What ideas have you had so far?
A space traveller is on a mission to determine the mass of the recently discovered
planet U, whose radius is known to be three times that of the earth. In a heroic act the
traveller measures his weight on U to be 130N. If he weighs 700N on earth, what is the
mass of U relative to that of the earth?
Technically, the first equation is
where is the gravitational constant (not 9.8 meters per second squared). The equation is a useful approximation when everything is happening at more or less the same distances from the Earth's center. Essentially, you have
The first equation in this post is the more correct equation, especially when your distance away from Earth's center is changing by a lot.
Does that make sense?
Your computation of the mass is correct. What more can you do?
The radii need to be squared. I don't think you're going to need to know the radius of the Earth. What you do need to know is that the second planet has a radius that's three times the other.Anyway For the force between the man and Earth I have [LaTeX ERROR: Convert failed] . Do I have to find these out? AS for the force between the man and U [LaTeX ERROR: Convert failed] . There are too many unknowns
Try taking the ratio of one equation to the other, and see what cancels out.
Also I was a bit confused about the meaning of 'relative'. For example if there were 2 trains going in the same direction, one travelling at 50,the other at 30m/s, you would say the relative speed of the former was 20. But here we are dividing to find the relative mass. Why the difference?