On Creating Imaginary Worlds: Science Fiction

[Bowler1]

I'm not knocking Sir Kerub on wanting a humanoid life form, but it feels too Star Trex for my liking, too easy. Limbs, feathers, scales, eyes (lots), arms, appendages, legs in profusion, everything you'd want to kick start Captain Kirks libido as he chases down the local alien life, intelligent or otherwise, he didn't seem fussy. This is the fun bit of SciFi for me, why stick to our boring old model and shapes?

Chrispy, the source of all very weird and odd knowledge, I walk proudly in your shadow! The radiation answer is logic Spock would appreciate.

 

[Patrick Mahon]

I've seen this discussed before on-site. As I understand it, it depends, at least partly, upon density and mass, rather than just size, so if a planet was larger than Earth, it might have less gravity, compared to size, than Earth if its mass was less per metre cubed. I could be wrong, but there's also the distance from the centre of gravity involved, I think. I'm still looking for the set of equations to work this out for myself.

Abernovo - sorry to come to this very late, but in case it's still useful...

The gravitational force between two masses m1 and m2 at a distance r is given by F = G m1 m2 / r^2, where G is the Gravitational constant,

and the relationship between a force on a body of mass m1 and the acceleration this imparts is given by Newton's second law, F = m1 a

So equating these, the acceleration due to gravity on a body at the surface of a planet of radius r and mass m2 is

a = G m2 / r^2

There are some assumptions in here (e.g. that the planet is perfectly spherical, so you can replace the entire planet, for gravitational purposes, by the same mass all placed at its centre), but for most purposes this is good enough.

So if we set our units so that a = 1 for the Earth, then if we invent another planet with four times the mass of the Earth, but that has twice the radius, then its surface gravity will be the same as Earth's (though its average density would be half of Earth's). But if we invent a planet with twice the mass of the Earth and half the radius, then its surface gravity would be 8 times ours (and its average density would be 16 times ours).

Disclaimer: I graduated in maths & physics in 1990, so if I've embarrassed myself with a massive error in the above, can someone point it out gently please?