Page 94 - Satellite Communications, Fourth Edition

74 Chapter Two

2.33. Determine, for the satellite listed in the NASA bulletin of App. C, the rate
of regression of the nodes, the rate of change of the argument of perigee, and
the nominal mean motion n 0 .
2.34. From the NASA bulletin in App. C, verify that the orbital elements
specified are for a nominal S–N equator crossing.

2.35. A satellite in exactly polar orbit has a slight eccentricity (just sufficient
to establish the idea of a perigee). The anomalistic period is 110 min. Assuming
that the mean motion is n n 0 calculate the semimajor axis. Given that at epoch
the perigee is exactly over the north pole, determine the position of the perigee
relative to the north pole after one anomalistic period and the time taken for
the satellite to make one complete revolution relative to the north pole.
2.36. A satellite is in an exactly polar orbit with apogee height 7000 km and
perigee height 600 km. Assuming a spherical earth of uniform mass and radius
6371 km, calculate (a) the semimajor axis, (b) the eccentricity, and (c) the orbital
period. (d) At a certain time the satellite is observed ascending directly overhead
from an earth station on latitude 49°N. Give that the argument of perigee is 295°
calculate the true anomaly at the time of observation.

2.37. The 2-line elements for satellite NOAA 18 are as follows:
NOAA 18
1 28654U 05018A 05154.51654998-.00000093 00000-0-28161-4 0 189
2 28654 98.7443 101.8853 0013815 210.8695 149.1647 14.10848892 1982
Determine the approximate values of (a) the semimajor axis, and (b) the latitude
of the subsatellite point at epoch.
2.38. Using the 2-line elements given in Prob. 2.37, determine the longitude,
of the subsatellite point and the LST at epoch.
2.39. Equation 2.34, gives the GST in degrees as

2
GST 99 .9610 36000 .7689 T 0.0004 T UT
where T is the number of Julian centuries that have elapsed since noon, January
0, 1900. The GST equation is derived from (Wertz 1984) GST s 180 UT
where a s is the right ascension of the mean sun. Determine the right ascension
of the mean sun for noon on June 5, 2005.

2.40. Assuming that the orbits detailed in Table 2.5 are circular, and using
Eq. (2.2) to find the semimajor axis, calculate the regression of the nodes for
these orbits.

2.41. Determine the standard zone time in the following zones, for 12 noon
GMT: (a) 285°E, (b) 255°E, (c) 45°E, (d) 120°E.