Question

taking the earth to be uniform sphere of radius 6400 km, calculate the total energy needed to raise a satellite of mass 2000 kg to a hight of 800 km above the ground and to set it into circular orbit at that attitude​

Answer 1

Explanation:

Initial energy= R

GMm

Here, m=mass of the satellite and M=mass of the earth

Final energy= (R+h)

GMm

Change in energy=Final energy-Initial energy

R+h

GMm

R

GMm =GMm[

R(R+h)

h

]=

R

2

GM

m[

R+h

Rh

]

Energy needed=g.m(

R+h

Rh

)

where,g=

R

2

GM

∴Energy needed =10×2000[

6400×10

3

+800000

6400×10

3

×800000

]=1.4×10

10

J