THE MATHEMATICAL ASPECTS OF A LUNAR SHUTTLE LANDING

As the lunar shuttle with its load of tourists began its descent from orbit for a landing at Tranquility Base, an old, familiar sight appeared to the shuttle pilots— “earthrise.” Just as it had appeared for the first time to the astronauts aboard Apollo 8 in December of 1968 so many years ago, it now appeared for the first time to many of the tourists. There were the usual oohs and aahs as they tried to comprehend what they were seeing. The spell was broken by the pilot's announcement that they would be landing in a few minutes and that passengers should fasten their seat belts for safety. Just as the computer readout showed “ALT. 500 ft, SPEED 50 fps, REMAINING FUEL 100 units,” the automatic landing system failed. The pilot disengaged the disabled system and took manual control. The amount of fuel to be burned each second must now be entered manually in order to bring the shuttle in for a safe landing. A maximum of ten units may be burned each second, and three units per second are needed to offset acceleration due to the lunar gravity. If x units per second are burned, there is a decrease in velocity v of x − 3 feet per second (fps).