Use the following information to complete the problems below:
G: 6.67 x 10-11 N m2 kg-2
Radius of the moon:
1.74 x 106 m
Radius of the earth:
6.37 x 106 m
Mass of the moon:
7.34 x 1022 kg
Mass of the earth:
5.98 x 1024 kg
Distance between the centers of the earth and moon: 3.84 x 108 m
1. A rocket launches from Earth’s surface to reach a stable circular at 5 Earth radii above Earth’s surface.
a. What is the speed of this rocket once it establishes a stable circular orbit?
b. What must be the launch velocity of a rocket in order to achieve a stable circular orbit a distance above
Earth’s surface equal to 5 earth radii?
2. An asteroid headed directly toward Earth, has a speed of 12 km/s relative to the planet when it is at a
distance of 10 Earth radii from Earth’s center. Neglecting the effects of Earth’s atmosphere on the asteroid,
find the asteroid’s speed when it reaches Earth’s surface.
3. There is a point on the line joining the centers of the earth and moon where the gravitational forces add to
zero.
a. Determine the location of this point.
b. With what velocity would a body have to be launched from Earth’s surface in order to just reach this
point with zero velocity?
c. If a body is given a velocity just slightly greater than that calculated in (b), what is its velocity just as it
reaches the moon’s surface?
d. Relative to a zero gravitational potential far away from both the earth and the moon, what is the
potential energy for a 1-kg object at the “zero-gravity” position calculated in (a)?