I was asked on the radio this week "how much does the Earth weigh?"Assuming a constant density, Mass goes up by the cube of the radius, and since acceleration due to gravity decreases by the square the distance, surface gravity would increase at the same rate as the radius.
More accurately, we were of course discussing the mass of the Earth, and the answer, which I happened to know, is about 6 x 1024kg.
Later, driving to work, I began to think - as you do - what I would have said if the questioner had enquired instead about the mass of the Moon.
Naively, I reasoned that gravity is about 20% of that felt on the Earth's surface, so the Moon must have a mass 20% that of Earth.
Intrigued, I later looked it up. The stated mass of the Moon is about 7 x 1022kg. That's only about 1% of the mass of the Earth.
Is the acceleration due to gravity on the lunar surface as large as it is (almost 20% of the Earth's despite the lunar mass being only 1% of Earth mass) because the Moon is correspondingly smaller, so the inverse square law being what it is (GmM/r2) it works out that way?
Lazily, I've not done the maths to check...
The Moon's radius is 1738 km, ad the Earth's is 6378. 6378/1738 = ~3.7, so you might expect surface gravity on the Earth to be 3.7 times that of the Moon. However, the Moon is not as dense as the Earth, ( the Earth is roughly 1 2/3 times more dense. 3.7 * 5/3 = 6 The Moons surface gravity is roughly 1/6 that of the Earth's.
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