perplexus.info :: Science : Designing Planets

Designing Planets (Posted on 2019-01-04)

You are asked to design a planet of mass M and uniform density p such that it has the maximum possible acceleration due to gravity g at a point on its surface.

Find the shape of this planet, and then find g.

Take G as the universal gravitational constant.

No Solution Yet Submitted by Danish Ahmed Khan

Rating: 1.0000 (1 votes)

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Solution (not my own) (spoiler)

| Comment 1 of 5

I was somewhat surprised it is NOT a sphere, but this kind of shape.

https://physics.stackexchange.com/questions/12703/maximal-gravity

I admit that I had the general idea to look for a symmetrical shape that would have a point closer to the volume center of gravity, but I suspected a sphere would be the answer. And, I would never had been able to do the math.

Hoping someone on the site can actual do this without help so I can applaud him/her.

Posted by Kenny M on 2019-01-04 20:43:12

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