I’m interested in astronomy and physics, and thought it would be fun to try to calculate the shape of a planet based on its mass, size (polar radius) and rate of spin. If this sounds interesting to you, please read over my paper!

The Shape of a Planet

There is some fault there, my calculated ‘equatorial bulges’ are too large. I’d greatly appreciate it if some mathsy person could read over the paper and let me know what mistake/s I’ve made. I’d be happy to pay a $50 reward if you can tell me what I’ve done wrong and I agree with you! Thanks.

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G is 9.81 Newtons

Your calculation for the size of the bulge based on centrifugal forces alone is fairly accurate. But once such a bulge exists, it exerts a gravitational force which increases its own size. You can see my calculations on my blog; they agree with Newton, so hopefully you will find them agreeable too. If you feel like rewarding me, please buy my Ebook from Amazon and write a sparkling review.

Ah, thank you very much, William Newtspeare!

I had thought my calculations or method must have been wrong, but I’m very pleased to hear that they agree with Newton’s, and the extra bulge is due to an additional factor.

I was aware that the bulge itself would change the gravitational field, but did not think this would make much of difference. It appears I was wrong about that, and I’m very happy to hear it! (as this means the rest of my paper might be correct)

I will print and read with interest your paper on “The earth’s equatorial bulge”. I bought a copy of your e-book, will read it ASAP and give a good review supposing, as I expect, that I will like it. 🙂 Thank-you very much.

My paper shows a way to find the shape of an object such as a planet, which is essentially fluid, based on its spin and the field of forces it is embedded in, using a little calculus. The idea is that the stable surface must be ‘flat’ such that a ball sitting on it would not roll.