Question about gravity and planets

In summary, the weight of a person on a planet with 4 times the mass and 2 times the diameter of Earth would be 16 times more than their weight on Earth. The diameter of the planet does matter in this equation as it affects the value of r in the equation. However, if the radius was mistakenly thought to be half, the weight would only be 4 times more.
  • #1
jakeowens
34
0
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
 
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  • #2
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 [tex] F= G \frac{Mm}{r^2} [/tex] where M is mass of Earth and r is radius of earth, according to your example,

[tex] F= G \frac{4Mm}{(\frac{1}{2r})^2} [/tex]

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

you get,

[tex] F= 16 G \frac{Mm}{r^2} [/tex]

so it weighs 16 times more on earth.

The diameter of the planet matters, because the equation depends on r.
 
Last edited:
  • #3
misogynisticfeminist said:
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 [tex] F= G \frac{Mm}{r^2} [/tex] where M is mass of Earth and r is radius of earth, according to your example,

[tex] F= G \frac{4Mm}{(\frac{1}{2r})^2} [/tex]

I think this equation should be:

[tex] F= G \frac{4Mm}{(2r)^2} [/tex]

The 4 and the 22 will cancel out and you'll end up with 1g.
 
  • #4
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.
 
  • #5
ohhh thought the radius was half.
 

1. What is gravity?

Gravity is a natural phenomenon by which all objects with mass are brought towards one another. It is a fundamental force in the universe that governs the motion of planets, stars, and galaxies.

2. How does gravity affect planets?

Gravity is responsible for keeping planets in orbit around the sun. The force of gravity between the planet and the sun keeps the planet moving in a circular or elliptical path around the sun. Gravity also causes planets to have a spherical shape, as it pulls the mass of the planet towards its center.

3. Why do different planets have different levels of gravity?

The level of gravity on a planet depends on its mass and size. The more massive and larger a planet is, the stronger its gravitational pull will be. This is why larger planets like Jupiter have a stronger gravitational force than smaller planets like Mercury.

4. Can gravity be turned off?

No, gravity is a fundamental force in the universe and cannot be turned off or controlled by humans. It is always present and affects all objects with mass.

5. How does gravity affect the motion of objects on a planet's surface?

Gravity causes objects to fall towards the center of a planet, which is why we feel the effects of gravity on Earth. The strength of gravity on a planet's surface depends on its mass and size. Objects with less mass, such as a feather, will fall slower than objects with more mass, such as a bowling ball, due to the force of gravity.

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