Physics
posted by Abby .
a) What will an object weigh on the Moon's surface if it weighs 500 N on Earth's surface? (b) How many Earth radii must this same object be from the center of Earth if it is to weigh the same as it does on the Moon?
Alright, I know how to do part a. but I'm having issues on figuring out how to do part b. Please help!

a) 1/6 of the weight on Earth.
b) g and weight at the surface are proportional to M/R^2 of the attracting body (Earth or moon). But M is proportional to R^3, assuming uniform density. Therefore g is prooprtional to R. Earth would have to be 1/6 its present radius to have the same g value as the moon. That is less the moon's actual radius.