How do the sun, earth, and moon move?

     
Everyone knows the moon orbits the Earth and that the Earth orbits the Sun. But what about the path of the moon around the Sun? What does that look like? I will go ahead & state that this is a difficult thing lớn show. Why? Scale, that’s why. Let me give some values for the <…>

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Everyone knows the moon orbits the Earth and that the Earth orbits the Sun. But what about the path of the moon around the Sun? What does that look like? I will go ahead & state that this is a difficult thing khổng lồ show. Why? Scale, that's why. Let me give some values for the sizes of these things, then I will make some sort of diagram.

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Radius of the Sun: 6.95 x 108 m.Radius of the Earth: 6.38 x 106 m.Orbital radius of the Earth around the Sun: 1.5 x 1011 m.Radius of the moon: 1.7 x 106 m.Orbital radius of the Moon around the Earth: 3.48 x 108 m.

Here is one attempt at drawing these three objects.


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Image from Vpython
The objects all have the correct scale - but the Sun is in the wrong place (hopefully, this is obvious). The Earth and moon are the correct distance apart relative lớn their size. What about the Sun? In this diagram, the Earth & moon are about 11 centimet apart (at least on my monitor). If you could see the whole Sun, it would be about 40 cm across. Where would the Sun be? You if you had a cut out of Sun, that piece of paper would have to lớn be 43 meters off to the side. Yup. I said 43 meters. The sun is pretty far away.


And this is the problem. How do you show the orbit of the Earth and moon around the Sun? You really can't, at least not khổng lồ scale. Most textbooks kết thúc up making a plot where nothing is lớn scale. Here is something you might see.


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Image from Vpython
It sort of works, right? It shows that the Earth orbits the Sun and the moon orbits the Earth. But what would it look lượt thích to scale? I am not sure what the best way lớn show this will be. Let me first assume perfectly circular orbits for both the moon and the Earth. I'm not going to lớn show the Sun - here is just a part of their path.

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This just shows half a month. If I wanted lớn show a longer time period, the motion of the Earth & moon around the Sun would make it super-difficult to see the motion of the moon relative to the Earth.

Maybe it will help if I plot the distance from the Sun for both the Earth & the moon. Here is that plot over about 1 month.

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You might notice that the distance from the Earth to lớn the Sun changes. I put in an initial velocity to lớn give the Earth a circular orbit. However, I also included the gravitational force on the Earth from the moon. This causes a bit of a wobble (but it isn't really important for this discussion).

The real question that I want khổng lồ look at is: does the moon orbit the Earth more or the Sun more? Which is more important? Let me try another plot. Here is the radial component of the acceleration of the moon over one month. Remember, from my last moon post we can break the forces (and thus the acceleration) into two types. There is a radial component that changes the direction of the momentum và a parallel component that changes the magnitude of the momentum. So, this is just the magnitude of the radial component.

Xem thêm: Xem Phim Mười Lăm Năm Chờ Đợi Di Trú, Xem Phim Mười Lăm Năm Chờ Đợi Chim Di Trú

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But what does this even mean? Well, this says that no matter where the moon is in relationship lớn the Earth it has a radial acceleration in the direction of the Sun. It does not accelerate away from the Sun. If it did, it would have a negative radial acceleration component. Why does this look so similar to the radial position plot? Think of this. When the moon is on the far side of the Earth (so farther away from the Sun than the Earth is), it has both the Earth và the Sun pulling it towards the Sun. With this greater force comes a greater acceleration & it is further away from the Sun. So, the plots look similar but they are not the same.