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The mass of the Earth is about 5.97×10 24 kg , and the radius of the Earth is ab

ID: 1558529 • Letter: T

Question

The mass of the Earth is about 5.97×1024  kg , and the radius of the Earth is about 6380  km . At the surface of the Earth, the magnitude of acceleration due to gravity acting alone is about 9.80  m/s2 . What is the approximate magnitude of the acceleration due to gravity acting alone at an altitude of 1000  km above the surface of the Earth? This altitude is far above the Earth's atmosphere (the International Space Station orbits at an altitude of about 400 km).

E- 9.80

A- 7.31  m/s2 B- zero C- 398  m/s2 D- 3.98  m/s2

E- 9.80

Explanation / Answer

earth gravitational acceleration is given by

g = GM/r^2

where G is a constant M is mass of earth and

r is radius of earth since it is the formula for g at earth's surface

at a height above earth's surface the formula changes as

g*= GM/(r+h)^2

so by dividing above two equations we get

g*/g = (r/(r+h))^2

g* = 9.8 * (6380/7380)^2 = 7.324 m/s^2

so the answer is A