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We had this question which discussed if space craft had to be corrected in their orbits from the movements from the people inside. (No as their net movement cancels each force out)

Following on from that, the SpaceX Dragon capsule was detached last year and moved away from the ISS by a mechanical arm.

Did the course of the ISS have to be corrected to account for the force exerted on itself by the mechanical arm when pushing the SpaceX Dragon capsule away, and it's now reduced weight due to the loss of the capsule and the old equipment it took with it?

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The ISS orbital speed is 7.71 km/s or 27 756 km/hour.

I'm sure the best thrust it could give the Dragox-X with the robotic arm is an order of 20km/h and with Dragon-X weighing roughly 8 tons with the payload, and ISS weighing 450 ton, less than 2% of that speed has been transferred to the station. That means its speed changed by 0.2km/hour, which is 2/277000 or 0.0007% of its orbital speed.

I can assure you, 0.0007% speed change doesn't need to be compensated for. That's much less than what it loses daily to atmospheric friction.

OTOH, if the thrust was applied off-center, it could have made ISS to spin (slowly, albeit it would bring the solar panels out of optimal alignment eventually), and that would need to be compensated for.

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    $\begingroup$ @RhysW: Wikipedia: Dry mass 4,200 kg plus payload to ISS 3,310 kg - I guess it's not flying back home empty. OTOH most of its fuel is depleted, so if anything, I overestimate the weight (and its impact) rather than underestimate. $\endgroup$
    – SF.
    Jul 24, 2013 at 12:46
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    $\begingroup$ It might help if you calculated the amount the orbit of the ISS would drop (or raise) from letting go of the Dragon. Just a suggestion. $\endgroup$
    – PearsonArtPhoto ♦
    Jul 24, 2013 at 13:50
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    $\begingroup$ This is a really... cavalier treatment of the underlying physics. While your conclusion is certainly correct (the qualitative result, not the numbers), the assumptions and methods are very questionable, IMHO. $\endgroup$
    – user29
    Jul 24, 2013 at 22:46
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    $\begingroup$ @SF. My problem is not with the precision, but the assumptions you make and the way you set up the calculations. For instance, the arm/Dragon combo isn't providing thrust at all, it's essentially just moving the whole system's center of mass. $\endgroup$
    – user29
    Jul 24, 2013 at 23:48
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    $\begingroup$ @Chris: In that case the change of the orbit - by a meter or so - compared to 2km/month orbital decay, is completely insignificant. I picked about the most pessimistic scenario. $\endgroup$
    – SF.
    Jul 25, 2013 at 5:29

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