Good approximations, all. But everyone has neglected the change in gravitational acceleration over a 1 km distance! If the surface gravity at about 6000 km from the center of the earth is 9.81 m/s^2, the gravity at 6001 km will be about 9.80 m/s^2. So to get a fully accurate answer, you really have to do the calculus.
Of course, to get a really, really accurate answer, you need to do tensor calculus using the Einstein equation of general relativity, rather than mucking about with Newton’s Law of Universal Gravitation. You guys are so 18th century!
That’s not correct. The mass of an object does affect the force exerted on it by gravity. In fact the force is proportional to the mass. But the acceleration of an object due to gravity doesn’t depend on mass because the mass cancels out:
F = ma
a = F/m
