Re: orbit phasing

"Ben Crowell" <crowell08@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote in message news:48532074$0$7070$4c368faf@xxxxxxxxxxxxxxxxx
I'm planning a story that involves a crewed spacecraft starting out
at one of Titan's Trojan points, and getting to Titan with a
minimum of delta-v. Websurfing has revealed that this kind of maneuver
is called "orbit phasing," and that it's a common thing to need to do
when spacecraft dock. What I haven't had any luck finding is any info
on the theory behind it. Seems to me that the most straightforward
technique would be to do a burn to go into an elliptical orbit tangent
to the original circle, complete n orbits, and then do another burn to
get back into the original circular orbit, with a different phase. You
can do any phase change with an arbitrarily small amount of delta-v,
but it might require a large n, which would be extremely time-consuming.
(Titan's orbit has a period of 16 days.) Is there some better way of
doing orbit phasing that doesn't have such a harsh tradeoff of time
versus delta-v? Does anyone know of any books that discuss this kind
of thing? I suspect that for applications like docking with the ISS,
you typically only need very small phase changes (since you can plan
the launch window so as to put you pretty darn close), whereas my story
requires a large phase change of 60 degrees.

Your restrictions pretty much apply if you don't want to burn huge amounts of fuel.

Both orbits start out with period P of 16 days. If you change your period by a small amount x day, it will take about (1/6) P/x days to reach Titan's orbital position. You then need a similar burn to match period and hence velocity with Titan. Titan has an atmosphere, so you could (if your ship's design allows it) use aerobraking, hence reduce fuel requirements as you could kill the relative speed in the atmosphere. You didn't say whether you wanted to go into orbit around Titan or actually land there.

Approximate with the circular orbit assumption. Titan's orbital speed is 2 pi x 1.22 x10^6 / (16 x 86400) km/s or 5.55 km/s, so e.g. a 1/16 change in orbital speed (P change is about x=1 day) is only about 350 m/s. That will get you there in about 2.5 to 3 days, with a second burn of the same amount to match speeds, but you may want to go into orbit instead. To halve that time, double the amount of delta-V.

All in all, the changes involved in the leisurely rendezvous are about the same as the delta-v changes for a lunar lander launching to join up with an orbiting command module.

Of course everything above will be in elliptical orbits and detailed calculations will need to be done, but the order of magnitude of the speed/delta-v relationship is about right, I think.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

.

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