Answer:
E = 3.194 x 10⁹ J = 3.194 GJ
Explanation:
The formula for the absolute potential energy is:
U = - GMm/2r
where,
G = Gravitational Constant = 6.67 x 10⁺¹¹ N m²/kg²
M = mass of Earth = 5.972 x 10²⁴ kg
m = mass of satellite = 470 kg
r = distance between the center of Earth and satellite
Thus, the energy required from engine will be difference between the potential energies.
E = U₂ - U₁
E = - GMm/2r₂ - (- GMm/2r₁)
E = (GMm/2)(1/r₁ - 1/r₂)
where,
r₁ = Radius of Earth + 350 km = 6371 km + 350 km = 6721 km = 6.721 x 10⁶ m
r₂=Radius of Earth + 2350 km=6371 km + 2350 km= 8721 km = 8.721 x 10⁶ m
therefore,
E = [(6.67 x 10⁺¹¹ N m²/kg²)(5.972 x 10²⁴ kg)(470 kg)/2](1/6.721 x 10⁶ m - 1/8.721 x 10⁶ m)
<u>E = 3.194 x 10⁹ J = 3.194 GJ</u>
