What would happen if earth's radius were somehow expanded?

Question

Would would happen to your weight if the earth were somehow expanded to a larger radius (but with no change in mass)? What about if the earth shrunk?

Answer 1

Expanded: you weight will decrease as a function of the square of the increase (doubling radius, weight divided by 4)

Contracted: weight goes up.

You have to remember that gravity would be the same if all of Earth's mass was concentrated in an object the size of a marble, with you at the same distance from the center as you are now (i.e. the rest of the earth would have no mass, like empty space with just a thin shell for the surface). Thus the gravity law which states that the force of attraction is proportional to the mass, and inversely proportional to the square of the distance, is exactly predicting what you would see.

Answer 2

I refer you to Newton's law of gravitational attraction. http://en.wikipedia.org/wiki/Newton%27s_law_of_gravity
The only factor that changes in your scenario is the distance between the two masses (yourself and the Earth), and that goes as r^-2. So, if the Earth expanded to a larger radius, you would weigh less. And if the Earth shrunk, you would weigh more. Neglecting fringe effects, of course.

Answer 3

If the radius of the planet increased, the distance from the center of mass would increase and the acceleration on the surface would decrease. If the planet shrunk, it would increase.

In either case, we'd be screwed ☺


Doug

Answer 4

the continents would move apart.