If a planet were the same size as Earth, but twice as massive, would you weigh less or more on it?

Question

If a planet were the same size as Earth, but twice as massive, and you weighed 100 pounds on Earth, what would you weigh there?

gp4rts- Thanks. That really helps me a lot. I'll choose that as best answer as soon as it will let me.

Answer 1

The formula for gravitational attraction is

F = G*m1*m2/r^2

If earth is m1 and you are m2, everything stays the same except m1, which doubles. That means F (weight) also doubles, so you would weigh 200 lb.

Answer 2

Yes,

gp4rts gave you the formula to figure it out, but not the answer or the reason.

If an object is denser, has more mass, then you will weigh more on that object. In your example on a planet that is the same size of Earth, but twice as massive, then you would weigh twice as much; 200 lbs.

Answer 3

Gravity is a function of Mass- so two times mass would make the 100 pounder weigh 200 Lbs: all other things being equal. For example if earth shrank to its Schwartzchild radius (ping pong ball/ golfball size), it would be a black hole: not even light could escape. So distance from the center of gravity becomes vital in that aspect. But were the earth to suddenly have doubled its mass without changing size (maintained radius) then we'd weigh twice as much.

Answer 4

Of course you're welcome to choose any answer as best, but the one you've selected is *wrong.* So far what everyone has ignored is the equation for weight ==>
WEIGHT = MASS x GRAVITATIONAL ACCELERATION

If Earth doubled its mass you'd have 1.1754^25 kg

Now you have to find the *new* gravitational acceleration on the surface of this more massive Earth ==>
GRAVITATIONAL ACCELERATION = G x M / R^2

'G' is the gravitational constant
'M' is the new mass we just got for Earth (..1.1754^25 kg..)
'R' is Earth's radius (...6,128 km..)

Solving the above for the gravitational acceleration on the more massive Earth gives 20.9 meters/sec/sec

The important thing now is to understand that the above gravitational acceleration is for *any* mass on Earth's surface.

Next, weight.....

WEIGHT = MASS x GRAVITATIONAL ACCELERATION

Let's say that your mass --- which is not the same thing as weight --- is 14 kg.

WEIGHT = 14 x 20.9 m/sec/sec = 292 pounds

On the original Earth the gravitational acceleration is about 9.8 m/sec/sec, so with a mass of 14 you'd weight 137 pounds

Answer 5

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