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‫الرحيم‬‫الرحمن‬‫اهلل‬‫ـم‬‫ـ‬‫س‬‫ب‬
Sheet #1: Orbits and Launching Methods
1.1 A satellite is in a circular orbit around the earth. The altitude of the satellite’s orbit above the
surface of the earth is 1,400 km.
a) What are the centripetal and centrifugal accelerations acting on the satellite in its orbit? Give
your answer in m/s2
. [Ans:6.5885007 m/s2
, 6.5885007 m/s2
]
b) What is the velocity of the satellite in this orbit? Give your answer in km/s.[Ans:7.1586494 km/s]
c) What is the orbital period of the satellite in this orbit? Give your answer in hours, minutes, and
seconds. [Ans:1 hour 53 minutes 46.92 seconds]
Note: assume the average radius of the earth is 6,378.137 km and Kepler’s constant has the
value 3.986004418*105 km3/s2.
1.2 A satellite is in a 322 km high circular orbit. Determine:
a) The orbital angular velocity in radians per second; [Ans:0.0011512 radians/s]
b) The orbital period in minutes; and [Ans:90.97 minutes]
c) The orbital velocity in meters per second. [Ans:7,713.066 m/s]
Note: assume the average radius of the earth is 6,378.137 km and Kepler’s constant has the
value 3.986004418*105 km3/s2.
1.3 An observation satellite is to be placed into a circular equatorial orbit so that it moves in the same
direction as the earth’s rotation. Using a synthetic aperture radar system, the satellite will store
data on surface barometric pressure, and other weather related parameters, as it flies overhead.
These data will later be played back to a controlling earth station after each trip around the
world. The orbit is to be designed so that the satellite is directly above the controlling earth
station, which is located on the equator, once every 4 hours. The controlling earth station’s
antenna is unable to operate below an elevation angle of 10o to the horizontal in any direction.
Taking the earth’s rotational period to be exactly 24 hours, find the following quantities:
a) The satellite’s angular velocity in radians per second. [Ans:0.0005090221 radians/s]
b) The orbital period in hours. [Ans:3.43 hours]
c) The orbital radius in kilometers. [Ans:11,543.96 km]
d) The orbital height in kilometers. [Ans:5,165.83 km]
e) The satellite’s linear velocity in meters per second. [Ans:5876.1306 m/s]
f) The time interval in minutes for which the controlling earth station can communicate with the
satellite on each pass. [Ans:62.72 minutes]
1.4 The orbit for an earth-orbiting satellite has an eccentricity of 0.15 and a semi major axis of 9000
km. at a given observation time during a south to north transit, the height above ground is
measured as 2000 km.
Find the corresponding true anomaly. [Ans:70.14o
]
Note: Assume a mean value of 6371 km for the earth’s radius.
Sana’a University
Faculty of Engineering
Department of Electrical Engineering
Communications and Electronics Section
Communication Systems
2014/2015 2nd
Semester
Prepared by: ALHAJ, Adeeb M., Eng.
Supervised by: NOSARY, Ali N., Dr.

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1.5 Refer to Figure 1.1. Satellite A is orbiting Earth in a near-Earth circular orbit of radius 7000 km.
Satellite B is orbiting Earth in an elliptical orbit with apogee and perigee distances of 47000 km
and 7000 km respectively. Determine the velocities of the two satellites at point X.
(Take 𝝁=39.8×1013m3/s2.) [Ans: The velocity of satellite A at point X=7.54 km/s]
[Ans: The velocity of satellite A at point X=9.95 km/s]
Figure 1.1 Figure for Problem 1.5
1.6 Refer to Figure 1.2. The semi-major axes of the two satellites shown in the figure are 18000 km
(satellite 1) and 24000 km (satellite 2). Determine the relationship between their orbital periods.
[Ans: The orbital period of satellite 2 is 1.54 times that of satellite 1]
Figure 1.2 Figure for Problem 1.6