In a futuristic scenario, you are assigned the mission of making inoperative an

Question

In a futuristic scenario, you are assigned the mission of making inoperative an enemy satellite that is in a circular orbit around Earth. You know you cannot destroy the satellite, as it is well protected against attack. But you can try to knock it out of its orbit so it will fly away and never return. What is the minimum amount of work applied to the satellite that is required to accomplish that? The satellite's mass and altitude are 9.99 × 102 kg and 2.79 × 102 km. Earth's mass and radius are 5.98 × 1024 kg and 6.37 × 103 km.

Explanation / Answer

The total energy of the satellite in it's orbit Et = KE + GPE

Orbit radius .. R = 6.37 x 10^6m + 2.79 x 10^5m = 6.65 x 10^6m

gravitatinal attraction provides the centripetal force (satellite mass m)
G.Me.m / R² = mv² / R from here ½mv² (KE) = G.Me.m / 2R

Gravitatinal potential energy GPE = -G.Me.m / R

Et = KE+GPE = (G.Me.m / 2R) - (G.Me.m / R)
Et = - G.Me.m / 2R
Et = - (6.67x 10^-11)(5.98 x 10^24)(9.99 x 10^2) / (2 x 6.65 x 10^6) .= 2.996 x 10^10 J

The 'never return' point is infinity .. where Earth's grav attraction is zero
Net energy at infinity = 0 .. {GPE = 0, KE = 0 (minimum)}

Orbit energy (Et) + min energy (work) required = 0 (at infinity)

-2.996 x 10^10 J + E(min) = 0

E(min) = 2.996 x 10^10 J

Minimum amount of work applied to the satellite to knock it out is 2.996 x 1010 J

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