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 9.53 × 102 kg and 2.31 × 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

Etotal = KE + PEg

Radius of orbit , R = 6.37 x 106 m + 2.31 x105m = 6.601 x 106 m

The gravitaional force equal to centripetal force as long as orbit around Earth
G.Me.m / R² = mv² / R

From this equation, the kinetic energy can be expresses as,

½mv² (KE) = G.Me.m / 2R

Now, write equation for gravitaional potential energy

PEg = -G.Me.m / R

Substitute these equation in total energy equation,

Etotal = KE + PEg

= (G.Me.m / 2R) - (G.Me.m / R)

= - G.Me.m / 2R

Substitute given values,

Etotal = - (6.67 x 10-11)(5.98 x1024)(9.53 × 102 kg) / (2 x 6.37 x106)

= - 2.98  x 1010 J

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

E(min) = 2.98  x 1010 J

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