Question

The space shuttle is in a 350 km -high circular orbit. It needs to reach a 510 km -high circular orbit to catch the Hubble Space Telescope for repairs. The shuttle's mass is 6.50×104 kg .

How much energy is required to boost it to the new orbit?

Express your answer with the appropriate units.

Answer 1

here,

height of circular orbit

h1 = 3.5 * 10^5 m

height of telescope circular orbit ,

h2 = 5.1 * 10^5 m

mass of the shuttle , ms = 6.5 * 10^4 kg

mass of earth , me = 5.98 * 10^24 kg

radius of earth , r = 6.37 * 10^6 m

the energy neede , E = G*me*ms /2( h1 + re) - G*me*ms /2( h2 + re)

E = 6.67 * 10^-11 * 5.98 * 10^24*6.5 * 10^4 *0.5*[ ( 1/(3.5 * 10^5 + 6.37 * 10^6 )) - {1/( 6.37 * 10^6 +5.1 * 10^5 )} ]

E = 4.486 10^10 J

energy is required to boost it to the new orbit is 4.486* 10^10 J