Ain Shams University
Faculty of Engineering
Communication Dept.
Undergraduate Studies
ECE 453 - Satellite Comm.
Fall 2015
Sheet 2
Satellite Motion Laws
Q1] State the difference between a satellite trajectory & orbit. Give an example with a
neat sketch.
Q2] Explain what the terms centrifugal and centripetal mean with regard to a satellite
in orbit around the earth.
Q3] Derive a relation between the velocity of an orbiting satellite and its orbital radius.
Then derive a relation between the orbital period and satellite radius.
Q4] The Odin Satellite orbits the Earth at distance 600 Km from sea level. Assume that
the Earth’s radius is 6378 Km, the Earth’s mass is 5.972 × 1024 Kg and the
gravitational constant, G = 6.67408 × 10-11 m3Kg-1s-2. Find:
i) The satellite velocity in Km/s.
ii) The time taken to complete one cycle around the Earth.
Q5] A satellite is in a steady circular orbit around the earth. The altitude of the
satellite’s orbit above the surface of the earth is 1,400 Km.
i) What are the centripetal and centrifugal accelerations acting on the
satellite in its orbit? Give your answer in m/s2.
ii) What is the velocity of the satellite in this orbit? Give your answer in
km/s.
iii) What is the orbital period of the satellite in this orbit? Give your answer
in hours, minutes, and seconds.
Note: assume the average radius of the earth is 6378.137 km and Kepler’s
constant has the value 3.986004418 × 105 Km3/s2.
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Q6] A satellite is in a 322 Km high circular orbit. Determine:
i) The orbital velocity in meters per second.
ii) The orbital period in minutes.
iii) The orbital angular velocity in radians per second.
Note: assume the average radius of the Earth is 6378.137 Km and Kepler’s
constant has the value 3.986004418 × 105 Km3/s2.
Q7] A satellite is moving in an elliptical orbit of eccentricity (e = 0.737) as shown in the
figure below, with a perigee height = 500 Km. Find:
i) The satellite velocity at perigee.
ii) The satellite velocity at apogee.
iii) The period of one orbital cycle.
Assume that the radius of the Earth is 6378.137 Km and Kepler’s constant has the
value 3.986004418 × 105 Km3/s2.
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