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. Express your answer as a factor or fraction of
your weight on Earth. Show all work.

Answer 1

weight W = M g

g , and the weight, are proportional to M/R^2

M/R^2 is 4Me/(16 Re^2) = (1/4) Me/Re^2
on the new planet.
Me = earth mass
Re = earth radius

Weight will be four times less on the new planet

Answer 2

The "M" in the first equation is the object mass, not the earth mass. I should have used m.

The answer is the same