Sunday 8 September 2019

newtonian gravity - Why does the moon stay with the Earth?


Naturally, I know it to be true that the moon goes around the Earth and that the Earth goes around the sun.


However, attempting to picture this has confused me a bit. Why doesn't the moon just get left behind?


I'll draw a diagram to show what I'm imagining:


Image of Sun, Earth & Moon


What I'd expect to happen after this image is the Earth to move along v, while having it's direction of motion changed due to the gravitational force with the sun, and the moon to move along v, while having it's direction of motion changed due to the gravitational force with the Earth.


My slight issue and where I think I might be missing something, is why doesn't the Earth's speed just mean it can just fly away from the moon and just leave it flying in it's tangential velocity?


I know I'm missing something here, so if anyone could point that out, it'd be greatly appreciated! Sorry if it seems obvious!



I've thought along the lines that the moon might also be following the Earth's orbit of the sun but the law of universal gravitation would, as far as I know, stop that being true since it's of a differing mass.


Edit: Alternatively, why doesn't the Earth just smash into the moon?



Answer




is why doesn't the Earth's speed just mean it can just fly away from the moon



The moon and the Earth fall towards each other due to their mutual gravitation. The Earth doesn't have enough speed, relative to the Moon, to 'just fly away'. Equivalently, the Moon doesn't have enough speed, relative to the Earth to 'just fly away'.


Here's an image I found from Britannica:


enter image description here


So, as you can see, the speed of the Moon around the Sun is, on average, the same as the speed of the Earth around the Sun though there is a periodic variation.




Alternatively, why doesn't the Earth just smash into the moon?



Why do you think it should? The Moon is in orbit around the Earth just as the ISS and satellites are in orbit around the Earth. Are you asking why orbits exist at all?


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