Question

Suppose that you travel to a planet that has 4 times the Earth's mass and 4 times the Earth's radius. Calculate how much more or less you would weigh on this planet compared to your weight on Earth.

Answer 1

Mass on the planet would be 4 times the mass on Earth.

Explanation:

Given -  

Let the mass of Earth = Me

Let the radius of Earth = Re

Mass of the planet, Mp = 4Me

Radius of the planet, Rp = 4Re

Weight on other planet, W = ?

Weight on planets is determined by the gravitational force

Gravitational force, F = GMm/r²

where, G = gravitational constant

M = Mass of the planet

m = our mass

r = radius of the planet

Gravitational force on Earth:

F = G X Me X ma/ Re²                                       (ma = mass on earth)

Gravitational force on planet :

F = G X 4Me X mₓ/ (4Re)²                                  (mx = mass on other planet)

Dividing both the equations, we get

mx = 4ma

Therefore, mass on the planet would be 4 times the mass on Earth.