Inverse cube gravity field?

Question

I once heard that if the sun created an inverse cube gravity field the Earth would quickly spiral into it. Why would the sun do that?

Answer 1

Gravity is a force defined by an inverse square field. The farther you get from the source, gravity has a weaker and weaker pull. With the square, when you double the distance you divide the gravity force by 4.

Now if it were an inverse cubed field, the Sun would have even less pull on the bodies in our Solar System. And if it just suddenly changed one day (which it never would), and everything else stayed the same (including Earth's relative orbital velocity). Earth would actually probably spin out and away from the Sun if the velocity was greater than escape velocity(dont feel like doing the calculations to see if thats true.) But if Earth did not reach escape velocity from that orbit, then it would in fact spiral down to a lower orbit closer to the sun. (The closer you are to the center of gravity the faster you need to orbit to maintain said orbit.)

In an inverse cubed field if you double distance you divide gravity's pull by 8.

Answer 2

An inverse cube law, where gravity twice as far away is 8 times weaker, would result in the Earth spiraling away from Sun. The inverse square law, where gravity twice as far away is 4 times weaker, is just right so that orbits are stable. If the field were inverse first power, so that gravity twice as far away were only twice as weak, then the Earth would spiral into the Sun.

Answer 3

As arwyawen said.......an inverse cubed gravitational field would be a very weak field indeed. The Sun wouldn't be able to hold onto the Earth as is it, given its present orbital velocity. The force of gravity would be an order of magnitude too weak to hold onto the planet, and the planet would fly away out of its orbit.

It would also have very important consequences to a great raft of other things, such as star formation and evolution, universal expansion, clustering of galaxies etc etc. Without going into the details, much of what we see, if not all, wouldn't exist if we had an inverse cubed gravitational field.

Answer 4

It would not. The gravitational field is always inverse square. However, the differential gravitational field (also known as tidal force) is inverse cube. The result is that tidal force can become very strong near a planet, but quite weak at a distance.

Around a black hole, it is not the gravitational force that is destructive, but the tidal force. As different parts of an object try to orbit at different velocities, the object gets torn apart.