Page 92 - Satellite Communications, Fourth Edition

72 Chapter Two

2.12. Explain what is meant by the ascending and descending nodes. In what
units would these be measured, and in general, would you expect them to change
with time?
2.13. Explain what is meant by (a) line of apsides and (b) line of nodes. Is it
possible for these two lines to be coincident?

2.14. With the aid of a neat sketch, explain what is meant by each of the
angles: inclination; argument of perigee; right ascension of the ascending node.
Which of these angles would you expect, in general, to change with time?

2.15. The inclination of an orbit is 67°. What is the greatest latitude, north and
south, reached by the subsatellite point? Is this orbit retrograde or prograde?
2.16. Describe briefly the main effects of the earth’s equatorial bulge on a
satellite orbit. Given that a satellite is in a circular equatorial orbit for which
the semimajor axis is equal to 42,165 km, calculate (a) the mean motion, (b) the
rate of regression of the nodes, and (c) the rate of rotation of argument of perigee.

2.17. A satellite in polar orbit has a perigee height of 600 km and an apogee
height of 1200 km. Calculate (a) the mean motion, (b) the rate of regression of
the nodes, and (c) the rate of rotation of the line of apsides. The mean radius of
the earth may be assumed equal to 6371 km.

2.18. What is the fundamental unit of universal coordinated time? Express the
following times in (a) days and (b) degrees: 0 h, 5 min, 24 s; 6 h, 35 min, 20 s;
your present time.

2.19. Determine the Julian days for the following dates and times: midnight
March 10, 1999; noon, February 23, 2000; 16:30 h, March 1, 2003; 3 P.M.,
July 4, 2010.

2.20. Find, for the times and dates given in Prob. 2.19, (a) T in Julian centuries
and (b) the corresponding GST in degrees.

2.21. Find the month, day, and UT for the following epochs: (a) day 3.00, year
1999; (b) day 186.125, year 2000; (c) day 300.12157650, year 2001; (d) day
3.29441845, year 2004; (e) day 31.1015, year 2010.

2.22. Find the GST corresponding to the epochs given in Prob. 2.21.
2.23. The Molnya 3-(25) satellite has the following parameters specified: perigee
height 462 km; apogee height 40,850 km; period 736 min; inclination 62.8°.
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.