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General Chemistry/Numbers Used to Describe Atoms

Numbers
The Atomic number is the number of protons in the nucleus of an atom. This number determines the element type of the atom. For instance, all neon atoms have exactly ten protons. If an atom has ten protons, then it must be neon. If an atom is neon, then it must have ten protons.

The atomic number is sometimes denoted Z. Continuing with the example of neon, $$Z=10$$.

The Neutron number is the number of neutrons in the nucleus of an atom. Remember that neutrons have no electric charge, so they do not affect the chemistry of an element. However, they do affect the nuclear properties of the element. For instance, Carbon-12 has six neutrons, and it is stable. Carbon-14 has eight neutrons, and it happens to be radioactive. Despite these differences, both forms of carbon behave the same way when forming chemical compounds.

The neutron number is sometimes denoted N.

The Mass number is the sum of protons and neutrons in an atom. It is denoted A. To find the mass number of an atom, remember that A = Z + N. The mass number of an atom is always an integer. Because the number of neutrons can vary among different atoms of the same element, there can be different mass numbers of a given element. Look back to the example of carbon. Carbon-14 has a mass number of 14, and Carbon-12 has a mass number of 12. Every carbon atom must have six protons, so Carbon-14 has eight neutrons and Carbon-12 has six neutrons. Isotopes of the same element have nearly identical chemical properties (because they have the same number of protons and electrons). Their only difference is the number of neutrons, which changes their nuclear properties like radioactivity.

Notation
There is a convenient way of writing the numbers that describe atoms. It is easiest to learn by examples.

Atomic Mass
The mass of an atom is measured in atomic mass units (amu). An atom's mass can be found by summing the number of protons and neutrons. By definition, 12 amu equals the atomic mass of carbon-12. Protons and neutrons have an approximate mass of 1 amu, and electrons have a negligible mass.

Usually, a pure element is made up of a number of isotopes in specific ratios. Because of this, the measured atomic mass of carbon is not exactly 12. It is an average of all the masses of all the isotopes, with the more common ones contributing more to the measured atomic mass. By convention atomic masses are given no units.

Moles
A mole is defined as the amount of an element whose number of particles are equal to that in 12g of C-12 carbon, also known as Avogadro's number. Avogadro's number equals 6.022 × 1023. Moles are not very confusing: if you have a dozen atoms, you would have 12. If you have a mole of atoms, you would have 6.022 × 1023. Why is this ridiculously large number important? It can be used to convert between atomic mass units and grams. One mole of carbon-12 is exactly 12 grams, by definition. Similarly, one mole of any element is the atomic mass of that element expressed as a weight in grams. The atomic mass is equal to the number of grams per mole of that element.

Moles are also important because every 22.4 liters of gas contain 1 mole of gas molecules at standard temperature and pressure (STP, 0 °C and 1 atmosphere of pressure). Avogadro discovered this. (That's why it's his number.) A container filled with fluorine gas would have to be 22.4 L large to hold one mole of F2 molecules. Knowing this fact allows you to determine the mass of a gas molecule if you know the volume of the container. This holds true for every gas.

Why every single gas? Atoms and molecules are tiny. The volume of a gas is mostly empty space, so the molecules have an insignificantly small volume. As you will eventually learn, this ensures that there is always one mole of gas atoms for every 22.4 liters at STP.


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Video Capture, Transcoding, and Authoring/Capturing composite VirtualDub NTSC

Readers are encouraged to comment on the scenarios presented here. Rather than edit the section (unless there is an obvious error), please add the comments in a Notes section following the scenario, for example:

Using ATI All-in-Wonder 2006
From Joseph Hall as of 03 May, 2006:

Here is a procedure that works for me.

I have VirtualDub set up the following way:

 * Preferences:
 * Timing:
 * Compression: HuffYUV

My S-video composite output (from a DirecTV box, etc.) is connected to the S-video input of the AIW 2006 dongle. The analog out is also connected to the dongle.

My computer is an Athlon 3400+ X2 running Win XP 64-bit, with 2GB RAM and IDE drives. I run the 32-bit VirtualDub because there is no 64-bit port of HuffYUV (as far as I know). With no other load, or only low-priority background load (such as an "idle" priority TMPGenc batch task), capture generally proceeds fine with no dropped frames and a handful of inserted frames. Some players may not play the resulting AVI-encapsulated HuffYUV stream with perfect A/V sync, but I have learned that the A/V sync is typically fine anyway.

TMPGenc Xpress (4.0) will play the HuffYUV stream with the correct A/V sync in its preview mode (in the clip editor or filter editor). If the A/V sync is correct there, it should be correct after encoding. I can't speak for other encoders at this time, because I am happy with TMPGenc.

A few dropped frames may be okay. If there is a burst of dropped frames, the resulting capture may or may not have good A/V sync. I rarely have dropped frames but every so often I have a source that has a spot that seems to cause dropped frames. Maybe this is because of some peculiarity of those frames that causes HuffYUV to take longer than usual to do the encoding. Several dropped frames in a second or two may not derail A/V sync, but more probably will. Special attention to fragmentation on the recording drive is not necessary in my experience.

Normally I get inserted frames one at a time spaced in intervals of at least a few minutes. A burst of inserted frames may also result in an A/V sync problem, usually due to some other task competing for disk (most likely) or CPU (less likely).

The data rate of the capture depends on the source material. Compression seems to range from about 2.7:1 to nearly 4:1 (on 2.2:1 letterboxed source). 30 GB/hr is a ballpark for capture of a clean but detailed signal from S-video.

Contributors
Joseph N. Hall

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


text:
Talk:General Chemistry/Measurement

is this module even necessary anymore? The wikibook already as a good enough appendix. Hoogli

title: Talk:General Chemistry/Measurement


text:
Parkour/Exercises/The Lunge

When done correctly, the Lunge will help to stretch the hamstrings and work out quads. Holding the stretch for fifteen seconds will increase effectiveness.

Steps

 * 1) Start in a karate-like stance, with one leg in front of the other and front shoulder facing forward.
 * 2) Squat down a small amount, bending your knees.
 * 3) Quickly move your front leg out in front of you and place it so you are almost in a split.
 * 4) Lean onto your front knee, placing pressure on it and stretching the back leg.
 * 5) Keep your body sideways and make sure your front knee is only at a right angle. Also keep your front foot facing straight and your back foot outwards.

title: Parkour/Exercises/The Lunge


text:
Astrodynamics/Introduction

Introduction to Astrodynamics
Astrodynamics is the study of the interaction and motions of objects in space. While there are many generalized ways of studying astrodynamics, it makes the most practical sense to study the earth and the actions of objects in orbit around the earth. Similarly, it is more practical to study the gravitational effects of our sun than it is to study the gravity of any arbitrary star. This book will provide the basic mathematical foundation for the study of astrodynamics but will take specific care to focus on man-made craft launched from the earth, intended to orbit the earth.

What Will This Book Cover?
This book will cover the necessary concepts and mathematics to study orbital motion. This book will focus on theory, although with a strong focus on practical applications of that theory. This book will focus on the earth and spacial objects that interact with earth including the sun, the moon, comets, asteroids, man-made orbital satellites, and ballistic missiles.

This book will not cover astronomy or astrophysics in a general sense.

Who Is This Book For?
This book is for engineers and physicists alike. It will be directed towards undergraduate students in a science or engineering program, who have had at least 1 semester of physics and two or three semesters of calculus.

What Are The Prerequisites?
Readers of this book should be familiar with vector calculus and multi-variable calculus. Readers should know and understand calculus-based physics of motion. This book will not discuss vectors, vector arithmetic, vector calculus, multi-variable calculus, or basic physics. For those topics, you should consult the following books:

 * Calculus
 * Modern Physics
 * Engineering Analysis

Readers who are unfamiliar with vector calculus will be at an extreme disadvantage when reading this book, and are encouraged to read the necessary passages of Calculus first. Because of the frequent use of conic sections, the student may also wish to read Conic Sections as well.

Mathematical Notation
This book will use a simplified notation to express equations.

 * Complicated mathematical formulae that need to be rendered with LaTeX will be moved to a new line, and indented. Important equations like this will be labeled on the right. Rendered equations should never be in-line with text in a paragraph, because the spacing is different.
 * Scalar values or scalar-valued functions will be written in lower-case italics, such as i. Because nearly everything in astrodynamics is a function of time, we will leave off the argument (t) from our functions. I.e. we will write the distance of a satellite from earth as r even though it's the function of time r(t).
 * Greek or other non-Latin characters will not be made italic, because they are difficult to see in the body of text.
 * Vectors and vector-valued functions will be written in bold. For example, r is a position vector. If the vector changes with time, the (t) will be implied. If we use a scalar and a vector with the same letter in the same place, such as r and r, we know that the scalar value is the euclidean distance of the vector:
 * $$r = |\mathbf{r}|$$

 * Time derivatives of functions will be expressed in dot notation:
 * $$\dot{\mathbf{r}} = \frac{d\mathbf{r}}{dt}$$
 * $$\dot{r} = \frac{d}{dt}|\mathbf{r}|\neq\left|\frac{d\mathbf{r}}{dt}\right|$$

Wikipedia
Astrodynamics is a large topic, and there is no way to discuss all information of peripheral interest. This book will link extensively to related articles in Wikipedia. Links to Wikipedia articles represent departure points for additional reading and are not required for the understanding of the material in this book. Also, articles in Wikipedia are written with different styles, and frequently with different terms and mathematical notation as is used in this book. This book uses a consistent vocabulary and mathematical notation, and no attempt will be made to synchronize this book with any Wikipedia articles.

title: Astrodynamics/Introduction


text:
Template:Astrodynamics

Astrodynamics

title: Template:Astrodynamics


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Astrodynamics/History

History of Astrodynamics
The study of the sun, moon, and stars has been a subject of prominence among humans for many thousands of years. Because the revolution of the earth and other planets around the sun, and the daily rotation of the earth on its axis create regular patterns of motion, the study of the stars and planets was used as a method to tell time. The location of the north star, polaris, and the constellation "the southern cross" were used by ocean navigators to travel the seas in the times before magnetic compasses. Many religious ceremonies and beliefs also grew around the stars and their constellations.

The study of the motions of the stars and planets has also been a major driving force behind mathematics and science. Some of the fruits of this study are the optical lense (for use in telescopes) and the field of calculus. Many modern inventions and technologies were also furthered because of modern space exploration. It is for all these reasons that we are studying astrodynamics.

Early History
Since ancient times, the heavens have been studied. It was known by the 2nd millennium BC, that certain lights in the night sky did not remain fixed with respect to the background stars. The Ancient Greeks referred to these as planetes asteres, "wandering stars" and their motions were studied extensively, even in ancient times. Theories of their motions eventually culminated in the third century with the Almagest, written by Claudius Ptolemy. The Ptolemaic system placed earth at the center of the universe with seven planets (the moon, Mercury, Venus, the sun, Mars, Jupiter and Saturn) which revolved about the earth on successively larger crystalline spheres which were again bounded by the sphere of fixed stars. Complex motions of the planets were explained via epicycles, which will not be discussed in great depth here. Despite modern understanding of the flaws in the Ptolemaic system, it was fairly accurate and remained the basis of astronomy and cosmology until the 17th century.

The Renaissance
Nickolaus Copernicus, having taken several measurements of the motions of various planets, came to the conclusion that the sun was the center of the universe, and that the earth rotated around the sun. Copernicus' model also assumed that the orbits of the planets were circular, which left a few inconsistencies from his measurements, but the model was much more simplistic then the Ptolemaic model.

Urban myth holds that Copernicus' theory was dismissed by the Catholic Church, when in reality Copernicus' book was funded by a church cardinal, and was dedicated to the current pope. It wasn't for nearly 100 years later, after Kepler had begun publishing that the church denounced the idea as heretical.

150 years after Copernicus, Galileo Galilei began to observe the heavens with a telescope that he constructed; contrary to popular belief, he did not invent the telescope, but he was the first to use it for astronomical purposes. He made several discoveries including the four largest moons of Jupiter, phases of Venus, sunspots, rings of Saturn and the topography of the moon. These discoveries challenged long held notions that the Earth was the center of the universe and that the planets were perfect ethereal spheres.

Galileo also helped lay the groundwork of the concepts of kinematics and inertial coordinate frames, both of which are important foundations of Classical Mechanics.

Johannes Kepler
Tycho Brahe, a Danish nobleman, was a keen observer and machinist, and used his talents to compile a listing of the most accurate observations of stars and planets that had ever been taken up to that point. However, Brahe lacked the intuition to fit that data to a mathematical model. Brahe's assistant, Johannes Kepler, an accomplished mathematician was tasked with using the data to compute future positions of the planets.

Following Brahe's death, Kepler inherited the body of data which he used to derive laws to accurately describe the motions of the planets. While Kepler did not understand the physical basis behind his discoveries, his three laws of planetary motion still bear his name today.

Isaac Newton
Isaac Newton, the famous mathematician and physicist, used his new invention calculus to derive the orbital motion of a planet as an ellipse. However, it wasn't until after being prodded by Edmond Halley, a fellow scientist, that he was persuaded to publish his work, Principia Mathematica with his results.

Halley, Newton's only contemporary that was able to understand the new calculus, was able to use Newtons results to predict the path and the time of return for the comet that still bears his name.

Lagrange and Gauss
Gauss is known as an amazing mathematician, but many of the results he produced were due to his study of astronomy. Gauss developed many of the mathematical tools that we use today to study orbits. One of his developments, Least Mean Squares curve fitting, was developed to apply an orbit to a series of inexact measurements, but has since found uses in nearly every branch of engineering, science, and mathematics.

Einstein and Relativity
In the early 20th century, understanding of physics was again revolutionized, this time by Albert Einstein with his Theory of Relativity. The special theory, published in 1905, posits that the speed of light is constant for all inertial frames of reference, which has the effect of unifying the concepts of space and time and also the concepts of mass and energy. The general theory, published in 1917, expanding relativity beyond inertial reference frames describes gravity as a curvature in space-time resulting from the presence of matter and energy. Relativity has withstood numerous tests and experiments and remains one of the pillars of modern physics.

However, in most applications (including astrodynamics), Newtonian physics serves as a sufficient description of the motion of bodies and the effects of relativity can be ignored. Notable exceptions to this are GPS systems with rely on extremely precise time signals and must account for slight time dilation that occurs as a result of relativistic physics. Another notable example from celestial mechanics is the orbit of Mercury, which experiences precessional effects that cannot be explained by classical physics.

title: Astrodynamics/History


text:
Parkour/Exercises/The Handstand Push-Up

The Handstand Push-Up is similar to a regular push up, but requires more balance and strength. It strengthens core, back and upper body muscles.

Steps

 * 1) Place palms on the floor and lean.
 * 2) Place the top of your head against the floor between your palms creating a triangle.
 * 3) Lean your body up until only your hands and head are touching the floor.
 * 4) Push your head off the floor until only your hands are holding you up.
 * 5) Keep yourself balanced while going down to the floor and pushing back up.

title: Parkour/Exercises/The Handstand Push-Up


text:
Astrodynamics/N-Body Problem

N-Body Problem
Newton's law of universal gravitation only accounts for two bodies, m1 and m2. However, in space there are frequently more bodies to be concerned with. We can generalize the problem to say that there is a number N bodies to deal with, and create an equation that can deal with an arbitrary number of bodies.

All of the bodies together are known as a system of bodies.

When studying the N-body problem, it is important to focus on a single body, whose motion is of primary interest. We assume that this body, known as the ith body is able to move freely, but the other N - 1 bodies are stationary. The force of gravity between an arbitrary body n and the body i is given by the law of universal gravitation:

 * $$\mathbf{F}_{gn} = -\frac{Gm_im_n}{r_{ni}^3}\mathbf{r}_{ni}$$

Where rni is the distance vector between object n and object i. We can express this vector in terms of the location vectors of the two bodies:

 * $$\mathbf{r}_{ni} = \mathbf{r}_i - \mathbf{r}_n$$

The total force of gravity on the ith object is given as:

 * $$\mathbf{F}_g = -\sum_{k=1}^{N-1}\frac{Gm_im_k}{r_{ki}^3}\mathbf{r}_{ki}$$

We also know that the force of gravity on the ith body from the ith body (the force of gravity on itself) must be zero. We can also define a new force vector, FO that consists of all the force elements that can act on a body, besides gravity. Some of these elements are drag, solar radiation pressure, magnetic field pressure, and thrust (in the case of a man-made satellite or rocket). We can define the total force on the object, FT as a sum of the gravitational force and the other forces:

 * $$\mathbf{F}_T = \mathbf{F}_{gn} + \mathbf{F}_O$$

Recalling Newton's second law, the complete equation of motion of a particle in the N-body system is:

 * $$m_i\ddot{\mathbf{r}}_i=-\sum_{k=1}^{N-1}\frac{Gm_im_k}{r_{ki}^3}\mathbf{r}_{ki}+\mathbf{F}_O$$

Simplified Two Body Problem
The equation of motion in its general form is impossible to solve. In the context of astrodynamics, it is generally sufficient to deal with only two bodies at a time, and the equation of motion becomes significantly easier to solve. Solutions also exist for certain three-body systems, which will be discussed in later chapters.

To solve for the motion of an object in a two body system, two simplifying assumptions can be made:
 * 1. The bodies are spherically symmetric and can be treated as point masses.
 * 2. There are no external or internal forces acting upon the bodies other than their mutual gravitation.

The shapes of large celestial bodies are close to spheres. By symmetry, the net gravitational force attracting a mass point towards a homogeneous sphere must be directed towards its centre. The shell theorem (also proven by Isaac Newton) states that the magnitude of this force is the same as if all mass was concentrated in the middle of the sphere, even if the density of the sphere varies with depth (as it does for most celestial bodies). From this immediately follows that the attraction between two homogeneous spheres is as if both had its mass concentrated to its center.

Smaller objects, like asteroids or spacecraft often have a shape strongly deviating from a sphere. But the gravitational forces produced by these irregularities are generally small compared to the gravity of the central body. The difference between an irregular shape and a perfect sphere also diminishes with distances, and most orbital distances are very large when compared with the diameter of a small orbiting body. Thus for some applications, shape irregularity can be neglected without significant impact on accuracy.

Planets rotate at varying rates and thus may take a slightly oblate shape because of the centrifugal force. With such an oblate shape, the gravitational attraction will deviate somewhat from that of a homogeneous sphere. This phenomenon is quite noticeable for artificial Earth satellites, especially those in low orbits. At larger distances the effect of this oblateness becomes negligible. Planetary motions in the Solar System can be computed with sufficient precision if they are treated as point masses.

Two point mass objects with masses m1 and m2 and position vectors r1 and r2 relative to some inertial frame of reference experience gravitational forces:

 * $$ m_1 \ddot{\mathbf{r}}_1 = \frac{-G m_1 m_2}{r^2} \mathbf{\hat{r}}$$

 * $$ m_2 \ddot{\mathbf{r}}_2 = \frac{G m_1 m_2}{r^2} \mathbf{\hat{r}}$$

where $$\mathbf{r}$$ is the relative position vector of mass 1 with respect to mass 2, expressed as:

 * $$ \mathbf{r} = \mathbf{r}_1 - \mathbf{r}_2 $$

(Please note that the two diagrams are misleading in their capitalizations of M1, M2, R1, and R2, but significantly more importantly, the direction of the r vector in diagram two is pointing in the opposite direction)

Dividing by their respective masses and subtracting the second equation from the first yields the equation of motion for the acceleration of the first object with respect to the second:

 * $$ \ddot{\mathbf{r}} = - \frac{\mu}{r^2} \mathbf{\hat{r}}$$

where μ is the gravitational parameter and is equal to

 * $$ \mu = G(m_1 + m_2)$$

In many applications, a third simplifying assumption can be made:
 * 3. When compared to the central body, the mass of the orbiting body is insignificant. Mathematically, m1 >> m2, so μ = G (m1 + m2) ≈ Gm1.

This assumption is not necessary to solve the simplified two body problem, but it simplifies calculations, particularly with Earth-orbiting satellites and planets orbiting the sun. Even Jupiter's mass is less than the sun's by a factor of 1047, which would constitute an error of 0.096% in the value of μ. Notable exceptions include the Earth-moon system (mass ratio of 81.3), the Pluto-Charon system (mass ratio of 8.9) and binary star systems.

Under these assumptions the differential equation for the two body case can be completely solved mathematically and the resulting orbit follows Kepler's laws of planetary motion. The orbits of all planets are to high accuracy Kepler orbits around the Sun. The small deviations are due to the much weaker gravitational attractions between the planets, and in the case of Mercury, due to general relativity. The orbits of the artificial satellites around the Earth are, with a fair approximation, Kepler orbits with small perturbations due to the gravitational attraction of the sun, the moon and the oblateness of the Earth. In high accuracy applications for which the equation of motion must be integrated numerically with all gravitational and non-gravitational forces (such as solar radiation pressure and drag) being taken into account, the Kepler orbit concepts are of paramount importance and heavily used.

title: Astrodynamics/N-Body Problem


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Astrodynamics/The Earth

The Earth is an object of special importance, not because it has any special characteristics, but because it is our starting point. All satellites that we launch start on the surface of earth, and all our observations are made from its surface. The only exception to the second rule is that some observations are made from satellites that have been previously launched from earth. Most of the practical applications of astrodynamics are centered around the earth (orbiting satellites, ballistic missiles, etc.), and so we will focus much of our attention on it.

Size and Shape
Generally, it is thought that the Earth has a spherical shape. One of the most prominent reasons for this is that whenever we do calculations based on it, we approximate it to a sphere having a radius of approximately 6300 km. This is also further exacerbated by the fact that pictorial representations of the Earth such as The Blue Marble  show it to be a sphere. However, the Geodetic data shows Earth to be more of an Oblate Spheroid. The Oblateness refers to a bulge at the equator, which is termed as the Equatorial bulge and is caused by the centrifugal force of the Earth's rotation around its own axis. This means that the diameter across the Equatorial plane is more than 42 kilometers longer than the diameter at the poles.

Orbit and Rotation
One earth rotation on its axis, such that the sun is at the same place in the sky, is known as a solar day. A solar day is 24 hours by definition.

The period of the Earth's rotation is known as a solar year. A solar year is equal to 365.25 solar days.

The Earth's orbital plane is not parallel with the Earth's equator. This tilt in the orbital plane causes the seasons.

Equinoxes
When the sun appears directly over the equator, and the day is the same length as the night, it is called the equinox. The equinox between the months of March and April is known as the vernal equinox. The autumnal equinox is the transition between the months of September and October.

Solstices
When the sun appears at its highest or lowest point in the sky at the equator, it is called a solstice. Summer solstice is when the day's length is at its longest and winter solstice is when the day's length is at its shortest. The solstices for the northern and southern hemisphere are opposite because of the earth's tilt, meaning that summer solstice in the northern hemisphere is winter solstice for the southern hemisphere and vice versa, this is because the sun's position in the sky is different for both hemispheres.

Equatorial Plane
The Earth's equator is a circle. The plane containing this circle is the equatorial plane. To someone standing on the surface of the Earth, this plane is everything that is at right angles from the north (or south) celestial pole. If they are standing at Earth's north (or south) pole, then the points in the direction of the horizon are on the equatorial plane.

Canonical Units
The distance between the earth and the sun can be difficult to measure, and the units involved can make calculations difficult. However, we can define a new unit, the astronomical unit (AU) that is the average distance between the earth and the sun. 1 AU = 149 597 870.691 km.

title: Astrodynamics/The Earth


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Astrodynamics/Time

Time is a fundamental quantity in physics, and nearly all of our equations deal either directly or indirectly with the passage of time.

Solar Day
A solar day is the time it takes for the Earth to make one complete rotation about its axis with respect to the sun. With respect to inertial space, a solar day equates to approximately 360.986° of rotation. Because of the Earth's slightly elliptical orbit and the obliquity of its rotation axis with respect to its orbital plane, the time between successive transits of the sun are not identical. The sun occasionally lags or leads the mean value of its position in the sky. Thus two types of solar time exist: apparent and mean. Apparent solar time refers to the absolute position of the sun in the sky. Mean solar time refers to the position of the mean sun, which divides the day into 24 hours.

Sidereal Day

The sidereal day is the length of time it takes the earth to make one complete rotation with respect to the stars. A sidereal day is slightly shorter than a solar day: 23h56m04s.09054 of mean solar time, or 0.9972695664 mean solar days.

To complicate matters slightly, sidereal time is also expressed in hours, minutes and seconds. Thus one solar day is equal to 24h03m56s.55536 of sidereal time or 1.0027379093 sidereal days. Sidereal time can best be understood as an angular measure of the Earth's orientation. Greenwich Mean Sidereal Time (GMST) is the sidereal time at the prime meridian and is essentially the angle between the vernal equinox direction and the vector pointing from the Earth's center to the crossing of the prime meridian and the equator.

Universal Time
Universal Time (UTC) is basically the mean solar time at the prime meridian. It is based solely on the rotation of the Earth with respect to background stars.

It is related to International Atomic Time (TAI), which is a high precision time base based on a weighted average of atomic clocks at national laboratories around the world. Because the rotation of the Earth is non-uniform, periodically leap seconds must be added or subtracted to convert to UTC. Because the rotation of the Earth is slowing gradually with time due to tidal effects from the moon, leap seconds have only ever been added. Since June 30, 2012, TAI is exactly 35 seconds ahead of UTC.

Converting from Universal to Sidereal
Sidereal time can be approximated from the current date and universal time to within 0.1 seconds by the following equation :

 * $$GMST = 6.697374558 + 0.06570982441908 D_0 + 1.00273790935 H + 0.000026 T^2$$

Where
 * $$ D_0 = JD_0-2451545.0$$
 * $$ D = JD-2451545.0$$
 * $$ T = D/36525$$

The H term is the current universal time. JD is the current Julian date and JD0 is the exact Julian date of the previous midnight, this value will end with .5. Generally, the final term can be omitted as it accounts for variations that occur over the course of centuries.

To use this equation, one must be familiar with the concept of Julian dates. The concept was introduced in the 16th century as a way to keep track of astronomical events without needing to deal with complex calculations relating to calendar dates. The Julian date is a running count of days elapsed since noon on January 1, 4713BC. Fractions of the day are expressed as a decimal value. Conversion algorithms exist for converting calendar date to Julian date, but they can be quite complicated and will not be discussed here. Below is a reference chart of Julian dates at noon on January 1st of several years. The Julian day number can be calculated by adding the day number of the year and subtracting 1. Please note that Julian dates are integer values at noon, NOT at midnight

title: Astrodynamics/Time


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Astrodynamics/Coordinate Systems

Coordinate Systems
Before orbits can be discussed, it is necessary to define the coordinate systems that will be used to describe them. Multiple systems are used in the study of space, and by extension astrodynamics.

Every coordinate system consists of three mutually perpendicular axes that describe the three-dimensional coordinates of all points in space. Each particular system is defined by three geometric objects: an origin, a reference direction and a fundamental plane. The origin defines the center from which the axes originate, three options for origins will be discussed in detail here: topocentric, geocentric and heliocentric. The reference direction defines the x-axis. The fundamental plane contains the x-axis and defines the z-axis as the direction normal to the plane. The y-axis completes the right-hand system defined by the other two vectors:

 * $$\mathbf{\hat{y}} = \mathbf{\hat{z}} \times \mathbf{\hat{x}}$$

Positions in these systems may be expressed either as spherical or rectangular coordinates. Generally, spherical coordinates are used in astronomy and other ground-based observations where objects are sufficiently far away to not have discernible parallax.

One can define coordinate systems centered on planets and other large bodies, but these are analogous to geocentric coordinate systems and will not be discussed in great detail. Additional astronomical coordinate systems have been defined, such as galactic and supergalactic, but these are currently of little practical use in astrodynamics.

Topocentric-Horizon
The topocentric-horizon system, also known as the "SEZ" system is a system of coordinates for use by observers on the surface of the earth. The surface of the observer forms the fundamental plane, that is tangent to the surface of the earth. The positive horizontal vector S is due south, the positive horizontal vector E is east, and the vector Z normal to the surface of the earth (up) is the third axis. Notice that the unit vectors change with time, which means that the topocentric-horizon system is a non-inertial system.

We can introduce a new vector, the vector re, which is the position vector from the center of the earth to a point on the surface of the earth. It is important to note that the length of this vector is not a constant, because the Earth is not a perfect sphere. The Z vector, which is normal to the surface of the earth does not necessarily pass through the center of the earth, and so it cannot be used to define the re vector.

Geocentric-Equatorial
The geocentric-equatorial coordinate system uses the center of the earth as the origin, and uses the circle of the Earth's equator as the fundamental plane with the positive vertical axis is the north pole of the earth. Two different coordinate frames are generally employed: the Earth-centered, Earth fixed (ECEF) frame, which is non-inertial; and the Earth-centered Inertial (ECI) frame, which is inertial.

Earth-centered inertial (ECI)
The ECI system is fixed in space, and does not rotate with the earth. The unit vectors that we will be using with the geocentric-equatorial system are I (for the vernal direction), J for the second direction in the equatorial plane), and K (for the direction of the north pole).

Ecliptic
The heliocentric-ecliptic coordinate system uses the center of the sun as the origin, and is supremely useful for discussing orbits where the sun is the prime focus. The Earth's orbit forms the fundamental plane, and the vertical axis is the normal vector to that fundamental plane.

Perifocal
The perifocal coordinate system is used to describe a satellite's position within its orbit. In a completely unperturbed orbit, the motion of the satellite is completely confined to one plane of motion, the perifocal system reduces orbital motion from three dimensions to two dimensions, greatly simplifying computations. This is most useful in the process of orbit propagation. Coordinates for the perifocal system are generally expressed as PQW. The fundamental plane is the orbital plane. The P vector points from the prime focus to the periapsis point. The Q vector is in the fundamental plane, rotated 90° from the P vector, in the direction of the orbital motion. The W vector is normal to the orbital plane, and points in the direction of the angular momentum, h. Position and velocity vectors exist entirely within the orbital plane and thus can be described exclusively in terms of P and Q.

Noninertial Derivatives
A problem arises when we have two coordinate systems, the first is a fixed system (a, b, c) and the second is rotating with respect to the first and is (d, e, f). We know that (d, e, f) is rotating in (a, b, c) with an angular velocity vector ω. That is, we can say:

 * $$\mathbf{D}' = \mathbf{\omega}\times\mathbf{D}$$
 * $$\mathbf{E}' = \mathbf{\omega}\times\mathbf{E}$$
 * $$\mathbf{F}' = \mathbf{\omega}\times\mathbf{F}$$

We have a vector X that is defined in both systems:

 * $$\mathbf{X} = X_a\mathbf{A} + X_b\mathbf{B} + X_c\mathbf{C} = X_d\mathbf{D} + X_e\mathbf{E} + X_f\mathbf{F}$$

The time derivative of A can be defined as:

 * $$\frac{d}{dt}\mathbf{A}|_{(a, b, c)} = \frac{d}{dt}\mathbf{A}|_{(d, e, f)} + \mathbf{\omega} \times \mathbf{A}$$

title: Astrodynamics/Coordinate Systems


text:
Astrodynamics/Motion Constants

Specific Energy and Angular Momentum
Angular momentum, kinetic energy and gravitational potential energy are all proportional to the mass of the orbiting body. However, when on the topic of orbital mechanics, it is more convenient to discuss the specific angular momentum and specific energy which are simply the angular momentum and energy per unit mass. Thus two objects in identical orbits may have very different masses, but will have the same specific angular momentum and the same specific energy (assuming, of course, that the masses of both bodies are negligible compared to the mass of the central body). Throughout this text, unless otherwise noted, the terms "angular momentum" and "energy" will refer to their specific counterparts.

Conservation of Angular Momentum
We already have two fundamental vectors that are used to analyze orbits: the position vector r, and the velocity vector v. We know from basic Newtonian mechanics that the velocity vector is the time-derivative of the position vector:

 * $$\dot{\mathbf{r}} = \mathbf{v}$$

And that:

 * $$\dot{r} = v$$

Starting with our motion equation we derived earlier, we can derive the angular momentum of the body.

 * $$\ddot{\mathbf{r}} + \frac{\mu}{r^3}\mathbf{r} = 0$$

We use the cross-product with the position vector r on both sides of the equation:

 * $$\mathbf{r} \times \ddot{\mathbf{r}} + \mathbf{r} \times \frac{\mu}{r^3}\mathbf{r} = 0$$

The second term cancels out because we know that r × r = 0.

 * $$\mathbf{r} \times \ddot{\mathbf{r}} = 0$$

We can substitute our above results into our equation to produce:

 * $$\frac{d(\mathbf{r} \times \dot{\mathbf{r}})}{dt} = 0$$

Because the derivative is zero, we know that the result must be a constant. We can integrate both sides, introducing the constant vector of integration, h:

 * $$\mathbf{r} \times \mathbf{v} = \mathbf{h}$$

Because we know that h is a constant, this equation shows that angular momentum is conserved in an orbital system. This constant is known as the angular momentum of the orbit, and is highly important in future calculations.

Meaning of h
h is a vector that is perpendicular to both r and v. r and v are both located in a single plane, known as the orbital plane. The entire orbit is located in this plane. However, the vector h is normal to the orbital plane, which means that it is perpendicular to the orbital plane. The scalar value h is the magnitude of this vector, and is defined as:

 * $$h = |\mathbf{h}|$$

Alternate Definitions of h
The magnitude value h can be derived from the magnitude values r and v as such:

 * $$h=rv\cos\phi$$
 * $$h=rv\sin\gamma$$

Where γ is the angle between the vectors r and v, and φ is the compliment of γ. φ is known as the flight angle of the satellite. γ is known as the zenith angle.

Conservation of Energy
Similar to the angular momentum, we can derive the conservation of energy equation. Instead of performing a cross product on both sides by the position vector r, we can perform the dot product by the velocity vector v:

 * $$\dot{\mathbf{r}} \cdot \ddot{\mathbf{r}} + \dot{\mathbf{r}} \cdot \frac{\mu}{r^3}\mathbf{r} = 0$$

We know that the second derivative of r is the same as the first derivative of v:

 * $$\mathbf{v} \cdot \dot{\mathbf{v}} + \frac{\mu}{r^3}\mathbf{r} \cdot \dot{\mathbf{r}} = 0$$

In general, a result of the dot product is that:

 * $$\mathbf{x} \cdot \dot{\mathbf{x}} = x\dot{x}$$

We can apply this result to our equation:

 * $$v\dot{v} + \frac{\mu}{r^3}r\dot{r} = 0$$

From the chain rule, we know that:

 * $$\frac{d}{dt}\frac{v^2}{2} = v\dot{v}$$

And:

 * $$\frac{d}{dt}\frac{\mu}{r} = -\frac{\mu}{r^2}\dot{r}$$

Plugging these results into our equation gives us:

 * $$\frac{d}{dt}\left(\frac{v^2}{2} - \frac{\mu}{r}\right) = 0$$

To generalize the equation, an additional constant term c must be added:

 * $$\frac{d}{dt}\left(\frac{v^2}{2} - \frac{\mu}{r} +c \right) = 0$$

Again, the derivative is equal to zero, so we know that the function has a constant value. We integrate both sides, and we call our new constant of integration the energy of the system:

 * $$\mathcal{E} = \frac{v^2}{2} - \frac{\mu}{r} + c$$

Kinetic Energy
From classical mechanics, the first term van be identified as the specific kinetic energy of the moving body:

 * $$\mathcal{E}_k = \frac{v^2}{2}$$

This represents the amount of work necessary to accelerate the body from a state of rest to its current velocity.

Potential Energy
The second and third term combined represent the specific potential energy of the moving body:

 * $$\mathcal{E}_p = -\frac{\mu}{r} + c$$

This represents the amount of work necessary to move the body from a given reference distance to its current distance from the center of the central body. The reference distance is defined by the c term in the equation. For instance, to define the surface of the Earth as having zero potential energy, c would be set to equal μ/r0, where r0 is the radius of the Earth. In this particular case, bodies below the radius of the earth would have negative potential energy and bodies above would have positive potential energy. It is most convenient, however, to set the reference distance to be infinite, which reduces the expression for the potential energy to:
 * $$\mathcal{E}_p = -\frac{\mu}{r}$$

This will result in potential energy values that are globally negative. This may seem counter-intuitive at first, but calculations are greatly simplified.

Total Mechanical Energy
The expression for the total specific mechanical energy of the system thus becomes:

 * $$\mathcal{E} = \frac{v^2}{2} - \frac{\mu}{r}$$

This quantity is important in determining the shape of the orbit and will be discussed in detail in the next chapter.

Derivation of Kepler's Laws from Newton's Laws
Now that the constants of motion have been defined, it is possible to derive Kepler's laws from Newton's laws of motion and gravitation.

First Law
As stated previously, the equation of motion for an object in the restricted two body problem is:
 * $$\ddot{\mathbf{r}} = -\frac{\mu}{r^3}\mathbf{r}$$

Taking the cross product of both sides with the angular momentume vector yields:
 * $$\ddot{\mathbf{r}}\times\mathbf{h} = -\frac{\mu}{r^3}\mathbf{r}\times\mathbf{h}$$

Because the h vector does not change with time, the left side is equivalent to:
 * $$\ddot{\mathbf{r}}\times\mathbf{h} = \ddot{\mathbf{r}}\times\mathbf{h}+\dot{\mathbf{r}}\times\dot{\mathbf{h}}=\frac{d}{dt}(\dot{\mathbf{r}}\times\mathbf{h})$$

Meanwhile the left side becomes:
 * $$-\frac{\mu}{r^3}\mathbf{r}\times(\mathbf{r}\times\dot{\mathbf{r}})=-\frac{\mu}{r^3}\left(\mathbf{r}(\dot{\mathbf{r}}\cdot\mathbf{r})-\dot{\mathbf{r}}(\mathbf{r}\cdot\mathbf{r})\right)$$

 * $$=\frac{\mu}{r^3}\left(\dot{\mathbf{r}}r^2-\mathbf{r}r\dot{r}\right)$$

 * $$=\mu\left(\frac{\dot{\mathbf{r}}}{r}-\frac{\mathbf{r}\dot{r}}{r^2}\right)$$

 * $$=\mu\frac{d}{dt}\left(\frac{\mathbf{r}}{r}+\mathbf{B}\right)$$

Where B is a constant of integration. Thus the equation becomes:

 * $$\dot{\mathbf{r}}\times\mathbf{h}=\mu\frac{\mathbf{r}}{r}+\mathbf{B}$$

Taking the dot product of both sides with r:
 * $$\mathbf{r}\cdot(\dot{\mathbf{r}}\times\mathbf{h}) = \mu r+\mathbf{B}\cdot\mathbf{r}$$

Recalling properties of triple vector products:
 * $$\mathbf{r}\cdot(\dot{\mathbf{r}}\times\mathbf{h})=\mathbf{h}\cdot(\mathbf{r}\times\dot{\mathbf{r}})=\mathbf{h}\cdot\mathbf{h}=h^2$$

The equation becomes:
 * $$h^2=\mu r+Br\cos\nu$$

Rearranging the equation:

 * $$r(\nu)=\frac{h^2/\mu}{1+B/\mu\cos\nu}$$

This equation is identical to the polar equation of a conic section centered at one focus:
 * $$r(\theta)=\frac{p}{1+e\cos\theta}$$

Where e is the eccentricity of the conic section and p is the semi-latus rectum of the conic section. For an ellipse:
 * $$p=a(1-e^2)$$

Where a is the semi-major axis.

This derivation shows that in addition to elliptical orbits, a body is also capable of parabolic or hyperbolic trajectories (both of which will be discussed shortly). Thus, stated generally, Kepler's first law becomes:
 * The trajectory of an object in a gravitational field is a conic section with the central body at one focus

Second Law
The angular momentum vector:
 * $$||\mathbf{h}||=||\mathbf{r}\times\mathbf{v}||=rv\cos\phi$$

Where φ is the flight path angle and vcosφ is the component of the velocity vector which is normal to the position vector. From polar calculus, this can be re-expressed as:
 * $$v\cos\phi=r\dot\nu$$

Thus the equation for angular momentum becomes:
 * $$h=r^2\frac{d\nu}{dt}$$

Recalling from calculus, the differential element of area in polar form is:
 * $$dA=\frac{r^2d\nu}{2}$$

Combining these equations gives:

 * $$\frac{dA}{dt}=\frac{h}{2}$$

The angular momentum is already known to be constant in the restricted two body problem, so this is the mathematical expression of Kepler's second law. This equation holds true for parabolic and hyperbolic as well as elliptical trajectories.

Third Law
Because the third law only deals with closed orbits, it is only valid for elliptical orbits. The result from the previous section can be rewritten as:
 * $$dA=\frac{h}{2}dt$$

Integrating both sides over one complete orbit yields:
 * $$\pi ab = \frac{h}{2}T$$

Where πab is the area enclosed by the entire ellipse and T is the orbital period. The semi-minor axis can be rewritten in terms of semi-latus rectum and semi-major axis:
 * $$b = \sqrt{a^2(1-e^2)}=\sqrt{ap}$$

Recall that angular momentum is related to the semi-latus rectum via:
 * $$p=\frac{h^2}{\mu}$$

Combining these equations and reducing gives the expression for orbital period:

 * $$T=2\pi\sqrt{\frac{a^3}{\mu}}$$

Which can be reduced to Kepler's third law:

 * $$T^2\propto a^3$$

title: Astrodynamics/Motion Constants


text:
Astrodynamics/Orbit Basics

Trajectory Equation
The trajectory equation, which gives us the shape of the orbit is given as:

 * $$r = \frac{\frac{h^2}{\mu}}{1 + \frac{B}{\mu}\cos\nu}$$

Where B is a constant of integration, and ν (Greek letter nu) is the angle between the semi-major axis and the position vector r.

Conic Sections
Let us digress a little bit from the theory of an orbit, and discuss conic sections. People are typically familiar with conic sections (circle, elipse, parabola, hyperbola) from studying elementary algebra. However, the form in which most people are not familiar with these conic sections is in the standard cartesian coordinate system. If we use a polar coordinate system instead, we can see that the conic sections all have a similar equation format. We can generalize, and say that all conic sections have the following polar equation:

 * $$r = \frac{p}{1 + e\cos\theta}$$

Here, r is the radius, and θ is the angle. As θ travels around the circle, the value for r changes and the resulting points create the necessary conic sections. The variable p is known as the parameter, and the variable e is known as the eccentricity. We will discuss these variables, and describe how they relate to the trajectory equation below.

Parameter
Comparing the trajectory equation and the conic section equation, we can see that:

 * $$p = \frac{h^2}{\mu}$$

the variable p is a measure of the size of the conic section. Larger p means the orbit is larger. We can see that the size of an orbit is directly proportional to how much angular momentum the satellite has. Because of this relationship, we can get the vague sense that the more speed a satellite has, the larger the resulting orbit will be.

Eccentricity
The value for e, the eccentricity, determines the shape the orbit will take. This table shows the various values for e, and the resulting shape of the conic section:

Looking at our conic section equation, and the trajectory equation, we can see that:

 * $$e = \frac{B}{\mu}$$

We know that B is just a constant of integration that doesn't correspond to any natural quantity. We can calculate e directly without having to calculate B first. We can relate e to the energy and the angular momentum of the satellite by:

 * $$e = \sqrt{1 + \frac{2\mathcal{E}h^2}{\mu^2}}$$

We can also relate e and p together, using the length of the semi-major axis, a:

 * $$ p = a(1-e^2)$$

Eccentricity Vector
We can also define an eccentricity vector, e, as:

 * $$\mathbf{e} = \frac{\mathbf{v} \times \mathbf{h}}{\mu} - \frac{\mathbf{r}}{r}$$

This vector has the property that:

 * $$e = |\mathbf{e}|$$

And that e points towards the periapsis point (described below).

Orbits
We can see that the trajectory equation is in the form of a conic section, and because of this form it's actually possible to have orbits in the shape of any conic section. We will discuss some of them below.

Elliptical
An elliptical orbit is an orbit with eccentricity e < 1. Elliptical orbits are some of the most common orbits, and nearly all bodies that travel around the sun have elliptical orbits.

We know from the equations for p that the speed of the satellite affects the size of the orbit. We also know from the equation relating p and e that the speed can affect the shape of the orbit. Putting a satellite into a certain orbit then is a matter of giving the satellite the correct speed for that orbit. An elliptical orbit is an orbit that is created by a speed less than the escape speed. The escape speed, which we will talk about below, is the speed at which a satellite breaks free from the gravity of the prime focus and forms a parabolic or elliptical orbit.

There is a particular speed known as the circular speed at which an elliptical orbit becomes a perfect circle. All other speeds, besides the circular speed and below the escape velocity create an elliptical orbit.

The values for these speeds can be calculated by plugging in the appropriate values into the trajectory equation to create the desired conic section, and then solving for the kinetic energy. We will omit the derivations here.

Circular
A circular orbit is an orbit with eccentricity e = 0. A circle is a special case of the ellipse. Circular orbits are difficult to obtain, but not impossible. The speed necessary to maintain a circular orbit is known as circular speed. We can define circular speed as:

 * $$v_{cs} = \sqrt{\frac{\mu}{r}}$$

Where r in this case is the radius of the circular orbit.

Parabolic
A parabolic orbit is an orbit with eccentricity e = 1. The speed necessary to form a parabolic orbit is known as the escape velocity ve. The escape velocity is the minimum speed necessary to escape from the gravitational pull of the primary focus. Notice that when we obtain this minimum escape speed, we break free from the gravity of the prime focus, but our velocity approaches zero:

 * $$v_\infty = 0$$

We can define the escape velocity as:

 * $$v_{er} = \sqrt{\frac{2\mu}{r}}$$

In this case, r is the distance of the satellite from the primary focus, and ver is the escape velocity from the point r. For earth the velocity is equal to 2nd escape velocity which is 11.1799 km/s

Hyperbolic
A hyperbolic orbit has eccentricity e > 1. Hyperbolic orbits are sometimes also known as escape orbits, because a hyperbolic orbit allows a satellite to "break free" from the gravity of the prime focus, while maintaining some velocity. The amount of speed the satellite has over the escape velocity of the parabolic orbit is known as 'excess hyperbolic speed, vh and can be found by comparing to the launch velocity (or the velocity at periapsis) vl:

 * $$v_l = v_e + v_h$$

And compared to the parabolic orbit, we have our final velocity as:

 * $$v_\infty = v_h$$

Degenerate
People familiar with conic sections may recognize that there are also degenerate conics: points and straight lines. Degenerate conics occur for values of h = 0, which means that e = 1 (a parabola), but that the orbit will not be parabolic.

Apses
The line between the foci is known as the major axis (in an ellipse and a hyperbola). The points at the intersection of the curve and the major axis are known as the apses. The point nearest the primary focus is called the periapsis, and the point nearest to the secondary focus is called the apoapsis. There are several other words that can be used interchangeably:

Additional terms exist for other solar system bodies, but these are nore required for the purposes of this text.

Circles do not have points furthest or closest to the center, and so the periapsis and apoapsis are undefined on a circle. The parabola has a periapsis, but the apoapsis is considered to be at infinity.

The distance from the prime focus to periapsis can be calculated as:

 * $$r_p = \frac{p}{1 + e} = a(1-e)$$

The distance from the prime focus to the apoapsis can be calculated as:

 * $$r_a = \frac{p}{1-e} = a(1+e)$$

Notice that these equations arise by setting θ = 0° or θ = 180°, because the periapsis is located at zero degrees, and apoapsis is located at 180 degress.

Vis-Viva Equation
Note that the velocities at the apses must necessarily be perpendicular to the position vectors, thus:
 * $$||\mathbf{r}_p\times\mathbf{v}_p|| = r_p v_p = h$$
 * $$||\mathbf{r}_a\times\mathbf{v}_a|| = r_a v_a = h$$

The following expressions can be derived:
 * $$v_p = \sqrt{\frac{(1+e)}{(1-e)}\frac{\mu}{a}}$$
 * $$v_a = \sqrt{\frac{(1-e)}{(1+e)}\frac{\mu}{a}}$$

Recall the expression for specific mechanical energy:
 * $$\mathcal{E} = \frac{v^2}{2} - \frac{\mu}{r}$$

Plugging in values for rp, vp, ra, and va:
 * $$\mathcal{E} = \frac{v_p^2}{2} - \frac{\mu}{r_p}= \frac{v_a^2}{2} - \frac{\mu}{r_a}$$

Solving this equation in terms of a yields:

 * $$\mathcal{E} = \frac{v^2}{2} - \frac{\mu}{r}=-\frac{\mu}{2a}$$

Orbital Period
The period of an orbit can be given as:

 * $$T = 2\pi{\sqrt{a^3/\mu}}$$

Notice that the period only makes sense for an elliptical or circular orbit, because parabolas and hyperbolas never make a full revolution. Notice also that this equation proves Kepler's third law. We can see this by rearranging the exponents:

 * $$T^2 = \frac{4\pi^2}\mu a^3$$

Now it's clear that the square of the period is proportional to the cube of the major-axis, which is the mean distance from the sun.

The circular orbital period is similar to the elliptical, but with the circle radius, r:

 * $$T = 2\pi{\sqrt{r^3/\mu}}$$

title: Astrodynamics/Orbit Basics


text: The Grand Inquisitor/The Devil (Part 2)

title: The Grand Inquisitor/The Devil (Part 2)


text:
User talk:Snowflake~enwikibooks

Regarding edits made during May 4 2007
Please do not target one or more user's pages or talk pages for abuse or insults, unwarranted doctoring or blanking, as you did with User:Panic2k4. It can be seen as vandalism and may get you blocked from editing. Az1568(Talk) 01:27, 4 May 2007 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Snowflake. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Snowflake~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:42, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 05:30, 19 April 2015 (UTC)

title: User talk:Snowflake~enwikibooks


text:
Cookbook talk:Hummus

Great hummus recipe- Hummus sandwich.

Use either pita bread or regular white sandwich bread. In either case, toast the bread by whatever manner you see fit. In the case of a pita, open the pita and create a pocket. Smear the inside of the pita or the surface of the bread with hummus, then sprinkle lettuce, a little vinegar and some olive oil, along with any other seasonings. Close and enjoy.

title: Cookbook talk:Hummus


text:
User talk:71.146.88.131

Regarding edits made during May 4 2007
Please stop adding nonsense to Wikibooks. It is considered vandalism. If you would like to experiment, use the sandbox. Thank you. If this is an IP address, and it is shared by multiple users, ignore this warning if you did not make any unconstructive edits. Az1568(Talk) 01:54, 4 May 2007 (UTC)

title: User talk:71.146.88.131


text:
Talk:How to use a Motorola DVR/Programming the Remote

Maxent 50" plasma code is 1755. Others have reported that it's 11755.

If you use an EFC in a macro, does it count as one button or six? Random832 (talk) 03:10, 19 July 2008 (UTC)

EFC 109 changes resolution!

Alternate Remote for Motorola 6416 Phase III to get 30 second skip button
The URC remote model 1056B03 now provided by Time Warner cable in the Los Angeles area for their Motorola 6416 Phase III DVR no longer has a 30 second skip button (commercial skip) and can't be programmed to have a skip button using any techniques discussed in this article. According to a technician it is due to the fact that Time Warner wanted to have one remote for both the 6416 and their whole-house DVR and the whole-house DVR uses all of the extra buttons that were used for things like skip for other features. Whatever the case may be, the Logitech Harmony 200 works will with the DVR and can easily be programmed via a USB connection to a PC so that it has the 30 second commercial skip button. It was also necessary to program buttons for the preview (8 second skip back) and exit commands. But with the Logitech software it was simple drag and drop programming. Their may well be other, and perhaps even less expensive, universal remotes that will work as well, but if you are looking for a solution then the Logitech 200 does work well. Note that it seems like it has been discontinued in favor of the 300 which is a bit more expensive but still reasonable and probably would work also. The 200 can still be obtained retail for about 20 dollars US.

Pace/Cisco boxes
I'm looking for the 4 digit code(s) for any of Pace/Cisco cable boxes. The purported five digit codes, such as 01982 etc. Without the leading zero either don't work or give an error flash. Code search reveals nothing. It may as well not be in the remote's database. 66.114.93.6 (discuss) 13:15, 13 December 2016 (UTC)


text:
User talk:58.107.57.175

Crash Bandicoot the Wrath of Cortex
Hi. I have deleted the page Crash Bandicoot the Wrath of Cortex because it does not appear to be a textbook. If you do wish to write a textbook on the subject, then please recreate the page after reading WB:WIW and WB:NEW. Thanks. --Az1568(Talk) 03:24, 4 May 2007 (UTC)

Deletion of "The Emperor's New Groove" - Final Warning
This page has been deleted again because it is NOT suitable for Wikibooks. Please do not recreate it. Wikibooks is a project for the creation of free text book materials. If you create this page again then you may be blocked from editing Wikibooks.

Xania talk 21:49, 30 May 2007 (UTC)

title: User talk:58.107.57.175


text:
User talk:Yasya

Hello, and welcome to Wikibooks!

Here are some tips to help you get started:
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You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be a good idea to add this page to your "watchlist" so that you can see when any new information is posted there. You can do that by clicking the tab labeled "watch" at the top of the page.

Good luck! -- Herby talk thyme 06:59, 4 May 2007 (UTC)

Deleted page
No problem - can you let me know what the actual title was (I deleted two/three IIRC) and I'll get it back and place it in your user space for now? Hope that is ok - regards -- Herby talk thyme 06:59, 4 May 2007 (UTC)
 * Thanks a lot! This was "How a to write a good book for children?" --Yasya 13:56, 4 May 2007 (UTC)
 * OK it is now here and in your space. Let me know when you have what you want and I will delete it.  I'm guessing (as there have been five of these pages) that it is a class project of some sort?  If so could you get someone "in charge" to post in the Staff lounge so they can get some guidance on how to do things - thanks -- Herby  talk thyme 15:07, 4 May 2007 (UTC)
 * Hi Herby, thank you, we got what we needed, feel free to delete the page. I guess, we'll have a team working on the issues of 'compatibility' with the rest of wikibooks at our next f-2-f meeting this Thrusday. Thanks, --Yasya 01:54, 9 May 2007 (UTC)

Applied History of Psychology
Hello Yasya, thank you for replying to my message. We've had several classroom projects similar to yours here at wikibooks, and over time we've learned alot about how to help those projects operate smoothly. We've written some of what we know at Guidelines for class projects, although that page is just a draft. Also, we we would appreciate it if you would "sign in" at List of class projects. This way, the community will know about your project and can help you if you need help.

If you need any help, I'm available most of the time. You can leave me a message on my user talk page, or you can post a question at Staff lounge. There are plenty of cool things that you can do with the wiki software, and we can help you do all of them. Good luck, and don't hesitate to ask if you need anything. --Whiteknight (talk) 02:05, 9 May 2007 (UTC)
 * Thanks a lot, it's really very helpful! --Yasya 03:50, 9 May 2007 (UTC)

PsycholARTSical: Psyched about the arts
Looks like you're running this show. If you need anything, my talk page and WB:HELP are available. As well, you can often find someone to help out in the #wikibooks IRC channel. – Mike.lifeguard  | talk 22:05, 10 January 2008 (UTC)

title: User talk:Yasya


text: A-level Chemistry/OCR (Salters)/Index

title: A-level Chemistry/OCR (Salters)/Index


text:
User talk:66.206.34.250

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 10:30, 4 May 2007 (UTC)

Please stop adding nonsense to Wikibooks. It is considered vandalism. If you would like to experiment, use the sandbox. Thank you. -- Herby talk thyme 10:42, 4 May 2007 (UTC)

title: User talk:66.206.34.250


text:
Goats/Breeds

Australian Miniature Goats

Boer Goats

Savannah Goats

Kiko Goats

BoKi Goats (A cross of Kiko and Boer)

Cashmere Goats

British Alpine Goats

Golden Guernsey Goats

British Guernsey Goats

French Alpine Goats

Sable Goats

Nubian Goats

Oberhasli Goats

Fainting Goats

Boer Goats

Pygmy Goats

Angora Goats

Sanaan Goats

Alpine Goats

LaMancha Goats

Nigerian Dwarf Goats

Zalawadi Goats

Xinjiang Goats

Xuhai Goats

Zhongwei Goats

Zhiwulin Black Goats

Yemen Mountain Goats

White Shorthaired Goats

West African Dwarf Goats

Verata Goats

Valais Blackneck Goats

Uzbek Black Goats

title: Goats/Breeds


text:
Goats/Veterinary Care

Goats are relatively easy to take care of if provided good forage and play space.

 * ../Wethering/
 * ../Budding and Dehorning/
 * ../Hoof Trimming/
 * ../Parasites/
 * ../Travel Fever/
 * ../Blockage/
 * ../Mastitis/
 * ../Chilling/
 * ../Goat Anatomy/

title: Goats/Veterinary Care


text:
User:Grzegorj

Witaj na mojej stronie w Wikibooks!

Nazywam się Grzegorz Jagodziński, "grzegorj" jest wykorzystywanym przeze mnie akronimem (7 liter imienia + 1 litera nazwiska), który dzięki nietypowej budowie jest niepowtarzalny. Z wykształcenia jestem biologiem, z zamiłowania - także językoznawcą. Mieszkam w Libiążu, w woj. małopolskim. Mam (bardzo) skromny wkład w redagowaniu różnych wikiprojektów. Jestem autorem witryny internetowej poświęconej wielu interesujących mnie zagadnieniom. Tam też można znaleźć informacje o tym, jak się ze mną skontaktować w razie potrzeby.

Każdemu, kto zechce skorzystać z zawartości mojej witryny i uzna ją za przydatne źródło wiedzy, udzielam zgody do wykorzystania zawartych tam materiałów mojego autorstwa (wszystkiego, co nie jest oznaczone jako innego pochodzenia) przy redagowaniu Wikibooks, Wikisłownika, Wikipedii itp.

Welcome to my page in Wikibooks!

My name is Grzegorz Jagodziński, "grzegorj" is an acronym (7 letters of my first name and 1 letter of my surname) applied by me. Because of its untypical structure, it is unique. By my profession, I am a biologist, and I am also a linguist - hobbyist. I live in Poland, in Libiąż, a small town in Małopolskie Voivodship. I have (tiny) contributions in various wiki projects. I am the author of a website on many topics, interesting for me. You can also find information how to contact me there.

Everyone can use my texts from my website to contribute Wikibooks, Wiktionary, Wikipedia and other similar projects.

Grzegorj 13:35, 4 May 2007 (UTC)

title: User:Grzegorj


text:
User talk:LRainbowz,x

Hello, and welcome to Wikibooks!

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Feel free to get in touch with me (leave a message on my "talk page"). Thanks for your contributions so far! -- SB_Johnny | talk 13:04, 4 May 2007 (UTC)

A question about How to make a good book for children?
This book appears to be a class project. If so, please have the instructor or group leader get in touch with me or one of our administrators, so we can help you organize it according to our policies here on Wikibooks.

Thanks!-- SB_Johnny | talk 13:04, 4 May 2007 (UTC)

title: User talk:LRainbowz,x


text: Template:Babel

title: Template:Babel


text:
User talk:Soccer822

Hello, and welcome to Wikibooks!

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Feel free to get in touch with me (leave a message on my "talk page"). Thanks for your contributions so far! -- SB_Johnny | talk 13:15, 4 May 2007 (UTC)

A question about How to write a good book for children?
This book appears to be a class project. If so, please have the instructor or group leader get in touch with me or one of our administrators, so we can help you organize it according to our policies here on Wikibooks.

Thanks!-- SB_Johnny | talk 13:15, 4 May 2007 (UTC)

title: User talk:Soccer822


text:
User talk:Wikijunior12

Hello, and welcome to Wikibooks!

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Feel free to get in touch with me (leave a message on my "talk page"). Thanks for your contributions so far! -- SB_Johnny | talk 13:16, 4 May 2007 (UTC)

A question about How to write a good book for children?
This book appears to be a class project. If so, please have the instructor or group leader get in touch with me or one of our administrators, so we can help you organize it according to our policies here on Wikibooks.

Thanks!-- SB_Johnny | talk 13:16, 4 May 2007 (UTC)

title: User talk:Wikijunior12


text:
User talk:Sdysart

Hello, and welcome to Wikibooks!

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Feel free to get in touch with me (leave a message on my "talk page"). Thanks for your contributions so far! -- SB_Johnny | talk 13:18, 4 May 2007 (UTC)

A question about How to write a good book for children?
This book appears to be a class project. If so, please have the instructor or group leader get in touch with me or one of our administrators, so we can help you organize it according to our policies here on Wikibooks.

Thanks!-- SB_Johnny | talk 13:18, 4 May 2007 (UTC)

 * Hey, was up jump rope queen :)
 * --Lady aquarius23 17:26, 10 May 2007 (UTC)

title: User talk:Sdysart


text:
User talk:Gabby~enwikibooks

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Feel free to get in touch with me (leave a message on my "talk page"). Thanks for your contributions so far! -- SB_Johnny | talk 13:18, 4 May 2007 (UTC)

A question about How to write a good book for children?
This book appears to be a class project. If so, please have the instructor or group leader get in touch with me or one of our administrators, so we can help you organize it according to our policies here on Wikibooks.

Thanks!-- SB_Johnny | talk 13:18, 4 May 2007 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Gabby. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Gabby~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:10, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 04:59, 19 April 2015 (UTC)

title: User talk:Gabby~enwikibooks


text:
User talk:Joakim3000

Hello, and welcome to Wikibooks!

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Feel free to get in touch with me (leave a message on my "talk page"). Thanks for your contributions so far! -- SB_Johnny | talk 13:18, 4 May 2007 (UTC)

A question about How to write a good book for children?
This book appears to be a class project. If so, please have the instructor or group leader get in touch with me or one of our administrators, so we can help you organize it according to our policies here on Wikibooks.

Thanks!-- SB_Johnny | talk 13:18, 4 May 2007 (UTC)

title: User talk:Joakim3000


text:
User talk:Grzegorj

Welcome
Hello, and welcome to Wikibooks!

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Good luck! --Derbeth talk 13:20, 4 May 2007 (UTC)

A po polsku
Witaj na Wikibooks Grzegorzu. Na tutejszych Wikibooks mówi się tylko po angielsku, więc jest niewielki sens pisania o sobie po polsku. Wikibooks po polsku znajdują się w innym miejscu. Najlepiej wstaw na swoją stronę użytkownika wieżę Babel, żeby inni mogli wiedzieć, w jakim języku do ciebie pisać. Pozdrawiam, --Derbeth talk 13:20, 4 May 2007 (UTC)

Correction
Cześć Grzegorj, I hope you don't mind but I made a small correction to your userpage to correct a mistake. And as Derbeth said, witamy! Xania talk 20:26, 29 May 2007 (UTC)

title: User talk:Grzegorj


text:
Astrodynamics/Classical Orbit Elements

Orbit Parameters
It is possible to specify an orbit entirely using a set of 5 parameters. With these 5 parameters, we can specify precisely where an orbit is, how it is oriented in 3-D space, and what size it is. If we have an optional sixth parameter, we can determine exactly where the satellite is in its orbit at any arbitrary time t. These 6 parameters are called the Keplerian Elements.

However, before we discuss the 6 orbit parameters, we need to introduce a few new terms.

Angular Momentum
The vector that points from the center of the Earth to the satellite or object of interest is called r, and its velocity vector is called v. The vector that is perpendicular to both of these is called the specific angular momentum vector.

 * $$\mathbf{h} = \mathbf{r} \times \mathbf{v}$$

Ascending Node
The Earth's equator resides in a plane known as the fundamental plane (as it is in the geocentric-equatorial coordinate system, which we will be using in this section), and the orbit traced out by the vector r forms a plane known as orbital plane, which contains the vectors r and v. The line formed by the intersection of these two planes is known as the line of nodes.

We can find the vector n by taking the cross product of the angular momentum vector, h, and the unit vector K = <0, 0, 1>:

 * $$\mathbf{n} = \mathbf{K} \times \mathbf{h}$$

n is a vector on the line of nodes that points in the direction of the ascending node. The ascending node is the spot where the satellite crosses the equatorial plane in a northerly direction. Likewise, the descending node is the point where the satellite crosses the equatorial plane in the southerly direction.

In an equatorial orbit, n is undefined, and there are no nodes.

Prograde and Retrograde
Prograde or direct means the satellite is traveling around the earth from west to east. Retrograde means the satellite is traveling from east to west. An object with an inclination between 0 and 90 degrees is orbiting or revolving in the same direction as the primary body is rotating. An object with an inclination of exactly 90 degrees has a perpendicular orbit which is neither prograde nor retrograde. An object with an inclination between 90 degrees and 180 degrees is in a retrograde orbit.

Visual Representation

This image shows two planes, the orbital plane (pale yellow) and the plane of reference (gray). The earth, or prime focus is considered to be at the dot at the center of the two planes. Notice how the orbit crosses the ecliptic at two points: once going northward (the ascending node), and once going southward (the descending node). The descending node is not marked in this picture, but its location should be obvious. We will explain some of the other terms below.

Classical Elements
Now that we have the node vector, along with the vectors r, v, and h, we can find our 5 classical orbital elements.

Semi-Major Axis
The semi-major axis, a can be found via the Vis-Viva equation:
 * $$a=-\frac{\mu}{2\mathcal{E}}=-\frac{\mu}{2}\left[\frac{v^2}{2}-\frac{\mu}{r}\right]^{-1}$$

Where some terms remain undefined.

Eccentricity
The eccentricity e can be determined from the magnitude of the eccentricity vector:

 * $$\mathbf{e}=\left(\frac{v^2}{\mu}-\frac{1}{r}\right)\mathbf{r}-\frac{\left(\mathbf{r}\cdot\mathbf{v}\right)}{\mu}\mathbf{v}$$

Alternately, it can be expressed as:

 * $$e=\sqrt{1+\frac{2\mathcal{E}h^2}{\mu^2}}$$

though the eccentricity vector will be needed in the calculation of later elements.

Inclination ($$i$$)
The inclination, i is the angle between the K unit vector and the angular momentum vector h. It can be calculated using:

 * $$i = \arccos\frac{h_K}{h}$$

The angle of inclination is always less than 180°.

Longitude of the Ascending Node ($$\Omega$$)
The longitude of the ascending node, Ω, is the angle between the ascending node and the I unit vector. It can be calculated as:

 * $$\Omega = \arccos\frac{n_I}{n}$$

If the nJ component is greater than zero, then Ω is less than 180°. Otherwise, Ω is greater than 180°.

Argument of Periapsis ($$\omega$$)
The argument of periapsis is the angle in the orbital plane between the ascending node and the periapsis. We can calculate it as:

 * $$\omega = \arccos \frac{\mathbf{n} \cdot \mathbf{e}}{ne}$$

If eK is greater than 0, then ω is less than 180°. Otherwise, ω is greater than 180°.

Time of Periapsis Passage
The time of periapsis passage is the time when the satellite reaches periapsis. We define this time as Tp. It can be determined from observation. This is the sixth orbital parameter that allows calculating the position of a celestial object in any time.

Longitude of Periapsis ($$\Pi$$)
Longitude of the Periapsis is the sum of the Longitude of the Ascending Node and the Argument of Perigee

 * $$\Pi = \Omega + \omega$$

True Anomaly at Epoch ($$\nu_0$$)
True anomaly at epoch is the angle from the periapsis point to the satellite's radius vector at epoch T0, and is denoted $$\nu_0$$

Argument of Latitude at Epoch ($$u$$)
Argument of Latitude at epoch is the angle between the ascending node and the satellite at epoch

$$ u = \nu + \omega $$

True Longitude at Epoch ($$l$$)
True longitude at epoch is the angle between the reference direction (usually the vernal equinox ) and the satellite's position. It is measured from the reference direction to the ascending node (if one exists) in the reference plane and then from the ascending node to the satellite's position in the plane of orbit.

$$ l = \Omega + \omega + \nu = \Pi + \nu = \Omega + u$$

Finding r and v
From the five classical orbital elements, we can determine r and v.

 * $$\mathbf{r} = r\cos(\nu)\mathbf{P} + r\sin(\nu)\mathbf{Q}$$

 * $$\mathbf{v} = \sqrt{\frac{\mu}{p}}[-sin(\nu)\mathbf{P} + e\mathbf{Q} + \cos(\nu)\mathbf{Q}]$$

Where P and Q are unit vectors in the perifocal coordinate system. Using our coordinate transformations, we can convert these into geocentric-equatorial coordinates.

title: Astrodynamics/Classical Orbit Elements


text:
Horticulture/Podophyllum peltatum

The Mayapple (Podophyllum peltatum) is a herbaceous perennial plant in the family Berberidaceae, native to the eastern part of North America. Other common names include Devil's apple, Hogapple, Indian apple, Umbrella plant (for the shape of the leaves), Wild lemon (for the flavor of the fruit), Wild mandrake, and American mandrake (for the shape of rhizomes).

Description
The stems grow to 20-40 cm tall, with palmately lobed leaves up to 20-30 cm diameter with 5-9 deeply cut lobes. The plant produces two growth forms. The form with a single umbrella-like leaf does not produce any flower or fruit. Stems having a twin leaf (rarely three-leaf) structure, however, bear a single white flower 3-5 cm diameter with six (rarely up to nine) petals, between the two leaves; this matures into a yellow-greenish fruit 2-5 cm long. The plant appears in colonies in open woodlands. Individual shoots are often connected by systems of thick tubers and rhizomes.

Uses
The rhizome of the mayapple has been used for a variety of medicinal purposes, originally by Native Americans and later by other settlers.

All the parts of the plant, excepting the fruit, are poisonous. This plant can kill humans within 24 hours. Even the fruit, though not dangerously poisonous, can cause unpleasant red/yellow diarrhea. The plant contains podophyllotoxin, which is used as a cytostatic and topically in the treatment of genital warts.

title: Horticulture/Podophyllum peltatum