(Bertil Jonell) writes:

There has been a lot of work done on Hohman and Bielliptic transfers,
but has there been anything on constant-thrust transfersp? Of course, the
"optimum" in this case won't be lowest deltaV, but shortest time for a
given acceleration?

If you are talking about a transfer between two coplanar, circular orbits,
the optimum trajectory as acceleration asymptotes to zero is a constant
spiral under circumferential thrust, the delta-V requirement turns out
to be the difference between the circular orbit velocities of the initial
and destination orbits, and the time is whatever time is required to
deliver that delta-V with your (very small) acceleration.

For non-coplanar but still circular orbits, something called Edelbaum's
Approximation applies, and the delta-V becomes

DV = ( Vo^2 + Vf^2 - 2 Vo Vf cos (pi/2 Di) )^0.5

Vo = circular velocity of initial orbit
Vf = circular velocity of final orbit
Di = inclination change
pi = 3.14159...

These approximations are good enough for all but the most detailed
level of mission planning, so long as your maximum acceleration is
less than one hundredth or so the local acceleration due to gravity.

If either the initial or the destination orbit is noncircular, or if
third-body effects are involved, the situation gets rather complex
and is not amenable to analytic solution.


Does anyone have any pointers to online papers?

None that I know of. Most of the original work was done in the '60s,
and so mostly isn't available online. Most of what work has been
done recently, is either in-depth analysis of convoluted special
cases that assumes you've read all the papers from the '60s, or is
the internal, very proprietary work of comsat operators who have
started doing low-thrust partial orbit transfers using the ion or
plasma thrusters their birds now carry for stationkeeping purposes.


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