Is the shuttle ahead of the ISS in the orbit before docking.
Does the international space station catchup with the shuttle in the same orbit?
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Directions: The ISS is in a nearly circular orbit. The "v-bar" axis is oriented along the ISS's velocity vector, with +vbar being along the velocity vector and -vbar against it. The r-bar axis is oriented radially, with +rbar pointing toward the center of the Earth and -rbar pointing out into space.
The Shuttle docked with a specialized component on the ISS, Pressurized Mating Adapter 2 (PMA-2). The location of PMA-2 on the ISS bass changed a number of times. On the first five missions, PMA-2 was oriented upward, which meant docking on the -rbar. On the next two, PMA-2 was oriented downward, which meant docking on the +rbar. After that, PMA-2 has been oriented forward, which meant docking on the +vbar. In all cases, final approach was very slow. It took forty minutes for the Shuttle to go the last 320 feet With those vbar rendezvous.
Getting to that final approach was tricky. It's not like the movies. Rendezvous is a long process. The Shuttle approached the Station from behind, in a slightly lower orbit than the ISS. The rendezvous timeline started almost six hours prior to docking. The action started about two and half hours prior to the Ti burn. At this point, the Shuttle performed a height adjustment burn that made the Shuttle's apogee equal to the ISS' orbital altitude. Half an orbit later, at apogee, the Shuttle performed it's last phasing burn. This made the Shuttle's perigee about 40,000 feet lower than apogee. An orbit later (three hour prior to docking), the Shuttle performed the Ti (transition initiation) burn. This burn raised perigee to about 10,000 feet below apogee. The Ti burn started the final hop to the Station.
About 4/5 the way into this hop is when the crew took over. At this point, the Shuttle was about 600 feet below the ISS. The Shuttle began flying the Twice Orbital Rate V-Bar Approach (TORVA) to slowly bring the Shuttle up to the vbar and in front of the ISS. Once on the vbar, the Shuttle slowly worked its way toward the docking port, docking about forty minutes after arriving on the +vbar.
STS 135 Flight Data File / Rendezvous.
Pages 1-5 to 1-8 have nice diagrams of the rendezvous and docking. All Shuttle flights to the ISS that docked on the vbar followed very similar profiles.
History of Space Shuttle Rendezvous.
In addition to covering all Shuttle missions that involved rendezvous, this document contain a 50 page summary of pre-Shuttle rendezvous operations.