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User:JohnOwens/Orbital variables

< User:JohnOwens

From external pages How the variables are used (& re-used) on some of the pages I refer to.
Wikipedia:TeX markup

Mars Academy (http://www.marsacademy.com/orbmect/orbles1.htm)

Kind of cheesy name, but what the heck.

<math>m_1, m_2</math>mass of objects 1 & 2
<math>G</math>gravitational constant
<math>d</math>distance (scalar)
<math>r</math>distance (scalar)
<math>\bar{r}</math>displacement (vector)
<math>K_e</math>kinetic energy
<math>P_e</math>potential energy
<math>F_g</math>gravitational force
<math>E</math>mechanical energy
<math>\bar{A}, \bar{B}</math>arbitrary vectors
<math>A, B</math>their magnitudes
<math>\alpha</math>the angle between <math>\bar{A}</math> and <math>\bar{B}</math>
<math>\beta</math>complement of α
<math>\bar{v}</math>velocity, <math>\bar{r}'</math>
<math>k</math>specific mechanical energy
<math>\bar{L}</math>angular momentum
<math>\bar{h}</math>specific angular momentum, <math>{\bar{L} \over m}</math>
<math>\bar{a}, \bar{b}, \bar{c}</math>arbitrary vectors
<math>\bar{k}</math>vector constant of integration
<math>\gamma</math>angle between <math>\bar{r}</math> and <math>\bar{k}</math>
<math>p</math>semilatus rectum[?]
<math>a</math>semimajor axis
<math>c</math>(distance between foci)/2
<math>\mbox{d}</math>directrix[?] of a conic section
<math>x</math>distance between directrix and focus
<math>\theta</math>angle to <math>\bar{r}</math>
<math>r_p, r_a</math>distance at periapsis and apoapsis
<math>v_p, v_a</math>velocity/speed at periapsis and apoapsis

World of Physics (http://scienceworld.wolfram.com/physics/Two-BodyProblem)

<math>m_1, m_2</math>mass of objects 1 & 2
<math>M</math><math>m_1 + m_2</math>
<math>\mathbf{r}_1, \mathbf{r}_2</math>radius of objects 1 & 2
<math>\mu</math>reduced mass <math>{m_1\,m_2 \over m_1 + m_2} \equiv {m_1\,m_2 \over M}</math>
<math>\mathbf{r}</math>displacement from body 1 to body 2, <math>\mathbf{r}_2 - \mathbf{r}_1</math>
<math>a</math>distance between bodies, <math>r_1 + r_2</math>
<math>G</math>gravitational constant
<math>\mathbf{h}</math>angular momentum per mass, <math>{\mathbf{L} \over m} \equiv {\mathbf{r} \times \mathbf{p} \over m} = {\mathbf{r} \times \mathbf{r'}}</math>
<math>h</math>magnitude of <math>\mathbf{h}</math>
<math>\theta</math>angle from arbitrary direction
<math>E</math>orbital energy
<math>\mathcal{E}</math>specific energy
<math>\mathbf{A}</math>Laplace-Runge-Lenz vector[?], <math>\mathbf{r'} \times \mathbf{h} - {G\,M\,\mathbf{r} \over r}</math>
<math>p</math>semilatus rectum[?]
<math>u</math><math>{1 \over r}</math>
<math>B</math>arbitrary constant
<math>\theta_0</math>arbitrary constant
<math>a</math>semimajor axis
<math>\theta_0</math>argument of pericenter[?]
<math>a \equiv 2 E</math>
<math>b \equiv 2 G M m</math>
<math>c \equiv h^2 m</math>
<math>A(r) \equiv 2 \sqrt{a (a r^2 + b r - c)}</math>
<math>B(r) \equiv \ln{\left[b + 2 a r + A(r)\right]}</math>
<math>C(r) \equiv A(r) + b B(r)</math>

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