Question: if Dragon is about 200m lower than ISS, and they are moving at the same velocity at one instant, wouldn't that put them in different orbits?
Assuming ISS's orbit was perfectly circular, then Dragon would be moving too slow for its lower orbit, and would sink down, to its perihelion when on the opposite side of the earth, and so on, oscillating up and down, in an elliptical orbit with respect to ISS.
The only solution I see is for Dragon to artificially make its elliptical orbit circular by continuously thrusting upward. But I don't see this in the video stream. Have I got this all wrong?
EDIT s/too fast/too slow/ # and related edits, thanks mmaunder
I don't think 200m is enough to put them in significantly different orbits. Every once in awhile, dragon probably fires a thruster to make small adjustments.
edit, clarification: The problem is that the object closer to the earth will experience more gravitational force, which needs to be counteracted by orbiting faster, so that it's constantly falling 'tangent' to the earth. If they had the same angular velocity and the ISS was known to have a static distance from earth, Dragon would be slowly falling towards the earth because in order to maintain a static distance from earth, things above the ISS need to travel slower while things below need to travel faster.
At some point when they were a few meters away, the NASA video mentioned the Dragon was now "free floating". So, I think they were continuously gently firing the thrusters to maintain orbit until they got extremely close.
Think of energy. The higher orbit has higher energy with respect to the earth -- gravitational, and by virtue of comparing stable orbits, also kinetic. Dragon will "catch up" with the space station by converting some additional chemical energy (propellant) into kinetic energy, moving into and matching the station's orbit (and gaining the additional gravitational potential). (Or, given the small adjustment needed, perhaps mechanical energy, depending upon how the positional thrusters work -- compressed gas?)
Ugh, my physics classes are a long time away. Hope that's worded halfway comprehensibly.
Lower orbits have higher anglular velocity -- and it is angular velocity that dictates which craft gets ahead on orbit, because we're comparing angular position, not linear one.
For example, geostationary orbit (~36'000km radius) has period of 24h -- i.e., takes whole 24hours to cover all 360 degrees of rotation, having angular speed of 15deg/h, while Hubble's Space Telescope orbit (~560km radius) has period of 96minutes -- i.e., takes just over 1.5h to cover 360 degrees; with angular speed of 240deg/h.
Sure GEO has higher linear velocity and associated kinetic energy, but that's irrelevant.
I guess the Dragon was positioned under the Station so it gains the angular position slowly over time in a natural way.
Assuming ISS's orbit was perfectly circular, then Dragon would be moving too slow for its lower orbit, and would sink down, to its perihelion when on the opposite side of the earth, and so on, oscillating up and down, in an elliptical orbit with respect to ISS.
The only solution I see is for Dragon to artificially make its elliptical orbit circular by continuously thrusting upward. But I don't see this in the video stream. Have I got this all wrong?
EDIT s/too fast/too slow/ # and related edits, thanks mmaunder