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Orbit Problems

(See bottom of page for answers.)

1. satellite altitude

The period of Earth's moon is 27.3 d and has a mean orbital radius of 3.8 x 105 km. The Earth's radius is 6380 km. What is the altitude of a satellite orbiting the Earth once every 14.0 days? (search term: satellite altitude)

2. A satellite has a mass of 5850 kg and is in a circular orbit 4.1 * 105 m above the surface of a planet. The period of the orbit is two hours. The radius of the planet is 4.15 * 106 m. What is the true weight of the satellite when it is at rest on the planet's surface?

3. The orbit of the earth about the sun is almost circular. The closest and farthest distance are 1.47*108 and 1.52*108 km, respectively. Find the maximum variation in each of the following that result from the changing earth-sun distance in the course of 1 year.
a. kinetic energy
b. potential energy
c. total energy
d. orbital speed

4. At what horizontal velocity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth?

5. The rings of a Saturn-like planet are composed of chunks of ice that orbit the planet. The inner radius of the rings is 78,000 km, while the outer radius is 190,000 km. The mass of this planet is 6.14*1026 kg. Find the period of an orbiting chunk of ice at the inner radius.

6. Calculate the kinetic energy of a 1249 kg Earth satellite in a circular orbit with a radius of 13740 miles.

7. Neptune is an average distance of 4.5*109 km from the sun. Estimate the length of the Neptunian year gives that the Earth is 1.50 * 108 km from the sun on the average?

8. What linear speed must an Earth satellite have to be in a circular orbit at an altitude of 169km?
(a) in m/s
(b) What is the period of revolution?

9. Use the known period 27.3 days for the moon’s orbital motion around the earth. Given the radius of the orbit as 3.84x108m, calculate
a) the radius of the orbit of an earth satellite in a geosynchronous orbit with a period of 24 hours.
b) the mass of the earth.

10. Assume that you are agile enough to run across a horizontal surface at 8.5 m/s, independently of the value of the gravitational field. What would be the radius and the mass of an airless spherical asteroid of uniform density 1.1 x 103 kg/m3 on which you could launch yourself into orbit by running? What would be your period?

11. For a certain satellite with an apogee distance of ra=1.81*107m, the ratio of the orbital speed at perigee to the orbital speed at apogee is 1.11. Find the perigee distance rp, in meters.

12. Acceleration for a satellite is greater at its
a. same at both places
b. perigee
c. apogee

13. A satellite of mass 200 kg is launched from a site on Earth's equator into an orbit 200 km above the surface of Earth. Assuming a circular orbit and no air friction,
a. what is the orbital period of this satellite
b. what is the speed of the satellite in its orbit
c. what is the minimum energy necessary to place the satellite in orbit?


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