Weighing In on Different Planets: Radii and Mass

[lep007]

Homework Statement

Suppose you went to another planet having a larger radius than Earth but having the same total mass as Earth. Would this affect your weight? How?

Homework Equations

Not applicable...? I think.

The Attempt at a Solution

I don't really understand what radius and mass has to do with weight, sorry.

 

[denverdoc]

Welcome to the forum. There are some eqns that could be of value, but for now do you know how gravity varies with distance?

 

[lep007]

I think the gravitational force should get smaller when the distance becomes larger, right?

 

[denverdoc]

indeed it does, and in fact is an example where it falls with the square of the distance, that is twice as far, 1/4 the force. What you likely are not acquainted with is the idea Newton developed that if you could condense all the matter of the Earth into a small marble in the center, gravitational force would be the same as it is now.

 

[lep007]

I'm sort of confused; I know the one's mass wouldn't change, but if the radius was 3x larger than Earth's and yet the mass of the planet was the same, the planet would be more hollow, which means a lesser pull of gravity, which means weight would decrease?

 

[denverdoc]

bingo! the force from the mass in both cases is the same--picture those marbles of high density matter in the center and a person "standing" at R distance and 3R. The weight would be 1/9 on the fluffier planet.