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.

$F$	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

$m_{1},m_{2}$	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, $\mathbf {r} _{2}-\mathbf {r} _{1}$
$\mathbf {p}$	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 $\mathbf {h}$
$\theta$	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
$a\equiv 2E$
$b\equiv 2GMm$
$c\equiv h^{2}m$
$A(r)\equiv 2{\sqrt {a(ar^{2}+br-c)}}$
$B(r)\equiv \ln {\left[b+2ar+A(r)\right]}$
$C(r)\equiv A(r)+bB(r)$