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how much mass does the moon have?

how much mass does the earth have?

how much force needed to leave earth

how much force needed to leave the moon

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  • $\begingroup$ "Easier" is ambiguous. It takes less fuel to take off from the moon, but getting the rocket and the fuel to the moon is much harder than launching a rocket from earth. $\endgroup$ – MaxW May 12 '20 at 6:56
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    $\begingroup$ Is this a homework question? What have you tried? $\endgroup$ – gerrit May 12 '20 at 8:25
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    $\begingroup$ I’m voting to close this question because even if we technically accept homework questions, this one is too basic and shows no effort. $\endgroup$ – Carl Witthoft May 12 '20 at 13:13
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The moon has about 7 x 10^22 kg of mass. The earth has about 6 x 10^24 kg of mass. So the Earth masses about 10^2 (aka 100) times more than the moon.

To stay in orbit around the Earth, you've got to go faster than about 7800 meters per second sideways. To stay in orbit around the moon, you've got to go faster than about 1650 meters per second sideways.

So you've got to go a lot faster to orbit the Earth than the moon. But there's more than that: you can just start going sideways on the moon and get in orbit. As long as you don't smack into any mountains, you'll be fine. (Mostly, see the note below)

If you try to do that on the earth, you will burn up. Why? 7800 meters every second is very fast, and if you are in the air, you will squeeze the air a lot. When this happens, it gets very hot, and it burns you up. So you have to go up first, and then go sideways really fast only once you get above the atmosphere (which is about 150 km up). So you have to spend a lot more energy fighting gravity and going up and then a LOT more energy going sideways.

It's easier to take off from the moon because the moon is less massive and has no air.

Note: The moon is pretty lumpy, which means its gravity is pretty lumpy because the lumps (like mountains) pull you sideways when you pass them. So you won't actually stay in orbit very long unless you're in a very specific orbit, where the sideways pulls of the lumps cancel each other out. This is called a frozen orbit. Earth has the same problem, but the Earth is a lot larger than its lumps than the moon is, so it's not as big of an issue.

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To answer your question it is neccessary to compare the escape velocities of the Moon and the Earth.

The escape velocity does not depend on the mass $M$ of the celestial body alone, it also depend on its radius $r$.

$ v_2 = \sqrt{\frac{2GM}{r}} $

$G$ is the gravitational constant.

The escape velocity $v_2$ is 11.2 km/s for the Earth and only 2.3 km/s for the Moon. So it is much easier to leave the Moon than the Earth.

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  • $\begingroup$ Just to clarify that a bit, it's because the escape velocity varies depending on how far you are from the thing from which you're escaping. If you're very far away from it, your escape velocity can be very slow. If you're very close, it's much higher. That equation holds true even if you use an r that is not the radius of the body. But you can't get closer to the center than the surface, and you generally start from the surface (not always). So putting in r that is equal to the radius of the body is giving you the value of "escape velocity from the surface". $\endgroup$ – Anton Hengst May 11 '20 at 20:03

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