Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: chris on 08/06/2019 11:06:09
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I was asked on the radio this week "how much does the Earth weigh?"
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...
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Correct.
The square of the ratio of their radii is about 13, so the ratio of ge / gm would be around 600/7 x 13, say 6.5:1 in very round figures. If I recall from my childhood, we were taught the ratio to be about 6:1
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The moon is in free fall and is weightless.
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I was asked on the radio this week "how much does the Earth weigh?"
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...
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.
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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Thanks for your answers everyone.
The moon is in free fall and is weightless.
I did address that, in the second line of my post - "More accurately, we were of course discussing the mass of the Earth" and I didn't actually say anything about the weight of the moon, I asked about its mass.
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More accurately, we were of course discussing the mass of the Earth" and I didn't actually say anything about the weight of the moon, I asked about its mass.
OK, I guess we were going more on the topic title than that statement.
Most direct answer is that the moon masses about 7.35e25 grams. It is best worked out by observing the path of any object orbiting it and deducing the mass by plugging the acceleration into Newton's equation for gravitational acceleration g = GM/r², so M = gr²/G
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I didn't actually say anything about the weight of the moon, I asked about its mass.
Really.
Who wrote this then?
"How much does the moon weigh?"
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I remember it as "The Moon is about 1/80 the mass of the Earth."
According to Wikipedia:
- Mass of Earth: 6x1024 kg
- Mass of Moon: 7x1022 kg
- Earth:Moon mass = 86:1
- Maybe now I should remember a slightly different number!
As for the density of the Moon, Earth has a dense nickel/iron core
- Earth: 5.5 g/cm3
- Moon: 3.3 g/cm3
- The current popular theory is that the Moon was formed in a collision between the early Earth and a hypothetical Mars-sized planet called Theia
- This collision propelled a lot of (low density) crustal material into orbit, forming the Moon
- Earth was left with a bit of crustal material, and a large, dense iron core
I assume that this reduced coverage of crustal material allows the continents to float on the denser magma below, allowing continental drift to operate
- This avoids the thick crusts seen on Mars & Venus, and the volcanic hotspots seen there
- Continental drift allowed repeated reburial of carbon-containing minerals, preventing the CO2-dominated atmospheres of Mars and Venus.
See: https://en.wikipedia.org/wiki/Theia_(planet)
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It's vaguely interesting to know that the Earth is the densest of the planets. (Yay! we won!)
Saturn, on the other hand is less dense than water.
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I didn't actually say anything about the weight of the moon, I asked about its mass.
Really.
Who wrote this then?
"How much does the moon weigh?"
That was the title - it's what people ask meaning "mass", so I made it that to then address the issue in the post body, which I did...
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I watched a very interesting doco on space TV while I was recovering from my jetlag in Philadelphia last weekend. It highlighted that the "man in the moon" is a feature only of the Earth-facing side of the Moon. It is caused by vast lava lakes that squirted out and resurfaced large areas. The space-facing hemisphere, on the other hand, is a totally different structure, covered in impact craters and with no evidence of lava resurfacing. The theory advanced was that the young moon, much closer as it was to the Earth at the time, got its surface cooked by radiation from the molten Earth, which kept the crust thinner and more prone to rupture and lava release on the Earth-ward side.
I'd never really thought about it before...