Question about gravity and planets

[jakeowens]

If your on a planet that has 4x as much mass as earth, but only 2x the diameter, would you weigh 4x as much as you do on earth? Does the diameter of the planet even matter? or is it only the mass that affects how much you weigh.

Thanks

 

[misogynisticfeminist]

hmm, i'll try,

weight is w=mg, where g is the gravitational field strength at a point. Weight is the G force acting on you.

using $$F= G \frac{Mm}{r^2}$$ where M is mass of Earth and r is radius of earth, according to your example,

$$F= G \frac{4Mm}{(\frac{1}{2r})^2}$$

notice that half r is being squared, this gives you a quarter r ! If you bring everything up, and simplify,

you get,

$$F= 16 G \frac{Mm}{r^2}$$

so it weighs 16 times more on earth.

The diameter of the planet matters, because the equation depends on r.

 

[Grogs]

hmm, i'll try,

weight is w=mg, where g is the gravitational field strength at a point. Weight is the G force acting on you.

using $$F= G \frac{Mm}{r^2}$$ where M is mass of Earth and r is radius of earth, according to your example,

$$F= G \frac{4Mm}{(\frac{1}{2r})^2}$$

I think this equation should be:

$$F= G \frac{4Mm}{(2r)^2}$$

The 4 and the 2² will cancel out and you'll end up with 1g.

 

[Robokapp]

just sitck some values into it and see how it varies. pick F=forget about constant F=Mm/d^2 and replace everytihng you don't need by 1 and everytihng you need by 2 and 4 accordingly. work smart...work simple.

F=4Mm/(2D)^2 so the 4 cancels the 2^2.

 

[misogynisticfeminist]

ohhh thought the radius was half.