One of the critical principles I swore to instill concerns the power of abstraction and how to use it. The idea that one can make a simplified model of a more complicated system in order to illuminate fundamental properties and behaviors is central to the understanding of science and science history, and central to using those models to make useful predictions. I think most people eventually got that part. The real challenge, though, was teaching someone what sorts of things they needed to worry about in making their abstractions, what they could ignore, and how to tell the difference between the two.
So yes, simplifying assumptions are critical to solving complex problems, but if you simplify too much, you are solving a problem that no longer really helps you understand what is happening in the real world. So in teaching those intro Physics classes, I took extensive steps to be sure that the students understood what types of things we ignored when discussing topics such as Newton's laws, and we discussed at length why their lab experiments didn't quite come out as the simplified equations would have predicted. We would even work to improve experiments with things like vacuum chambers and lubricants to reduce troublesome complications like friction specifically so they could understand the abstract mathematical descriptions and where they broke down. Despite the fact that these same principles apply across any human endeavor even outside of science from relationship management to business strategy, students would often ask, "so what does this have to do with my life?"
Well today, with all the current hoopla around returning to the Moon and then heading on to Mars, NASA resurrected some old data that highlighted a catastrophic assumption they had made on prior Lunar missions, so that hopefully, we can re approach the Moon with improved confidence.
You see, back in 1972 during the Apollo 16 mission, the Astronauts launched a small satellite called PSF-2 into a low Lunar orbit (only about 60 km above the Moon's surface) in order to continue extended observations even as the manned mission returned to Earth.
To make a rather longer story short, the satellite ended up crashing into the moon despite the fact that there was no atmosphere to induce drag that would have eroded the orbit. So what happened?
It turns out that the scientists of the seventies had made a catastrophic assumption that tremendously simplified the orbital path planning calculations to get the spacecraft to the Moon and back. And as long as the command module was in a short-term lunar orbit and cruising all the way from Earth and back (a trip mostly far away from planetary or Lunar mass), there was no noticeable deviation from the planned paths that would indicate any problem with the simplified models. Everything was fine.
But when the tiny satellite was left in a long-term orbit close to the surface of the moon, its actual flight path began to deviate quite substantially from what the simplified model had foretold. Eventually it crashed into the Lunar surface. So, what was the simplification? What happened?
The problem was that the scientists of the day had assumed that the density of the entire Moon was roughly uniform. In retrospect, anyone who has dug a hole would know that earth is composed of loose material, water, pebbles, all of varying density, and it wouldn't we all that much of a stretch to realize that those inhomogeneities might extend to larger scales. But in truth, those deviations from the average density had never been an issue before, because in interplanetary (or earth-to-moon) travel, the distances from the planets were typically large enough, and the durations of orbits short enough, that the simplified models proved quite accurate for those purposes.
It wasn't until a new experiment that "looked" much more closely at the Moon for a longer period was conducted that we discovered that the heretofore ignored "higher-order" effects were indeed relevant. We now know that the Moon is quite lumpy.
"The Moon is extraordinarily lumpy, gravitationally speaking," Konopliv continues. "I don't mean mountains or physical topography. I mean in mass. What appear to be flat seas of lunar lava have huge positive gravitational anomalies—that is, their mass and thus their gravitational fields are significantly stronger than the rest of the lunar crust." Known as mass concentrations or "mascons," there are five big ones on the front side of the Moon facing Earth, all in lunar maria (Latin for "seas") and visible in binoculars from Earth.
The mascons' gravitational anomaly is so great—half a percent—that it actually would be measurable to astronauts on the lunar surface. "If you were standing at the edge of one of the maria, a plumb bob would hang about a third of a degree off vertical, pointing toward the mascon," Konopliv says. Moreover, an astronaut in full spacesuit and life-support gear whose lunar weight was exactly 50 pounds at the edge of the mascon would weigh 50 pounds and 4 ounces when standing in the mascon's center.
Above: Mascons on the Moon that make its gravitational field so lumpy, as mapped by the Lunar Prospector mission, are shown in orange-red. The five largest all correspond to the largest lava-filled craters or lunar "seas" visible in binoculars on the near side of the Moon: Mare Imbrium, Mare Serenitatus, Mare Crisium, Mare Humorum and Mare Nectaris. Image reference: Konopliv et al, Icarus 150, 1–18 (2001).
"Lunar mascons make most low lunar orbits unstable," says Konopliv. As a satellite passes 50 or 60 miles overhead, the mascons pull it forward, back, left, right, or down, the exact direction and magnitude of the tugging depends on the satellite's trajectory. Absent any periodic boosts from onboard rockets to correct the orbit, most satellites released into low lunar orbits (under about 60 miles or 100 km) will eventually crash into the Moon. PFS-2 released by Apollo 16 was simply a dramatic worst-case example. But even its longer-lived predecessor PFS-1 (released by Apollo 15) literally bit the dust in January 1973 after less than a year and a half.
Original Post at NASA's Bizarre Lunar Orbits.