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Orbiting is based on the principle of a "free fall" which means a vessel is traveling so fast it effectively falls "over" the horizon. Earth's gravity being 9.8m/s^2 is the way they determined just how fast a vessel would have to be to "orbit" Earth.
Now did someone send a "cavendish" device to the moon? And a scientist check its results after a year? If not, how did we know the density of the moon to be able to create a "command module" that is capable of reaching exactly the right speed to orbit the moon?
I think you are underestimating my perception of the principles of orbit. Maybe it's easier to paint me with the idiot brush but you can't say I'm wholly ignorant of the concepts.
No, there is no need (or point) to having "someone send a "cavendish" device to the moon" and it's hardly a "device" that you could use that way.
I most certainly won't "paint me with the idiot brush" for asking how strong gravitation on the moon was measured. It is also something I did not know until I tried to chase it up just now. It is something that astronomers spent quite a lot of time on after Newton.
The distance and diameter were easy to measure by astronomical means, and reasonably accurate values have been known for a very long time and the mass of planets with their own satellites is easy to determine from the orbital periods of these satellites. Those without satellites can be estimated by their effects on the orbits of other planets.
In the case of the moon, trying to estimate the mass simply by comparing its volume to that of the earth gives mass that is far too high, as the moon's average density (3,340 kg/m
3) is much less than that of the earth (5,514 kg/m
3).
Newton tried to estimate the moon's mass from relative tidal effects of the sun and the moon - and botched it up because of the complications of tidal flow in the estuary he was working from - yes, Newton made "mistakes" too.
Quite a number of method's were used by Laplace, Airy and others to home in on a more accurate figure. A description of all methods used is much more than I could tackle here and I'd probably get it wrong! Even events like the approach of the near earth asteroid Eros can give useful data.
These astronomers would not have been satisfied until they got results from the various methods that were in good agreement.
Summarising, it's not easy, but a good value of the mass and hence the moon's gravity was available long before any space missions were contemplated.
Of course, there were many moon missions, from simply crashing into the moon to orbiting the moon, well before any manned missions were contemplated. These enabled a refinement of the value.