|
For hyperbolic orbits, we proceed as follows:
B = cosh uJ = (1/e) (1 + rJ /a)
uJ’ = ln [ B + (B^2 - 1)^0.5 ] = arc-cosh(B)
(Depending on whether your calculator has an arc-cosh button on it.)
If sin QJ < 0 then uJ = -uJ’ else uJ = uJ’
MJ = e sinh uJ - uJ
For elliptical orbits, we proceed as follows:
sin uJ = (rJ /a) sin QJ / (1-e^2)^0.5
cos uJ = e + (rJ /a) cos QJ
uJ = arctan2(sin uJ , cos uJ)
MJ = uJ - e sin uJ
The proposed hyperbolic transfer orbit.
e = 6.33678
a = 0.1883722 AU
r1 = 2.179749 AU
Q1 = 5.098051 radians
u1' = 1.307609 radians
sin Q1 is negative.
u1 = -1.307609 radians
M1 = -9.550008 radians
The proposed elliptical transfer orbit.
e = 0.6519092
a = 1.319533
r2 = 1.005301
Q2 = 4.327089 radians
sin u2 = -0.9310417
cos u2 = +0.3655728
u2 = 5.086543 radians
M2 = 5.693351 radians
Jerry Abbott
|