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18 Astrodynamics<br />
18.1 Ellipse main parameters<br />
18.2 Table of common equations<br />
The following table contains the common relations to use for elliptic motion. Equation of ellipse is x2<br />
a 2 + y2<br />
b 2 = 1<br />
term to find<br />
conversion between E and θ<br />
position of satellite at time t<br />
Solve for E, then find θ. τ<br />
here is time at perigee and n<br />
is mean satellite speed.<br />
eccentricity e<br />
relation<br />
( θ<br />
tan =<br />
2)<br />
√ ( )<br />
1 + e E<br />
1 − e tan 2<br />
cos E = e + cos θ<br />
1 + e cos θ<br />
cos θ = e − cos E<br />
e cos E − 1<br />
E − e sin E = n (t − τ)<br />
√<br />
e = c a = ra−rp<br />
r a+r p<br />
= 1 + 2Eh2<br />
µ 2<br />
65
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