User:JohnOwens/Orbital variables

[edit] 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.

$F$	force
$m 1, m 2$	mass of objects 1 & 2
$G$	gravitational constant
$d$	distance (scalar)
$r$	distance (scalar)
$\bar{r}$	displacement (vector)
$μ$	$G\,m_1$
$K e$	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
$α$	the angle between $\bar{A}$ and $\bar{B}$
$β$	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
$γ$	angle between $\bar{r}$ and $\bar{k}$
$p$	semilatus rectum
$a$	semimajor axis
$c$	(distance between foci)/2
$d$	directrix of a conic section
$x$	distance between directrix and focus
$θ$	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

$m 1, m 2$	mass of objects 1 & 2
$M$	$m 1 + m 2$
$\mathbf{r}_1, \mathbf{r}_2$	radius of objects 1 & 2
$μ$	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, $\mathbf{r}_2 - \mathbf{r}_1$
$\mathbf{p}$	momentum
$a$	distance between bodies, $r 1 + r 2$
$G$	gravitational constant
$\mathbf{L}$	angular momentum, $\mathbf{r} \times \mathbf{p}$
$\mathbf{h}$	angular momentum per mass, ${\mathbf{L} \over m} \equiv {\mathbf{r} \times \mathbf{p} \over m} = {\mathbf{r} \times \mathbf{r'}}$
$h$	magnitude of $\mathbf{h}$
$θ$	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
$θ 0$	arbitrary constant
$a$	semimajor axis
$θ 0$	argument of pericenter
$a \equiv 2 E$
$b \equiv 2 G M m$
$c \equiv h^2 m$
$A(r) \equiv 2 \sqrt{a (a r^2 + b r - c)}$
$B(r) \equiv \ln{\left[b + 2 a r + A(r)\right]}$
$C(r) \equiv A(r) + b B(r)$