## Encyclopedia > User:JohnOwens Orbital variables

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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.
Wikipedia:TeX markup

Kind of cheesy name, but what the heck.

 $F$ force $m_1, m_2$ mass of objects 1 & 2 $G$ gravitational constant $d$ distance (scalar) $r$ distance (scalar) $\bar{r}$ displacement (vector) $\mu$ $G\,m_1$ $K_e$ kinetic energy $W$ work $P_e$ potential energy $F_g$ gravitational force $E$ mechanical energy $\bar{A}, \bar{B}$ arbitrary vectors $A, B$ their magnitudes $\alpha$ the angle between $\bar{A}$ and $\bar{B}$ $\beta$ complement of α $\bar{v}$ velocity, $\bar{r}'$ $v$ speed $t$ time $k$ specific mechanical energy $\bar{p}$ momentum $\bar{L}$ angular momentum $\bar{h}$ specific angular momentum, ${\bar{L} \over m}$ $\bar{a}, \bar{b}, \bar{c}$ arbitrary vectors $\bar{k}$ vector constant of integration $\gamma$ angle between $\bar{r}$ and $\bar{k}$ $p$ semilatus rectum[?] $a$ semimajor axis $c$ (distance between foci)/2 $\mbox{d}$ directrix[?] of a conic section $x$ distance between directrix and focus $\theta$ angle to $\bar{r}$ $e$ eccentricity $r_p, r_a$ distance at periapsis and apoapsis $v_p, v_a$ velocity/speed at periapsis and apoapsis

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

 $m_1, m_2$ mass of objects 1 & 2 $M$ $m_1 + m_2$ $\mathbf{r}_1, \mathbf{r}_2$ radius of objects 1 & 2 $\mu$ reduced mass ${m_1\,m_2 \over m_1 + m_2} \equiv {m_1\,m_2 \over M}$ $\mathbf{r}$ displacement from body 1 to body 2, $\mathbf{r}_2 - \mathbf{r}_1$ $a$ distance between bodies, $r_1 + r_2$ $G$ gravitational constant $\mathbf{h}$ angular momentum per mass, ${\mathbf{L} \over m} \equiv {\mathbf{r} \times \mathbf{p} \over m} = {\mathbf{r} \times \mathbf{r'}}$ $h$ magnitude of $\mathbf{h}$ $\theta$ angle from arbitrary direction $A$ area $t$ time $E$ orbital energy $\mathcal{E}$ specific energy $\mathbf{A}$ Laplace-Runge-Lenz vector[?], $\mathbf{r'} \times \mathbf{h} - {G\,M\,\mathbf{r} \over r}$ $e$ eccentricity $v$ velocity/speed $p$ semilatus rectum[?] $u$ ${1 \over r}$ $B$ arbitrary constant $\theta_0$ arbitrary constant $a$ semimajor axis $\theta_0$ argument of pericenter[?] $a \equiv 2 E$ $b \equiv 2 G M m$ $c \equiv h^2 m$ $A(r) \equiv 2 \sqrt{a (a r^2 + b r - c)}$ $B(r) \equiv \ln{\left[b + 2 a r + A(r)\right]}$ $C(r) \equiv A(r) + b B(r)$

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