A 200.-kg satellite is in circular orbit around the Earth and moving at a speed of $5.00 \mathrm{~km} / \mathrm{s}$. How much work must be done to move the satellite into another circular orbit that is twice as high above the surface of the Earth?

A satellite used in a cellular telephone network has a mass of $2180~\text{kg}$ and is in a circular orbit at a height of $750~\text{km}$ above the surface of the earth. What is the gravitational force $F_{grav}$ on the satellite?

A $2150-\mathrm{kg}$ satellite used in a cellular telephone network is in a circular orbit at a height of $780 \mathrm{~km}$ above the surface of the earth.What gravitational pull is there on the satellite? What percentage of its weight is this at the earth's surface?

Eris, the largest dwarf planet known in the Solar System, has a radius $R=1200 \mathrm{~km}$ and an acceleration due to gravity on its surface of magnitude $g=0.77 \mathrm{~m} / \mathrm{s}^2$. a) Use these numbers to calculate the escape speed from the surface of Eris. b) If an object is fired directly upward from the surface of Eris with half of this escape speed, to what maximum height above the surface will the object rise? (Assume that Eris has no atmosphere and negligible rotation.)

Standing on the surface of a small spherical moon whose radius is $6.30 \cdot 10^4 \mathrm{~m}$ and whose mass is $8.00 \cdot 10^{18} \mathrm{~kg}$, an astronaut throws a rock of mass $2.00 \mathrm{~kg}$ straight upward with an initial speed $40.0 \mathrm{~m} / \mathrm{s}$. (This moon is too small to have an atmosphere.) What maximum height above the surface of the moon will the rock reach?

A $2150 \mathrm{~kg}$ satellite used in a cellular telephone network is in a circular orbit at a height of $780 \mathrm{~km}$ above the surface of the earth What is the gravitational force on the satellite? What fraction of this force of the satellite's weight is at the surface of the earth?

In an experiment performed at the bottom of a very deep vertical mine shaft, a ball is tossed vertically in the air with a known initial velocity of $10.0 \mathrm{~m} / \mathrm{s}$, and the maximum height the ball reaches (measured from its launch point) is determined to be $5.113 \mathrm{~m}$. Knowing the radius of the Earth, $R_{\mathrm{E}}=6370 \mathrm{~km}$, and the gravitational acceleration at the surface of the Earth, $g(0)=9.81 \mathrm{~m} / \mathrm{s}^2$, calculate the depth of the shaft.

Land west of the San Andreas fault in southern California is moving at an average velocity of about 6 cm/y northwest relative to land east of the fault. Los Angeles is west of the fault and may thus someday be at the same latitude as San Francisco, which is east of the fault. How far in the future will this occur if the displacement to be made is 590 km northwest, assuming the motion remains constant?

What is the magnitude of the free-fall acceleration of a ball (mass $m$ ) due to the Earth's gravity at an altitude of $2 R$, where $R$ is the radius of the Earth?

A professional fireworks team shoots an 8-in. mortar straight upwards from ground level with an initial speed of 216 ft/sec. a. Write a function modeling the vertical position s(t) (in ft) of the shell at a time t seconds after launch. b. The mortar is designed to explode when the shell is at its maximum height. How long after launch will the shell explode? c. The spectators can see the shell rising once it clears a 200-ft tree line. For what period of time after launch is the shell visible before it explodes?

A carefully designed experiment can measure the gravitational force between masses of $1 \mathrm{~kg}$. Given that the density of iron is $7860 \mathrm{~kg} / \mathrm{m}^3$, what is the gravitational force between two $1.00-\mathrm{kg}$ iron spheres that are touching ?

Find all solutions of the equation cos 2x - sin x = 0 in the interval [0, 2pi).

In a binary star system consisting of two stars of equal mass, where is the gravitational potential equal to zero? a) exactly halfway between the stars, b) along a line bisecting the line connecting the stars, c) infinitely far from the stars, d) none of the above.

A man inside a sturdy box is fired out of a cannon. Which of the following statements regarding the man’s sensation of weightlessness is correct? a) The man senses weightlessness only when he and the box are traveling upward. b) The man senses weightlessness only when he and the box are traveling downward. c) The man senses weightlessness when he and the box are traveling both upward and downward. d) The man does not sense weightlessness at any time of the flight.