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

Mars Academy

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)
$\overline{r}$	displacement (vector)
$\mu$	$G{m}_1$
$K_e$	kinetic energy
$W$	work
$P_e$	potential energy
$F_g$	gravitational force
$E$	mechanical energy
$\overline{A},\overline{B}$	arbitrary vectors
$A,B$	their magnitudes
$\alpha$	the angle between $\overline{A}$ and $\overline{B}$
$\beta$	complement of α
$\overline{v}$	velocity, ${\overline{r}}^{\prime }$
$v$	speed
$t$	time
$k$	specific mechanical energy
$\overline{p}$	momentum
$\overline{L}$	angular momentum
$\overline{h}$	specific angular momentum, $\frac{\overline{L}}{m}$
$\overline{a},\overline{b},\overline{c}$	arbitrary vectors
$\overline{k}$	vector constant of integration
$\gamma$	angle between $\overline{r}$ and $\overline{k}$
$p$	semilatus rectum
$a$	semimajor axis
$c$	(distance between foci)/2
$\text{d}$	directrix of a conic section
$x$	distance between directrix and focus
$\theta$	angle to $\overline{r}$
$e$	eccentricity
$r_p,r_a$	distance at periapsis and apoapsis
$v_p,v_a$	velocity/speed at periapsis and apoapsis

World of Physics

$m_1,m_2$	mass of objects 1 & 2
$M$	$m_1+m_2$
${\mathbf{𝐫}}_1,{\mathbf{𝐫}}_2$	radius of objects 1 & 2
$\mu$	reduced mass $\frac{m_1{m}_2}{m_1+m_2}\equiv \frac{m_1{m}_2}{M}$
$\mathbf{𝐫}$	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, $\frac{\mathbf{𝐋}}{m}\equiv \frac{\mathbf{𝐫}\times \mathbf{𝐩}}{m}=\mathbf{𝐫}\times {\mathbf{𝐫}}^{\prime }$
$h$	magnitude of $\mathbf{𝐡}$
$\theta$	angle from arbitrary direction
$A$	area
$t$	time
$E$	orbital energy
${ℰ}$	specific energy
$\mathbf{𝐀}$	Laplace-Runge-Lenz vector, ${\mathbf{𝐫}}^{\prime }\times \mathbf{𝐡}-\frac{GM\mathbf{𝐫}}{r}$
$e$	eccentricity
$v$	velocity/speed
$p$	semilatus rectum
$u$	$\frac{1}{r}$
$B$	arbitrary constant
${\theta }_0$	arbitrary constant
$a$	semimajor axis
${\theta }_0$	argument of pericenter
$a\equiv 2E$
$b\equiv 2GMm$
$c\equiv h^{2}m$
$A(r)\equiv 2\sqrt{a(a{r}^2+br-c)}$
$B(r)\equiv \ln [b+2ar+A(r)]$
$C(r)\equiv A(r)+bB(r)$