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Orbit Inclination

Here is a question and answer from NASA’s “Ask Mission Control Center” segment which explains why 51.6° was chosen:
   
To: John Curry, flight director
Question: Why is the space station in a 51.6-degree inclined orbit instead of something less or something more?

Answer: The short answer is that 51.6 degrees is the lowest inclination orbit into which the Russians can directly launch their Soyuz and
Progress spacecraft. Both of these vehicles serve an important role in ISS operations.

The Soyuz – there is always one attached to ISS – serves as an escape vehicle in the event the ISS would need to be abandoned in an emergency. The Progress spacecraft is basically a cargo version of the Soyuz and is used to bring up fresh food and supplies to the ISS.

Ideally, one would want to launch due east from a launch site to maximize the cargo-to-orbit capability for a given launch vehicle. This is because the Earth, rotating from west to east, gives rockets a “free” head start in the right direction.

Launching due east from Kennedy Space Center would place the shuttle in a 28.5-degree inclination orbit. Notice that the inclination is the same as the latitude of KSC.

Launching due east from Russia’s main launch site, Baikonur, would place spacecraft in a 45.6-degree inclination orbit – the launch site latitude. However, doing so would also drop the lower stages of the boosters on China. To avoid this, the Russians crank up the minimum inclination to 51.6 degrees.

Although the shuttle does trade some payload capacity for propellant needed to make up the difference between launching at 28.5 degrees vs. 51.6 degrees, doing so allows the Russians to participate in the ISS program. It also has the added benefit to Earth Sciences since ISS flies over more of the Earth’s surface – about 75 percent, which covers about 95% of the inhabited lands – at the higher inclination orbit.