1) For an orbit with perigee altitude of 300 km and apogee altitude of 800 km, what is the magnitude of the position vector (in km) when the spacecraft has just passed perigee by 30 deg? 2) The...

1) For an orbit with perigee altitude of 300 km and apogee altitude of 800 km, what is the magnitude of the position vector (in km) when the spacecraft has just passed perigee by 30 deg?
Solution:
Ra = 800 + r+ = 6378+800 =1.12 +1 = 2.12 DU+
Rp = 300 + r+ = 6378+300 =1.04 +1 = 2.04 DU+
The orbit eccentricity,
e = ra – rp/ ra + rp
= 0.08/4.16 = 0.019
The specific angular momentum of the spacecraft,
Semi-latus Rectum , P = (1 + e) rp
P = (1 + 0.019) 2.04 = 2.08
Then, II = √ (u+ . P) = √ 2.08 = 1.44 DU+2/ TU+
2) The NPSAT-1 satellite was launched in June 2019 into a circular orbit of 720 km altitude by 24 deg inclination. What is its period in seconds?
Solution: As we know, V = √ GM/R
So, V = √ (6.67 x 1011x 5.97 x 10 24 / 7.1 x 106)
V = 7489 m/sec
Now, T is period in seconds and
T = 2π R / V
So,
T = 2π (7.1 x 10 6)/ 7489
T = 5957 seconds
3) For a spacecraft orbiting the earth with perigee altitude of 250 km and apogee altitude of 26,500 km, what is its specific mechanical energy (km2/sec2)?
Solution :
Specific mechanical energy of the satellite
ɛ = - u+/ 2a where 2a is ra + rp
rp = (6375 + 250) x 1000 = 6625000 km
ra = (6375 + 26500) x 1000 =...