User:JohnOwens/Orbital variables

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[edit] From external pages

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

Wikipedia:TeX markup new version

[edit] Mars Academy

Kind of cheesy name, but what the heck.

F force
m1,m2 mass of objects 1 & 2
G gravitational constant
d distance (scalar)
r distance (scalar)
\bar{r} displacement (vector)
μ G\,m_1
Ke kinetic energy
W work
Pe potential energy
Fg 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
rp,ra distance at periapsis and apoapsis
vp,va velocity/speed at periapsis and apoapsis

[edit] World of Physics

m1,m2 mass of objects 1 & 2
M m1 + m2
\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, r1 + r2
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
θ0 arbitrary constant
a semimajor axis
θ0 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)