Quote:
Originally Posted by cvannrederode
Yup, this is the heart of the matter. As a somewhat avid player of Kerbal Space Program, I can say transfer orbits are very much beyond a simple spreadsheet.
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Well, a Hohmann transfer orbit between circular orbits (or orbits that are close enough to circular) isn't, and even the orbital insertion isn't too bad as long as you have a high thrust drive (there is some loss due to spiraling. This is mostly ignorable as long as drive thrust exceeds planetary gravity)
Orbital velocity is roughly 30 km/s * sqrt( 2/r - 1/a ), where r is your actual distance from the sun and a is your semi-major axis. The semi-major axis of a transfer orbit is equal to (r1+r2)/2. Thus, for an Earth to Mars, we get:
Earth orbital velocity: r = a = 1, v = 30 km/s
Mars orbital velocity: r = a = 1.52; v = 24.3 km/s
Transfer orbit at Earth: r = 1, a = 1.26, v = 33 km/s. Delta-V at Earth: 3 km/s
Transfer orbit at Mars: r = 1.52, a = 1.52, v = 21.7 km/s. Delta-V at Mars: 2.6 km/s.
Now, for the orbital insertion effect, the velocity required is sqrt( escape velocity ^ 2 + transfer velocity ^2 ) - current orbital velocity (if in orbit). Thus, Earth Surface->Mars Transfer requires total sqrt( 11.2^2 + 3^2 ) = 11.6 km/s, Earth Low Orbit requires 11.6-7.9 = 3.7 km/s. Earth Transfer->Mars Surface is sqrt( 5^2 + 2.6^2 ) = 5.6 km/s, Earth Transfer->Mars Low Orbit is 5.6 - 3.5 = 2.1 km/s.
The orbital period of your transfer orbit is SMA^3/2 or 1.41 years in this case, a transfer takes half a period. The interval between solutions is y1*y2 / abs(y1-y2) = 1.88/0.88 = 2.14 years. All of this can be done in a spreadsheet.