An astronaut whose weight on Earth’s surface is 7.50×102N boards a spacecraft that climbs vertically to a circular orbit 4.0×102km above Earth’s surface. For this question, treat Earth as an isolated sphere of uniform mass density with radius 6.4×106m. Neglect atmospheric effects.
(a) Calculate the astronaut’s weight at the 4.0×102km orbital altitude. Express your answer to two significant figures.
(b) Determine the percentage difference between the orbital weight found in part (a) and the surface weight.
(c) Near Earth’s surface, introductory physics courses often treat the downward field strength g as constant. Using your numerical results, explain why this approximation is acceptable for everyday elevations such as the top of a 3km-high mountain.