1Calculate the acceleration due to gravity at distances d = 3R and d = 4R from the center of the earth and compare the values as the distance increases. Take g = 9.8 m/s² at the surface.
2The mass of the earth is \( 5.97 \times 10^{24}\ \text{kg} \) and its radius is 6371 km. Calculate the acceleration due to gravity at the International Space Station situated at an altitude of 400 km above the surface of the earth.
3The acceleration due to gravity of the earth is 9.8 m/s². If the mass of the moon is \( 7.35 \times 10^{22}\ \text{kg} \) and its radius is \( 1.74 \times 10^{6}\ \text{m} \), what is the acceleration due to gravity of the moon? Compare the acceleration due to gravity of the Earth and that of the Moon.
4Why is the value of g less at the top of a hill than at its bottom? Why is the difference small?
5Find g at the summit of Mount Everest, height 8848.86 m. Take the Earth's mass as \( 5.97 \times 10^{24}\ \text{kg} \) and its radius as 6371 km.
6What does the fact that \( (R+h)^2 \) is greater than \( R^2 \) tell us about g at a height h?
7A satellite is at a height above the surface equal to the Earth's radius. What is g there?
8Astronauts float in the International Space Station. Is the acceleration due to gravity zero there?
9How far from the center of the Earth must you go for g to become one hundredth of its surface value?