Download Gravity and Orbits

Gravity and Orbits
1. Find the orbital period and speed of a satellite orbiting Earth at an altitude of 1800 km
2. A moon orbits planet Y in a circular path with a radius of 9600 km. If it takes 137 minutes to
complete one orbit, find a) the acceleration ,
b) the mass of planet Y
c) If planet Y has a radius of 5600 km, what is the gravitational field strength at its surface?
3. Find the speed of an earth satellite orbiting with a 3.5 hour period
4. A planet orbits a certain star at a distance equal to the distance between earth and the sune, but has
a period of 1.5 earth years. What is the mass of the star? (answer in solar masses, eg 2 solar masses is
twice the mass of our sun)
5. If the earth had a second moon orbiting at twice the distance of the one we have now, what would
its orbital period be?
6. Find the velocity of a) Earth’s moon relative to Earth
b) Earth relative to the sun
7. How much work must be done to lift a 200 kg satellite to an altitude of 2000 km?
8. Find the escape velocity from the surface of the moon.
9. A black hole has a mass equal to 10 solar masses. Find the distance from the center at which the
escape velocity equals the speed of light. (This is the Schwarzschild radius or “event horizon”)
10. If a projectile is fired from the surface of the moon with an initial velocity of 800 m/s,
a) what is the maximum height reached?
b) at what height is the velocity equal to 200 m/s
11. A massive asteroid approaches Earth from a great distance at a speed of 3000 m/s. Find its velocity
at impact.
12. Find the total mechanical energy of a 400 kg Earth-satellite. (you must find its velocity first)
a) in a circular orbit 4000 km above Earth.
b) in an orbit with a period of 3.5 hours
c) Why is the total energy of an object in orbit always negative?
13. Find the energy required to place a 3000 kg satellite in a geosynchronous orbit. Assume it starts at
rest on Earth’s surface.
14 (challenge). A moon orbits a massive Neutron star at a distance of 7.5 x 10 8 m. Its orbital speed is
10.0% of the speed of light. Find the mass of the star. Does the relativistic mass increase affect the
speed?
15. (challenge) Find the energy required to place a satellite of mass “m” in an orbit at a height “H”
above a planet with radius “R” and mass “M”.