Dynamics cheat sheet

Maor axes a
a = r p(1 + e)
1 − e 2
= r a(1 − e)
1 − e 2
= − µ
2E
= √ b 2 + c 2
= p
1 − e 2
Minor axes b b = a √ 1 − e 2
r p = a(1 − e2 )
r p 1 + e
= a(1 − e)
r a = a(1 − e2 )
1 − e
r a = a (1 + e)
p
specific angular momentum h
Total Energy E
= h2
µ
1
1 − e
r p
r a
= 1−e
1+e
p = a ( 1 − e 2) = h2
µ = r p (1 + e) = r a (1 − e)
h = r p v p = r a v a = ⃗r × ⃗v = √ pµ
h = √ µr
(circular orbit)
E = v2
2 − µ r = − µ 2a
√ ( 2
v = µ
r a)
− 1
(vis-viva)
velocity v
√
2µ
v escape = (escape velocity for parabola)
r
√ µ
v radial =
p e sin θ
√ µ
v normal = (1 + e cos θ)
√
p
( )
µ 1 + e
v p =
a 1 − e
v perigee (closest)
v apogee (furthest)
v a =
√ µ
= (1 + e)
p
√ ( 2
= µ − 1 r p a)
√
µ
a
( ) 1 − e
1 + e
√ µ
= (1 − e)
p
√ ( 2
= µ − 1 r a a)
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