it was apparent there was no room for such a trial-and-error approach". He further remarked that he had difficulty animating the scenery since, in Japanese animation, one is "not allowed" to depict Japan in a realistic manner. Animators often traveled to foreign countries to do research on how to depict them, but such research had not been done before for a Japanese setting. While animating the movie, Takahata also created several different cuts of the scene in which Seita cremates Setsuko's body. Takahata spent a lot of time on this scene, trying to create the perfect iteration of it. Each of these cuts remained unfinished and unused in the end.

Most of the illustration outlines in the film are in brown, instead of the customary black. Black outlines were only used when it was absolutely necessary. Color coordinator Michiyo Yasuda said this was done to give the film a softer feel. Yasuda said that this technique had never been used in an anime before Grave of the Fireflies, "and it was done on a challenge". Yasuda explained that brown is more difficult to use than black because it does not contrast as well as black.

Grave of the Fireflies was Takahata's first animated film produced with Studio Ghibli.

Takahata insisted on working with well known animators Yoshifumi Kondō who was working for Nippon Animation at the time and Yoshiyuki Momose. Both animators played a pivotal role in creating fluid, realistic animations of the characters in the animation.

Takahata drew from his personal experience to create a realistic depiction of the air raid on Okayama. In an interview, he criticized TV shows and movies that had recreated images of incendiary bombs, "They include no sparks or explosions, I was there and I experienced it, so I know what it was like."

The film features Niteko-ike pond (ニテコ池), which is described as the "birthplace" of the novel and where Nosaka conducted his daily routines of dishwashing and personal ablutions. Notably, during the final days of the Pacific War, Nosaka, then 14 years old, sought refuge with his younger sister-in-law in a relative's house and nearby bomb shelters near the pond.

The location and background in the film is based on a style created by 18th century Japanese artist Hiroshige and his follower Hergé, who created Tintin. Film critic Roger Ebert examines the contrast of the style of the background in comparison to the cartoonish animation of the characters. He claims that there is an unusual amount of detail in the evocative landscape, while the characters are a take on the modern Japanese animation with childlike bodies and enormous eyes. The depiction of Seita and Setsuko have Ebert believe that this deliberate animation style embodies the true purpose of animation, which is to recreate the raw emotion of human life by simplifying reality to emphasize ideas. He concludes his analysis with saying, "Yes, it's a cartoon, and the kids have eyes like saucers, but it belongs on any list of the greatest war films ever made." According to Wendy Goldberg, Takahata's film also includes criticism of the emphasis on nationalism in Japan. In a particular scene, Seita's desire to join his father reflects a "national fantasy of war", which leads him to neglect his sister.

Music
The music for the film was composed by Michio Mamiya. The theme song, "Home Sweet Home", was performed by coloratura soprano Amelita Galli-Curci. Dialogue of the film is part of the soundtrack as the music and dialogue are not separated in any way. Mamiya is also a music specialist in baroque and classical music.

During an interview about his music, Mamiya stated that he creates his music to encourage peace. The songs in Grave of the Fireflies as well as other pieces by Michio Mamiya, such as Serenade No. 3 "Germ", express this theme.

The soundtrack album titled Grave of the Fireflies Soundtrack Collection (火垂るの墓 サウンドトラック集) was first released on April 5, 1997, by Studio Ghilbi Records and Tokuma Japan Communications and later released on June 25, 1988, by ''Animage. The soundtrack does not contain standalone music and instead features both dialogue and music as they appear in the film.

Another soundtrack album titled Grave of the Fireflies Image Album Collection (火垂るの墓 イメージ・アルバム集) was first released on April 5, 1997, by Studio Ghilbi Records and Tokuma Japan Communications, and later released on November 25, 1987, by Animage.

Themes and analysis
In his book about the film, Alex Dudok de Wit called Grave of the Fireflies an "unusually personal adaptation" of Nosaka's short story as Takahata had similar experiences during the war, though noted it deviated significantly in its portrayal of the children as ghosts in its opening sequence whereas the short story began immediately with the children losing their mother during the air raid.

Some critics in the West have viewed Grave of the Fireflies as an anti-war film due to the graphic and emotional depiction of the pernicious repercussions of war on a society, and the individuals therein. The film focuses its attention almost entirely on the personal tragedies that war gives rise to, rather than seeking to glamorize it as a heroic struggle between competing nations. It emphasizes that war is society's failure to perform its most important duty: to protect its own people.

However, Takahata repeatedly denied that the film was an anti-war film. In his own words, it "is not at all an anti-war anime and contains absolutely no such message". Instead, Takahata had intended to convey an image of the brother and sister living a failed life due to isolation from society and invoke sympathy particularly in people in their teens and twenties.

Since the film gives little context to the war, Takahata feared a politician could just as easily claim fighting is needed to avoid such tragedies. In general, he was skeptical that depictions of suffering in similar works, such as Barefoot Gen, actually prevent aggression. The director was nevertheless an anti-war advocate, a staunch supporter of Article 9 of the Japanese Constitution, and has openly criticized Japan's penchant for conformity, allowing them to be rallied against other nations. He expressed despair and anxiety whenever the youth are told to fall in line, a reminder that the country at its core has not changed.

Despite the public's emotional reaction, Takahata expressed that the purpose of the film was not to be a tragedy or make people cry. Moreover, he regretted depicting Seita as a boy from that era because he wanted him to come off as a contemporary boy who acted like he had time-traveled to the period. He didn't intend for it to be retrospective or nostalgic. He wanted the Japanese audience to recognize Seita's misguided attmpts to withdraw from society. Furthermore, he says that his decision to show the audience that Seita and Setsuko have died at the beginning of the movie is to protect the audience from heartbreak, "If an audience knows at the beginning of the film that the two will eventually die, they are more prepared to watch the film in the first place. I try to lessen an audience's pain by revealing everything at the beginning."

The fireflies in the film are portrayed as symbols of various themes such as the spirits of the lost children, the fires that burned the towns, Japanese soldiers, the machinery of war, and the regeneration of life through nature. Okypo Moon states in her essay "Marketing Nature in Rural Japan", that hundreds of fireflies were caught nightly in the 1920s and 1930s. In the 1960s and 1970s, there was a shift to reinstate this tradition and "there are now eighty five 'firefly villages' (hotaru no sato) registered at the Ministry of the Environment in Japan. The movie uses fireflies to visually represent both deadly and beautiful imagery, such as fire-bombs and kamikazes. Takahata chooses to use the kanji "fire" instead of the normal character for the word firefly in the title, which has been interpreted to represent the widespread burning of wooden houses in Japan. Critic Dennis H. Fukushima, Jr. believes that this modification of the title is to emphasize parallels between beauty and devastation, citing the relationship between fireflies, M-69 incendiary bombs, naval vessels, city lights, and human spirits.

In the book Imag(in)ing the war in Japan representing and responding to trauma in postwar literature and film, David Stahl and Mark Williams commend the film for not emphasizing Japanese victimhood to avoid responsibility for atrocities of the war they played a role in. They interpret that Seita's character embodies working towards healing historical trauma and victimization, because it is his nationalistic pride and selfishness which ultimately contributed to his sister's death.

Theatrical
The film was released on 16 April 1988, over 20 years from the publication of the short story.

The initial Japanese theatrical release was accompanied by Hayao Miyazaki's light-hearted My Neighbor Totoro as a double feature. While the two films were marketed toward children and their parents, the starkly tragic nature of Grave of the Fireflies turned away many audiences. However, Totoro merchandise, particularly the stuffed animals of Totoro and Catbus, sold extremely well after the film and made overall profits for the company to the extent that it stabilized subsequent productions of Studio Ghibli.

Grave of the Fireflies is the only theatrical Studio Ghibli feature film prior to From Up on Poppy Hill to which Disney never had North American distribution rights, since it was not produced by Ghibli for parent company Tokuma Shoten but for Shinchosha, the publisher of the original short story (although Disney has the Japanese home video distribution rights themselves, thus replacing the film's original Japanese home video distributor, Bandai Visual). It was one of the last Studio Ghibli films to get an English-language premiere by GKIDS.

Home media
Grave of the Fireflies was released in Japan on VHS by Buena Vista Home Entertainment under the Ghibli ga Ippai Collection on 7 August 1998. On 29 July 2005, a DVD release was distributed through Warner Home Video. Walt Disney Studios Japan released the complete collector's edition DVD on 6 August 2008. WDSJ released the film on Blu-ray twice on 18 July 2012: one as a single release, and one in a two-film set with My Neighbor Totoro (even though Disney has never owned the North American rights, only the Japanese rights).

It was released on VHS in North America by Central Park Media in a subtitled form on 2 June 1993. They later released the film with an English dub on VHS on 1 September 1998 (the day Disney released Kiki's Delivery Service) and an all-Regions DVD (which also included the original Japanese with English subtitles) on 7 October 1998. On 8 October 2002, it was later released on a two-disc DVD set, which once again included both the English dub and the original Japanese with English subtitles as well as the film's storyboards with the second disc containing a retrospective on the author of the original book, an interview with the director, and an interview with critic Roger Ebert, who felt the film was one of the greatest of all time. It was released by Central Park Media one last time on 7 December 2004. Following the May 2009 bankruptcy and liquidation of Central Park Media, ADV Films acquired the rights and re-released it on DVD on 7 July 2009. Following the 1 September 2009 shutdown and re-branding of ADV, their successor, Sentai Filmworks, rescued the film and released a remastered DVD on 6 March 2012, and planned to release the film on digital outlets. A Blu-ray edition was released on 20 November 2012, featuring an all-new English dub produced by Seraphim Digital.

StudioCanal released a Blu-ray in the United Kingdom on 1 July 2013, followed by Kiki's Delivery Service on the same format. It was the UK's tenth annual best-selling foreign language film on home video in 2019 (below seven other Japanese films, including six Hayao Miyazaki anime films). Madman Entertainment released the film in Australia and New Zealand.

Reception
The film was modestly successful at the Japanese box office, where it grossed ¥1.7 billion. As part of the Studio Ghibli Fest 2018, the film had a limited theatrical release in the United States, grossing $516,962.

The Ghibli ga Ippai Collection home video release of Grave of the Fireflies sold 400,000 copies in Japan. At a price of at least ¥4,935, this is equivalent to at least ¥billion in sales revenue.

The film received universal critical acclaim. Roger Ebert of the Chicago Sun-Times considered it to be one of the best and most powerful war films and, in 2000, included it on his list of great films. The film review aggregator website Rotten Tomatoes reported a 100% approval rating based on 46 reviews with an average rating of 9.30/10. The website's critical consensus reads: "An achingly sad anti-war film, Grave of the Fireflies is one of Studio Ghibli's most profoundly beautiful, haunting works." Metacritic assigned the film a score of 94 out of 100 based on 16 reviews, indicating "universal acclaim".

Filmmaker Akira Kurosawa praised the film and considered it his favourite Ghibli production. He wrote a letter of praise to Hayao Miyazaki, mistakenly believing he directed Grave of the Fireflies. Miyazaki himself praised the film as Takahata's masterpiece, but criticized Seita for not behaving how he believes the son of a navy lieutenant should behave.

The film ranked number 12 on Total Film's 50 greatest animated films. It was also ranked at number 10 in Time Out's "The 50 greatest World War II movies" list. Empire magazine ranked the film at number 6 in its list of "The Top 10 Depressing Movies". The film ranked number 19 on Wizard's Anime Magazine on their "Top 50 Anime released in North America". The Daily Star, ranking the film 4th on its list of greatest short story adaptations, wrote that "There is both much and little to say about the film. It is simply an experience—a trip through the lonely boroughs of humanity that the world collectively looked, and still looks, away from". Theron Martin of Anime News Network said that, in terms of the original U.S. Manga Corps dub, while the other voices were "perfectly acceptable", "Setsuko just doesn't sound quite convincing as a four-year-old in English. That, unfortunately, is a big negative, since a good chunk of the pathos the movie delivers is at least partly dependent on that performance".

On 25 December 2016, Toei Company made a Twitter post that read "Why did Kiriya have to die so soon?" (なんできりやすぐ死んでしまうん) in order to promote an episode of Kamen Rider Ex-Aid. The hashtag became popular, but Toei deleted the tweet after receiving complaints that referencing the Grave of the Fireflies line "Why do fireflies die so soon?" (なんで蛍すぐ死んでしまうん) was in poor taste. Before that, the ranking website Goo's readers voted the film's ending the number 1 most miserable of all anime films.

In June 2018, USA Today ranked it 1st on the 100 best animated movies of all time.

Well-known film director and critic Haruo Mizuno reviewed Grave of the Fireflies on his popular TV series. He praised the film for the honorary image of the soldiers of Japan through the depiction of the fireflies, and the moving depiction of a heartbreaking experience many people of Japan had lived through.

After seeing the reactions of the audience after a screening of the film at Festival « Pour éveiller les regards », Jean-Jacques Varret, head of Les Films du Paradoxe, knew he had to distribute it in France. It was released in two Parisian arthouses and the reaction was modest. Following the release however, Les Films du Paradoxe chose to release the film on video cassettes and on the streaming service Canal+.

Public reactions
After the international release, it has been noted that different audiences have interpreted the film differently due to differences in culture. For instance, when the film was watched by a Japanese audience, Seita's decision to not come back to his aunt was seen as an understandable decision, as they were able to understand how Seita had been raised to value pride in himself and his country. Conversely, American and Australian audiences were more likely to perceive the decision as unwise.

Planned follow-up
Following the success of Grave of the Fireflies, Takahata drew up an outline for a follow-up film, based on similar themes but set in 1939 at the start of the second World War. This film was called Border 1939, based on the novel The Border by Shin Shikata, and would have told the story of a Japanese teenager from colonial Seoul joining an anti-Japanese resistance group in Mongolia. The film was intended as an indictment of Japanese imperialist sentiment, which is briefly touched upon in Grave of the Fireflies. Although Takahata finished a full outline (which is republished in his book Thoughts While Making Movies), the film was canceled before production could start due to the 1989 Tiananmen Square protests. Public opinion in Japan had turned against China, and Ghibli's distributor felt a film partly set there was too risky.

2005 live-action version
NTV in Japan produced a live-action TV drama of Grave of the Fireflies, in commemoration of the 60th anniversary of the end of World War II. The drama aired on 1 November 2005. Like the anime, the live-action version of Grave of the Fireflies focuses on two siblings struggling to survive the final months of the war in Kobe, Japan. Unlike the animated version, it tells the story from the point of view of their cousin (the aunt's daughter) and deals with the issue of how the war-time environment could change a kind lady into a hard-hearted woman. It stars Nanako Matsushima as the aunt, as well as Mao Inoue as their cousin.

2008 live-action version
A different live-action version was released in Japan on 5 July 2008, Reo Yoshitake as Seita, Rina Hatakeyama as Setsuko, Keiko Matsuzaka as the aunt, and Seiko Matsuda as the children's mother. Like the anime, this live-action version of Grave of the Fireflies focuses on two siblings struggling to survive the final months of the war in Kobe, Japan.

title: Grave of the Fireflies