The space shuttle typically orbits Earth at an altitude of about (300 mathrm{~km}). (a) By what factor

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The space shuttle typically orbits Earth at an altitude of about \(300 \mathrm{~km}\).

(a) By what factor is the shuttle's distance to the center of Earth increased over that of an object on the ground? 

(b) The gravitational force exerted by Earth on an object in the orbiting shuttle is how much smaller than the gravitational force exerted by Earth on the same object when it is sitting on the ground?

(c) What is the acceleration due to gravity at an altitude of about \(300 \mathrm{~km}\) ?

(d) While in orbit, the shuttle's engines are off. Why doesn't the shuttle fall to Earth?

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