[TriLUG] OT: how to dock a spacecraft?

[Joseph Mack NA3T]

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

-- 
Joseph Mack NA3T EME(B,D), FM05lw North Carolina
jmack (at) wm7d (dot) net - azimuthal equidistant map
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