1).

prove mathematically the truth of the following statement which appears in

the October 1945 paper:

The velocity of 8 km/sec. applies only to the closest possible orbit, one just outside the

atmosphere and the period of revolution would be about 90 minutes.

2).

Show that for the ellipse the differential element of area dA = r^2 dv/2,

where dis the differential of the true anomaly. Using Kepler’s second law,

show that the ratio of the speeds at apoapsis and periapsis (or apogee and

perigee for an earth-orbiting satellite) is equal to

(1 e)/(1 e)

3).

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

4).

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

n0

. (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.

any guidance will be much appreciated !