[TriLUG] OT: how to dock a spacecraft?

[David Both]

You cannot catch up in an orbit of the same height. As long as the orbits are in 
the same plane and assuming at the same altitude, the only way to do this is to 
fire the thrusters in the retro direction, to drop the chasing craft into a 
lower orbit. Lower orbits have shorter distance to go as they are closer to 
earth and must go faster (angular velocity from center of earth orbit) in order 
to stay in orbit because Earth's gravity is stronger (or you are deeper in the 
gravity well in Einsteinian physics) so in a lower orbit you catch up. Once you 
are within a decent range where orbital mechanics are less relevant than simple 
positional translation, you fire the thrusters in the forward direction in order 
to raise your orbit and become fairly stationary with the target. Then you can 
use translational thrusters to maneuver into a dock.

Very simplified, but I hope it helps.


On 06/24/2012 10:36 AM, Joseph Mack NA3T wrote:
> With the docking of the Chinese spacecraft, I realise once again that I don't 
> know how you do it.
>
> Defining the situation: you have the target and the capsule. Both are in 
> circular orbit and the capsule is just (say 100m) behind the target, so that 
> the line joining the two craft can be considered tangential to the orbit. The 
> capsule can fire thrusters tangentially (ie in the direction towards or away 
> from the target) or radially (towards or away from the earth). Let the 
> thruster impulses be of short duration.
>
> Define above and below the target to be with respect to the earth. Thus if 
> you're in a lower orbit, and you are close to the target, then the target is 
> above you and you're looking at the underneath of the target.
>
> Some basics (which may or may not be right):
>
> o tangential impulse:
>
> (I'm pretty happy with this part)
>
> if you're in circular orbit 100m behind the target, and you fire your 
> thrusters tangentially, thus increasing your speed (velocity?), your orbit 
> becomes elliptical. The ellipse is tangential to the original circular orbit 
> at the point when you fired the thrusters. The point at which you fired the 
> thrusters becomes the perigee of the elliptical orbit. 90deg around the orbit, 
> you reach your new apogee. To circularise your orbit, you fire your thrusters 
> again (tangentially?). If you don't fire your thrusters at apogee, you would 
> continue in the elliptical orbit returning to perigee at 180deg around the 
> orbit, when you would be 100m behind the target again.
>
> If you were on a flat surface on earth, to dock with a target, you would fire 
> your thrusters in the line joining you to the target. However in orbit, if 
> you're trying to dock with the target, firing your thrusters in a line with 
> the target (ie tangentially) will move you up or down (wrt earth, ie radially) 
> but not bring you closer (tangentially) to the target. Thus you can't use your 
> earthbound experience in driving cars or catching balls to dock in space.
>
> o radial impulse:
>
> (I have no clue here)
>
> If you're in circular orbit behind the target and you fire your thrusters 
> radially, you'll now have radial velocity and you'll execute SHM above and 
> below the original circular orbit.  Your orbit will now be elliptical with 
> apogee below the circular orbit and perigee above the circular orbit. Your 
> elliptical orbit will cross the circular orbit at 45, 135, 225 and 315deg 
> around the orbit from the point when you fired your thrusters. I expect you'll 
> be 100m behind the target each time you cross the circular orbit.
>
> Thus firing your thrusters tangentially doesn't bring you closer to the target 
> either.
>
> Not knowing if any of this is correct, I'm pretty much stuck. However I'll 
> press on regardless with a WAG.
>
> To catch up to the target, you drop to a slightly lower circular orbit (not 
> sure how you do this, but probably firing the thrusters tangentially). This 
> increases your speed and you pass underneath the target getting ahead of it by 
> the same amount that you were behind. You then move back to your original 
> circular orbit, when you will be in the same position at the target.
>
> If this is correct, then as you dock with the target, instead of approaching 
> it from behind, you will approach it from below.
>
> Anyone know what really happens?
>
> thanks Joe
>



-- 


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