Weighing In on Different Planets: Radii and Mass

In summary, the conversation discusses the relationship between radius, mass, and weight on different planets. It is determined that if a planet has a larger radius and the same total mass as Earth, the weight would decrease due to the decrease in gravitational force. This is based on Newton's concept that if all the mass of a planet was condensed into a small marble, the gravitational force would remain the same.
  • #1
lep007
3
0

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.
 
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  • #2
Welcome to the forum. There are some eqns that could be of value, but for now do you know how gravity varies with distance?
 
  • #3
I think the gravitational force should get smaller when the distance becomes larger, right?
 
  • #4
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.
 
  • #5
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?
 
  • #6
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.
 

Related to Weighing In on Different Planets: Radii and Mass

1. How does gravity affect an object's weight on different planets?

Gravity is directly proportional to an object's mass and inversely proportional to the square of the distance between the object and the center of the planet. This means that on planets with a greater mass or a smaller radius, the force of gravity will be stronger, resulting in a higher weight for objects on the surface.

2. Does an object's weight change on different planets?

Yes, an object's weight is dependent on the force of gravity acting on it. Since the force of gravity varies on different planets, an object's weight will also vary. However, an object's mass remains constant regardless of the planet it is on.

3. How is weight different from mass?

Weight refers to the force of gravity acting on an object, while mass refers to the amount of matter in an object. Weight can change depending on the force of gravity, but mass remains constant. For example, an object with a mass of 10 kilograms will have a different weight on Earth compared to Mars, but the mass will remain the same.

4. Can you calculate an object's weight on different planets?

Yes, an object's weight can be calculated using the formula W = mg, where m is the object's mass and g is the force of gravity. The value of g will be different for each planet, so the weight will vary accordingly.

5. How does the radius of a planet affect its gravitational pull?

The radius of a planet is directly proportional to the force of gravity acting on objects on its surface. This means that the larger the radius of a planet, the weaker the gravitational pull will be. For example, the force of gravity on Jupiter is weaker than that on Earth, due to Jupiter's larger radius.

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