Question

A satellite is moving with mean motion of 7.2815x10^-5 rad/s in a circular equatorial orbit with a semi major axis of 42150 km. Assume a mean earth radius of 6371 km, Kepler’s constant of 3.986005 x10⁵ km³/s² and k₁= 66063.1704 km^2. Determine:

            i)   Orbital period in hour, minutes and second.

            ii) Velocity of satellite.

            iii) Rate of regression of the nodes and

            iv) Rate of rotation of line of apsides

Answer 1

given, satellite
w = 7.2815*10^-5 rad/s
r = 42150 km
R = 6371 km
k = keplers constant = 3.986005*10^5 km ^3 / s^2
k1 = 66063.1704 km^2

i. orbital period = T
T = sqrt(k*r^3)
T = 5463428804202923581.8297 s
T = 91057146736715393.030 m
T = 1517619112278589.883 h
T = 63234129678274.578 d
T = 9033447096896.36 w
T = 172394028566.72 y
T = 172394028.56672 millenia
  
2. velocity of satellite = v
v = w*r = 3069.15225 m/s
  
3. rate of regression of nodes = wp
wp = -1.5*Re^2 J2 * w * cos i / (r ( 1 - e^2))^2
for circle, e = 0,
for orbit on equitorial plane, i = 0, cos(i) = 1
J2 for eartjh is 1.082*10^-3
wp = -1.5*6371,000^2* J2 * w /r^2
wp = -2.699*10^-9 rad/s
  
4. rate of rotation of line of apsides = w'
w' = 1.5(GM)(C - A)cos(eeta)/Cw*r^3(1 - e^2)^1.5
e = 0
w' = 1.5(GM)(C - A)cos(eeta)/Cw*r^3
herre
we need C - A to be able to calculate the whole rate of rotation of line of apsides