Planet X has the same mass as the Earth, but 1/2 the radius. (Planet X is more dense than the Earth). Suppose your mass is some 55 kg, so your weight at the sea level on Earth is about 120...

Planet X has the same mass as the Earth, but 1/2 the radius. (Planet X is more
dense than the Earth). Suppose your mass is some 55 kg, so your weight at the sea level on Earth is about 120 lb.
 
So, 
1) What would be your mass on the surface of Planet X?
 
2) What would be your weight on the surface of Planet X?
 
3) Suppose you stand on a top of a very tall ladder, and so your distance from the center of the Planet X is now equal to the Earth radius. What would be your weight there?

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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

Posted on

Hello!

1) Your mass is your own characteristic, it wouldn't change if you left Earth.

2) Your weight is the force with which you press on the surface. By Newton's Third Law this force has the same magnitude as the force with which the planet presses on you. Denote your mass as m, the mass of Earth as M, the mass of Planet X is given to be M also. Denote the radius of Earth as R, then the radius of Planet X is R/2.

And gravitational force on the surface of Planet X will be 4 times greater than on the Earth's surface by the Newton's Law of Universal Gravitation:

on Earth:  `F_E = G*(m*M)/(R^2)`

on Planet X:  `F_X = G*(m*M)/((R/2)^2)=4*G*(m*M)/(R^2) = 4*F_E.`

Of course 4*120lb = 480lb.

3) Again, by the Newton's Law of Universal Gravitation, your weight will be

`F'_X = G*(m*M)/R^2 = F_E.`

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