PHY 1053C
Gravitation Practice
1. An asteroid is headed toward a planet as shown below. The masses and distances are as indicated.
a) Calculate the force of gravity on the asteroid due to the planet.
b) Calculate the acceleration of the asteroid toward the planet.
c) If the asteroid embeds itself into the planet at a speed of 1000 m/s, then calculate the final recoil speed of the combined mass.
d) Calculate the force of the collision if the impact lasted for 0.3 s.
2. A 1500 kg space satellite is in orbit around a 1025 kg planet. The orbit is 6x108 m from the center of the planet. There is a 1027 kg star located 9x109 m from the center of the planet.
a) Find the net force on the space satellite at the point labeled A above.
b) What must the velocity of the satellite be at A in order to maintain the orbit?
c) Find the net force on the space satellite at the point labeled B above.
d) What must the velocity of the satellite be at B in order to maintain the orbit?
3. A local cable satellite is
orbiting the earth so that it is at the same spot over the earth at all times
(geosynchronous orbit meaning it has the same period of revolution as the
earth's daily rotation). The satellite
is orbitting at a distance of 4.23x10 km
from the earth's center.
a) What is the orbital speed of
the satellite (in m/s)?
b) What is the centripetal
acceleration of the satellite?
c) If the satellite has a mass of
100 kg, then what is the gravitational force of the earth on the satellite?
d) Calculate the mass of the earth
given the gravitational force of the earth on the satellite calculated from
part c).
4. You are flying at a constant speed in deep space in your 1000 kg space shuttle. Suddenly you spot a large asteroid which you determine to be 1000 m in front of you. Furthermore, your sensors indicate the asteroid has a mass of 1x1013 kg.
a) Calculate the force exerted on your ship due to the asteroid.
b) What is your acceleration toward the asteroid?
c) Calculate the external force necessary to accelerate your ship at 1 m/s2 away from the asteroid. Note that this force is applied to the ship from your rocket engines.