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Old 07-20-2011, 11:24 PM   #7
teviet
 
Join Date: May 2005
Default Re: [Spaceships] Voyage Time Calculation with Different Drives

Hohmann transfer orbits aren't so bad (the formulae are all on Wikipedia, no need to reproduce them here), but unfortunately you're not in such a nice, simple case here. In this case the fusion rocket has more than enough Δv for a Hohmann transfer orbit, but not so much that you can ignore the Sun's gravity. So you'd want a constrained minimum-time orbit, not a minimum-energy orbit, which would be an exercise in numerical integration rather than simple formulae.

If you want to make sails more appealing than rockets, may I suggest putting the jump point very close to the star? If the escape speed is more than about 2.5 times the typical Δv of your rockets, then a sail is the only efficient way to get there (it gets more efficient as you get closer to the star).

TeV

EDIT: To clarify, the orbital speed at a distance D (in AU) from a star of mass M (in Solar masses) is:

v_orbital = 18.5mps x square_root( M / D )

The escape speed is 1.41 times higher, so the required Δv is 0.41 times this number, or:

Δv = 7.67mps x square_root( M / D )

If your rocket's Δv is less than this, you can't approach or escape the jump point.

But if your jump point is fixed, rather than orbiting, then a sail is pretty much useless to approach it, unless it has an acceleration greater than the star's gravity at its location.

TeV

Last edited by teviet; 07-21-2011 at 12:10 AM. Reason: Added formula and clarification.
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