In July 1965, the USSR launched Proton I, weighing 12,200 kg (at launch), with a perigee height of 183 km, an apogee height of 589 km and a period of 92.25 minutes. Using the relevant data for the mass of Earth (5.975 × 10^24 kg) and the gravitational constant G (G = 6.6720 × 10^−11 Nm^2/kg^2 ), find the semimajor axis a of the orbit. Compare your answer with the number you get by adding the perigee and apogee heights to the diameter of the earth (Earth’s radius: 6378.533 km through the equator, 6356.912 km through the poles).
given
T = 92.25 min
= 92.25*60
= 5535 s
let r is the semi-major axis length
we know, T = 2*pi*r^(3/2)/sqrt(G*Me)
T^2 = 4*pi^2*r^3/(G*Me)
r^3 = G*Me*T^2/(4*pi^2)
r = (G*Me*T^2/(4*pi^2))^(1/3)
= (6.67*10^-11*5.975*10^24*5535^2/(4*pi^2))^(1/3)
= 6.76259*10^6 m
= 6762.590 km <<<<<<<-------------Answer
semi major axis length = (6378.533 + 6356.912 + 183 +
589)/2
= 6753.72 km <<<<<<<-------------Answer
In July 1965, the USSR launched Proton I, weighing 12,200 kg (at launch), with a perigee height of 183 km, an apogee hei...