Mathematics of Space Rendezvous ~ 1994 NASA STS-84 "Liftoff to Learning" (JSC-1801)

more at http://quickfound.net/

MATHEMATICS OF SPACE - RENDEZVOUS (LIFTOFF TO LEARNING SERIES)

'Educational video on the mathematics used for spacecraft rendezvous, intended for middle school grade level audiences. STS-84 crewmembers Precourt, Collins, Lu, Clervoy, Kondakova and Noriega present orbital mechanics math problems associated with a Shuttle rendezvous with Mir Space Station.'

Originally a public domain film from NASA, slightly cropped to remove uneven edges, with the aspect ratio corrected, and one-pass brightness-contrast-color correction & mild video noise reduction applied.

The soundtrack was also processed with volume normalization, noise reduction, clipping reduction, and/or equalization (the resulting sound, though not perfect, is far less noisy than the original).

https://en.wikipedia.org/wiki/Space_rendezvous

Wikipedia license: http://creativecommons.org/licenses/by-sa/3.0/

A space rendezvous is an orbital maneuver during which two spacecraft, one of which is often a space station, arrive at the same orbit and approach to a very close distance (e.g. within visual contact). Rendezvous requires a precise match of the orbital velocities and position vectors of the two spacecraft, allowing them to remain at a constant distance through orbital station-keeping. Rendezvous may or may not be followed by docking or berthing, procedures which bring the spacecraft into physical contact and create a link between them.

The same rendezvous technique can be used for spacecraft "landing" on natural objects with a weak gravitational field, e.g. landing on one of the Martian moons would require the same matching of orbital velocities, followed by a "descent" that shares some similarities with docking...

To properly understand spacecraft rendezvous it is essential to understand the relation between spacecraft velocity and orbit. A spacecraft in a certain orbit cannot arbitrarily alter its velocity. Each orbit correlates to a certain orbital velocity. If the spacecraft fires thrusters and increases (or decreases) its velocity it will obtain a different orbit, one that correlates to the higher (or lower) velocity. For circular orbits, higher orbits have a lower orbital velocity. Lower orbits have a higher orbital velocity.

For orbital rendezvous to occur, both spacecraft must be in the same orbital plane, and the phase of the orbit (the position of the spacecraft in the orbit) must be matched. The "chaser" is placed in a slightly lower orbit than the target. The lower the orbit, the higher the orbital velocity. The difference in orbital velocities of chaser and target is therefore such that the chaser is faster than the target, and catches up with it.

Once the two spacecraft are sufficiently close, the chaser's orbit is synchronized with the target's orbit. That is, the chaser will be accelerated. This increase in velocity carries the chaser to a higher orbit. The increase in velocity is chosen such that the chaser approximately assumes the orbit of the target. Stepwise, the chaser closes in on the target, until proximity operations (see below) can be started. In the very final phase, the closure rate is reduced by use of the active vehicle's reaction control system. Docking typically occurs at a rate of 0.1 ft/s (0.030 m/s) to 0.2 ft/s (0.061 m/s)...