Page 93 - Satellite Communications, Fourth Edition

Orbits and Launching Methods 73

2.24. Repeat the calculations in Prob. 2.23 for an inclination of 63.435°.

2.25. Determine the orbital condition necessary for the argument of perigee
to remain stationary in the orbital plane. The orbit for a satellite under this
condition has an eccentricity of 0.001 and a semimajor axis of 27,000 km. At a
given epoch the perigee is exactly on the line of Aries. Determine the satellite
position relative to this line after a period of 30 days from epoch.

2.26. For a given orbit, K as defined by Eq. (2.11) is equal to 0.112 rev/day.
Determine the value of inclination required to make the orbit sun synchronous.

2.27. A satellite has an inclination of 90° and an eccentricity of 0.1. At epoch,
which corresponds to time of perigee passage, the perigee height is 2643.24 km
directly over the north pole. Determine (a) the satellite mean motion. For 1 day
after epoch determine (b) the true anomaly, (c) the magnitude of the radius
vector to the satellite, and (d) the latitude of the subsatellite point.
2.28. The following elements apply to a satellite in inclined orbit: Ω 0 0°; w 0
90°; M 0 309°; i 63°; e 0.01; a 7130 km. An earth station is situated
at 45°N, 80°W, and at zero height above sea level. Assuming a perfectly spherical
earth of uniform mass and radius 6371 km, and given that epoch corresponds
to a GST of 116°, determine at epoch the orbital radius vector in the (a) PQW
frame; (b) IJK frame; (c) the position vector of the earth station in the IJK frame;
(d) the range vector in the IJK frame; (e) the range vector in the SEZ frame;
and (f) the earth station look angles.

2.29. A satellite moves in an inclined elliptical orbit, the inclination being
63.45°. State with explanation the maximum northern and southern latitudes
reached by the subsatellite point. The nominal mean motion of the satellite is
14 rev/day, and at epoch the subsatellite point is on the ascending node at
100°W. Calculate the longitude of the subsatellite point 1 day after epoch. The
eccentricity is 0.01.
2.30. A “no name” satellite has the following parameters specified: perigee
height 197 km; apogee height 340 km; period 88.2 min; inclination 64.6°.
Using an average value of 6371 km for the earth’s radius, calculate (a) the
semimajor axis and (b) the eccentricity. (c) Calculate the nominal mean motion
n 0 . (d) Calculate the mean motion. (e) Using the calculated value for a,
calculate the anomalistic period and compare with the specified value.
Calculate (f ) the rate of regression of the nodes, and (g) the rate of rotation
of the line of apsides.

2.31. Given that Ω 0 250°, w 0 85°, and M 0 30° for the satellite in Prob.
2.30, calculate, for 65 min after epoch (t 0 0) the new values of Ω, w, and M.
Find also the true anomaly and radius.
2.32. From the NASA bulletin given in App. C, determine the date and the
semimajor axis.