An asteroid 1 mi in diameter of density \(4 \,g/cm^{3}\) enters the earth’s gravity when it is at rest with respect to the solar system.
What is the speed of the asteroid with respect to the earth before entering the earth’s gravity?
What is the speed of the asteroid when it hits the surface of the earth?
What is the energy of the asteroid when it hits the earth’s surface?
How does this compare with the amount of solar energy which hits the surface of the earth every day if the solar constant is \(1.37 \,kW/m^{2}\text{?}\)
2.
A rock of mass 500 kg is dropped from a height of 1 m. While it is falling,
how hard does the earth pull down on the rock?
how hard does the rock pull up on the earth?
why doesn’t the earth move upward to meet the rock?
3.
If the the earth were a sphere of radius \(6.37\times 10^{6} \,m\text{,}\) the acceleration due to gravity at the surface of the earth were \(9.8 \,m/s^{2}\text{,}\) and the universal gravitational constant were \(6.67\times 10^{-11} \,N.m^{2}/kg^{2}\text{,}\) what would be the mass of the earth?
4.
What is the altitude of a communications satellite which remains stationary over one spot on the earth? Can this spot be the north pole?
5.
The Moon is 384,400 km distant from the Earth’s center, and it completes an orbit in 27.3 days.
Determine the Moon’s orbital speed.
How far does the Moon "fall" toward the Earth in 1 s?
Io, a small moon of Jupiter, has an orbital period of 1.77 days and an orbital radius of \(4.22\times 10^{5} \,km\text{.}\) From these data, determine the mass of Jupiter.
Ganymede, Jupiter’s largest moon, has an orbital period of 7.16 days. What is its orbital radius?
7.
Find the difference in potential energy of a satellite of mass \(m_{s}=2.50\times10^{3}\,kg\text{,}\) when it is at a distance of \(2.55 \times10^{9} \,m\) and when it is at the distance of \(4.30\times10^{7} \,m\) from the center of the earth.
8.
Three point masses of 30.0 kg, 50.0 kg, and 70.0 kg are located at the vertices of an equilateral triangle 1.00 m on a side. Find the resultant gravitational force on each mass.
9.
At what speed would the earth have to rotate such that the centripetal force at the equator would be equal to the weight of a body there? If the earth rotated at this velocity, how long would a day be? If a 900-N man stood on a weighing scale there, what would the scales read?
10.
Find the acceleration due to gravity, g at the bottom of a 400-km deep mine. Assume the radius of the earth is 6400km and has a uniform density.
