Marooned1969

Watched it again in 2017 - decent, not perfect. I don't expect astronauts to go slowly bonkers like the "Buzz" Gene Hackman character without being brought down earlier. The space station resembled Skylab, without the solar panels. The usual minor plot and portrayal problems, like launching the crew on a Saturn V when a S1B would do, but that might make sense if the launch included both the station and the service/command module. The Caidin book was 1964, this movie was released in 1969 (and presumably written and planned earlier), and Skylab was launched in 1973, so getting the Skylab details were not available to inform the script.

The movie rescue was possible because the eye of a hurricane passed right over the cape; some claim that this was predictable. Even in 2017, hurricane tracks are not fully predictable. What I found unbelievable was that a mission launched an hour or two later would not be under the orbital plane of the space station; rendezvous would require enormous orbital delta V to "catch up quickly".

Perhaps because of this movie, while Skylab was in orbit, a rescue vehicle was ready; a second S1B with a modified 5-seat Apollo capsule. A trained crew of two astronauts was available to fly it.

Skylab launched into a 50 degree inclination orbit, close to the 51.6 degree inclination of ISS. The Russians would have had a decent chance of reaching it, once per day. Perhaps the possibility of a Russian visit (or rescue) influenced the high inclination choice. A 50 degree inclination permits imaging of the entire continental US, up to the southern tier of Canada.

Reentering on RCS

One claims the RCS system (even if fully fueled) was inadequate for reentry, compared to the thrust of the main engine. Both were hypergolic, the RCS system used MMH/N₂O₄, which has a vacuum ISP of 336 seconds, assume a thrust velocity of 3000 m/s. There were 4 quads, each providing 440N of thrust, for a combined thrust of 1760N. The CSM massed 5560 kg, so the acceleration would be about 0.3 m/s. Each RCS quad was equipped with primary and secondary tanks containing 51.8 kg of MMH fuel and 102.6 kg of NTO oxidizer per quad, assume 600 kg total fuel, for a total impulse of 1.8e6 kg-m/s.

How much thrust is needed to reenter? The movie showed a foolishly high orbit, up in the van Allen belt, but presume that is more photogenic, and the real orbit was like Skylab, with an apogee altitude of 442 km and a perigee altitude of 434 km. For simplicity, assume a 6371 km spherical Earth and a gravitational parameter of 398600 km³/s². Assume that reentry perigee altitude is 70 km. Computing the apogee velocities for the mission orbit and the reentry orbit:

Call that 120 m/s; since the apogee thrust is small, and the thrusters might overheat, presume this happens over two orbits, 200 second burns for each, a total of 5560 kg * 120 m/s or 0.66e6 kg-m/s. Less than 40% of the initial RCS fuel is required. So an RCS reentry is indeed possible, unless (as the film posits) that system is depleted.