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User:JohnOwens/Orbital variables

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

Kind of cheesy name, but what the heck.

<math>F</math>	force
<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>\mu</math>	<math>G\,m_1</math>
<math>K_e</math>	kinetic energy
<math>W</math>	work
<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>v</math>	speed
<math>t</math>	time
<math>k</math>	specific mechanical energy
<math>\bar{p}</math>	momentum
<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>e</math>	eccentricity
<math>r_p, r_a</math>	distance at periapsis and apoapsis
<math>v_p, v_a</math>	velocity/speed at periapsis and apoapsis

<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>A</math>	area
<math>t</math>	time
<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>e</math>	eccentricity
<math>v</math>	velocity/speed
<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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