college physics
posted by Joe .
Although astronauts appear weightless, they are not. They only appear weightless because they are in free fall. If a 79 kg astronaut is orbiting Earth with an orbital radius of 5.31×107 m, determine how much the astronaut would weigh. Earth's mass is 5.974 1024 kg.

Your teacher is misleading you greatly. Be careful. I am wondering if you actually have a physics major teacher.
I will solve this question: If a 79 kg astronaut is orbiting Earth with an orbital radius of 5.31×107 m, determine how much the astronaut would weigh ON EARTH. Earth's mass is 5.974 1024 kg.
a) On Earth, the person weights 79*9.8 Newtons.
Now for this question: If a 79 kg astronaut is orbiting Earth with an orbital radius of 5.31×107 m, determine how much the astronaut would weigh in orbit. Earth's mass is 5.974 1024 kg.
Answer: zero, the astronaut is in free fall.
I suspect your teacher has something else in mind, but frankly, I have no idea. If you get many of these, I would drop the class, and get a qualified teacher. Physics is an important subject.
In orbit, there are two forces working: gravity, and centripetal force. To be weightless, those two are equal. Perhaps your teacher wants you to ignore centripetal force, and just figure the gravity force at that orbital radius. I just don't know. 
Hmm. I thought gravity provided the centripetal force. The object wants to fly off at a tangent, but gravity keeps bending the trajectory.
Is there another force besides gravity act work?