# User:JohnOwens/Orbital variables

## From external pages

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

Wikipedia:TeX markup new version

 ${\displaystyle F}$ force ${\displaystyle m_{1},m_{2}}$ mass of objects 1 & 2 ${\displaystyle G}$ gravitational constant ${\displaystyle d}$ distance (scalar) ${\displaystyle r}$ distance (scalar) ${\displaystyle {\bar {r}}}$ displacement (vector) ${\displaystyle \mu }$ ${\displaystyle G\,m_{1}}$ ${\displaystyle K_{e}}$ kinetic energy ${\displaystyle W}$ work ${\displaystyle P_{e}}$ potential energy ${\displaystyle F_{g}}$ gravitational force ${\displaystyle E}$ mechanical energy ${\displaystyle {\bar {A}},{\bar {B}}}$ arbitrary vectors ${\displaystyle A,B}$ their magnitudes ${\displaystyle \alpha }$ the angle between ${\displaystyle {\bar {A}}}$ and ${\displaystyle {\bar {B}}}$ ${\displaystyle \beta }$ complement of α ${\displaystyle {\bar {v}}}$ velocity, ${\displaystyle {\bar {r}}'}$ ${\displaystyle v}$ speed ${\displaystyle t}$ time ${\displaystyle k}$ specific mechanical energy ${\displaystyle {\bar {p}}}$ momentum ${\displaystyle {\bar {L}}}$ angular momentum ${\displaystyle {\bar {h}}}$ specific angular momentum, ${\displaystyle {{\bar {L}} \over m}}$ ${\displaystyle {\bar {a}},{\bar {b}},{\bar {c}}}$ arbitrary vectors ${\displaystyle {\bar {k}}}$ vector constant of integration ${\displaystyle \gamma }$ angle between ${\displaystyle {\bar {r}}}$ and ${\displaystyle {\bar {k}}}$ ${\displaystyle p}$ semilatus rectum ${\displaystyle a}$ semimajor axis ${\displaystyle c}$ (distance between foci)/2 ${\displaystyle {\mbox{d}}}$ directrix of a conic section ${\displaystyle x}$ distance between directrix and focus ${\displaystyle \theta }$ angle to ${\displaystyle {\bar {r}}}$ ${\displaystyle e}$ eccentricity ${\displaystyle r_{p},r_{a}}$ distance at periapsis and apoapsis ${\displaystyle v_{p},v_{a}}$ velocity/speed at periapsis and apoapsis
 ${\displaystyle m_{1},m_{2}}$ mass of objects 1 & 2 ${\displaystyle M}$ ${\displaystyle m_{1}+m_{2}}$ ${\displaystyle \mathbf {r} _{1},\mathbf {r} _{2}}$ radius of objects 1 & 2 ${\displaystyle \mu }$ reduced mass ${\displaystyle {m_{1}\,m_{2} \over m_{1}+m_{2}}\equiv {m_{1}\,m_{2} \over M}}$ ${\displaystyle \mathbf {r} }$ displacement from body 1 to body 2, ${\displaystyle \mathbf {r} _{2}-\mathbf {r} _{1}}$ ${\displaystyle \mathbf {p} }$ momentum ${\displaystyle a}$ distance between bodies, ${\displaystyle r_{1}+r_{2}}$ ${\displaystyle G}$ gravitational constant ${\displaystyle \mathbf {L} }$ angular momentum, ${\displaystyle \mathbf {r} \times \mathbf {p} }$ ${\displaystyle \mathbf {h} }$ angular momentum per mass, ${\displaystyle {\mathbf {L} \over m}\equiv {\mathbf {r} \times \mathbf {p} \over m}={\mathbf {r} \times \mathbf {r'} }}$ ${\displaystyle h}$ magnitude of ${\displaystyle \mathbf {h} }$ ${\displaystyle \theta }$ angle from arbitrary direction ${\displaystyle A}$ area ${\displaystyle t}$ time ${\displaystyle E}$ orbital energy ${\displaystyle {\mathcal {E}}}$ specific energy ${\displaystyle \mathbf {A} }$ Laplace-Runge-Lenz vector, ${\displaystyle \mathbf {r'} \times \mathbf {h} -{G\,M\,\mathbf {r} \over r}}$ ${\displaystyle e}$ eccentricity ${\displaystyle v}$ velocity/speed ${\displaystyle p}$ semilatus rectum ${\displaystyle u}$ ${\displaystyle {1 \over r}}$ ${\displaystyle B}$ arbitrary constant ${\displaystyle \theta _{0}}$ arbitrary constant ${\displaystyle a}$ semimajor axis ${\displaystyle \theta _{0}}$ argument of pericenter ${\displaystyle a\equiv 2E}$ ${\displaystyle b\equiv 2GMm}$ ${\displaystyle c\equiv h^{2}m}$ ${\displaystyle A(r)\equiv 2{\sqrt {a(ar^{2}+br-c)}}}$ ${\displaystyle B(r)\equiv \ln {\left[b+2ar+A(r)\right]}}$ ${\displaystyle C(r)\equiv A(r)+bB(r)}$