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The vertical axis of this plot in this answer to How far apart are ISS launch windows? is labeled

OMS2 Phase Angle (deg)

and I don't know what that is. It's possible that OMS is related to things discussed in answers to What are “Ohms burns” in the context of Scott Kelly, KSP, and the Space Shuttle?. The answer says

You can see the windows were 10 minutes long...

and if the ISS moves 360 degrees in 90 minutes or 4 degrees per minute, that's consistent with the windows being about 40 degrees long somehow, but I don't really understand what that axis represents nor why it goes from -50 to 700 degrees.

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OMS2 is the burn of the Space Shuttles' Orbital Maneuvering System that circularizes the orbit after launch. After it the shuttle was in the same orbital plane as the ISS, but some distance behind. To catch up with the ISS, the orbit was slightly lower (~ 80 km) and therefore faster.

The OMS2 Phase Angle tells how far behind the shuttle was. In other words, how large the distance between ISS and Shuttle was when the Shuttle entered orbit. The distance is given as an angle, which is much more convenient to deal with in a circular orbit than an actual distance. Note that it can be larger than 360°, meaning that the Shuttle is more than one full orbit behind ISS. This leads to different flight times until docking as is marked by the lighter "FD3" and darker "FD4" colour. "FD" stands for Flight Day. If the distance is small, the docking can be done on the third day of flight, for large angles a rendezvous is only possible on day 4.

There is no relation between the phase angle and the 10 minute length of the launch window. "Catching up" with the ISS is not severely constrained, there are other parameters (crew sleep and day light) that have larger influences on the flight time. The window is just 10 minutes short, because of Earth rotation: The shuttle won't end up in the same orbital plane as the ISS if launch is delayed too much. Some discrepancy can be compensated for by altering the launch trajectory and steering slightly off-course. But there are limits due to additional fuel needed and the load on the external tank if the shuttle has to fly at an angle and not straight ahead.

The two constraints of phase angle and planar window are independent from each other and sometimes don't overlap. For example, there is no FD4 opportunity on Apr 26 and some launch windows are cut short because the phase angle would be too large (i.e. > 584°).

There's a very detailed description in this document, an example ISS rendezvous is described starting on page 225: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110023479.pdf

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  • $\begingroup$ @OrganicMarble I meant to refer to the 10 minute length. These are not (as suggested in the question) due to the phase angle, but only due to the planar constraints (page 226). The phase angle windows alone are up to 300° or 75 minutes. $\endgroup$
    – asdfex
    May 17, 2020 at 9:20
  • $\begingroup$ @OrganicMarble Sure, the overlap between both planar and phase constraints is not perfect. The FD4 window on Apr 26 is even cut to 0 minutes (not existing at all). In the case you mention, the phasing window opens up a lot earlier (not shown), but the planar window is not met. On the other hand, these two cut windows wouldn't be used at all, because with this lift off time you could do a FD3 rendezvous as well. $\endgroup$
    – asdfex
    May 17, 2020 at 12:16
  • $\begingroup$ Cleaning up comments. $\endgroup$
    – Organic Marble
    May 17, 2020 at 13:31

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