# B Why doesn't the Moon get pulled into the Earth?

1. May 16, 2016

### cjp613

When the the Earth is between the Sun and Moon do the gravitational effects of the Earth and Sun combine to create a stronger pull on the Moon? If so, wouldn't this increased pull draw the Moon closer and closer to the Earth over time? I've looked for an answer to this, but haven't had any luck. I'd really appreciate if someone could explain how this works. Thanks.

2. May 16, 2016

### Staff: Mentor

Sure, but Earth is also pulled in the same direction by the sun.
That's not how orbits work. If the Earth had a larger mass, the moon would still orbit us. Actually, the mass of Earth is increasing slightly over time.

A somewhat surprising comparison: the gravitational force between moon and sun is always larger than the force between moon and Earth. The moon is always accelerating towards the sun - but the Earth is accelerating towards it in nearly the same way, so the large overall force from the sun does not influence the orbit of moon too much.

3. May 16, 2016

### cjp613

Thank you for the reply. I'm obviously still learning and that helped.

I'd really like to study this further. Are there any books or videos you would recommend that go into greater detail about the relationship between Earth, Moon and Sun?

Thanks again.

4. May 16, 2016

### newjerseyrunner

Isaac Newton had the same problem. He figured out that he could calculate the orbits of two objects, but he found that with multiple bodies, his equations would go unstable after a while. He mentioned that his formulas would not allow the solar system to be stable and that God comes in occasionally and fixes it. He would have needed perturbation theory to solve this, which he didn't have.

5. May 16, 2016

### cjp613

I'm not familiar with perturbation theory, but l will definitely look into it. Thank you.

6. May 17, 2016

### Janus

Staff Emeritus
As mfb has pointed out, both the Earth and Moon are being pulled on by the Sun, so they travel around the Sun in almost exactly the same orbit. That doesn't mean that the the relative positions of the Earth Moon and Sun don't have any effect on the Moon's orbit around the Sun, its just not what you might originally think it being. First consider when the Moon is in between the Earth and Sun. The Moon is slightly closer to the Sun, so while both are pulled by the Sun, the Moon being a bit closer is pulled on a bit stronger. This does tend to pull the Moon slightly away from the Earth.
Now consider when the Moon is on the opposite side of the Earth from the Sun. Now the Earth is closer and being pulled on a bit harder, But the effect is pretty much the same, it tends to pull the Earth and Moon apart. The result is that the Moon is pulled away slightly during both the Full and New moons. There is also a slight "squeezing" effect that pulls them together slightly when the Moon is directly ahead or behind the Earth in its orbit. This is basically the same effect that raises ocean tides on the Earth.
So why does this not end up with the Moon's orbit being slowly stretched into an thinner and thinner oval shape over time? Remember that the Moon and Earth orbit the Sun. In the time between a full moon and new moon (when the Moon and Earth are being pulled apart) the pair have moved roughly 15 degrees around the Sun. This means the Moon is also at point ~15 degrees removed from the point in its orbit where it last was in this situation. And when it happens again, it will at a point another 15 degrees away. The line along which the Moon's orbit is being stretched has moved to a different part of the Moon's orbit.

The point is that, as the Earth-Moon pair orbit the Sun, the direction of the "stretching" and "Squeezing" rotates with respect to the Moon's orbit. Since this effect tends to spread out over all points of the orbit over time ( a part of the orbit being stretched at one time will find itself being squeezed at another), it averages out to having no net effect on the Moon's orbit over the long run.

7. May 17, 2016

### cjp613

I really appreciate you taking the time to post. It was very helpful. Thanks