Question

Is the sun's gravitational pull on the moon greater or less than the earth's pull on the moon? The sun doesn't steal our moon away, so the earth must be pulling harder, right? If you do the calculation, you find out that's not true. The sun pulls more than the earth, so why don't we lose the moon?

Answer 1

If you use the masses of the sun, earth and the moon and and distances between them to calculate the attraction between them,

you will get,

Gravitational attraction between earth and the moon = 1.99*10²⁰ N

Gravitational attraction between the sun and the moon = 4.34*10²⁰ N

Hence sun's gravitational pull on the moon is roughly twice that of the earth's. But we still havethe moon.

For every astronomical object there is the region in which it dominates the gravitational attraction. This region is called Hill Sphere of that object. To be retained by earth, the moon must have an orbit that lies within the earth's Hill sphere.

In fact the stability of an orbit depends on the radius of the Hill sphere. A satellite will remain in the clutches of a planet for a long time if the orbit exist only inside 1/2 to 1/3 of the Hill radius.

Since the Moon's orbit about the Earth is approximately 1/4 of the Earth's Hill sphere radius, it remains with earth for a very long time (roughly 4.5 billion years) and will stay with us for few more billion years.