Phobos said:
Explain how the "moon's free fall" was measured during the Apollo missions.
As noted earlier, the difference in gravitational attraction between a planetary body and small masses like a baseball vs. a bowling ball is negligible for the purposes at hand.
When you see the footage of the astronauts, it's obvious when they
jumped up, it took longer for them to land than if they made the
same jump on Earth. Their steps were more like leaps. This longer "landing"
time on the moon equates to a large difference in the "free-fall" rates
between the moon and the Earth
toward the astronaut . That is,
if we focused on the Astronaut instead of the planetary masses as the cause of the g (neglecting the G caused by the planetary masses on the Astronaut as we neglect the G nowadays of the smaller mass in "regular" free-fall experiments) we would obtain a "free-fall" rate that is dramatically different
for different masses (Earth having a much greater "free-fall" rate toward
the astronaut than the Moon).
Maybe the above would be clearer if we spoke in terms of two different spheres being "dropped". In Galileo's experiment, one sphere, a baseball
is dropped from a height on Earth, then another sphere, a bowling ball
is dropped from the same height. The "identical" rate is used as experimental
support for the claim of Universality of Free Fall. If we focused on the baseball instead and compared the "free-fall" rate of the Earth to the baseball
with the "free-fall" rate of the Moon to the baseball (first dropping the baseball on the Earth from a height and then going to the moon and dropping
it from the same height), we see that the Universality of Free Fall claim doesn't hold water.
The former is like trying to find the differences in the dispacement of the
water level of the Pacific Ocean between one and two drops of water falling on it, then finding none, concluding that all masses cause the same displacement on a body of water, while the latter is like comparing the differences in water level by filling the Grand Canyon with all the water in the Red Sea, draining it and then filling it again with all the water in the Yellow River and noting that since the larger mass of water filled a larger volume
of the Grand Canyon, differences in mass must cause a difference in displacemnt on a body of water. Now, which experiment do you think is more instructive?