Explanation (Complete Conceptual Solution)

Total energy of a satellite in circular orbit:

\[ E = -\frac{GMm}{2r} \]

Using \( GM = gR_E^2 \)

\[ E = -\frac{gR_E^2 m}{2r} \]

Initial radius:

\[ r_1 = 1.5R_E \]

\[ E_1 = -\frac{gR_E^2 m}{2(1.5R_E)} \]

\[ E_1 = -\frac{gR_E m}{3} \]

Final radius:

\[ r_2 = 3R_E \]

\[ E_2 = -\frac{gR_E^2 m}{2(3R_E)} \]

\[ E_2 = -\frac{gR_E m}{6} \]

Energy supplied:

\[ \Delta E = E_2 - E_1 \]

\[ \Delta E = -\frac{gR_E m}{6} + \frac{gR_E m}{3} \]

\[ \Delta E = \frac{gR_E m}{6} \]

Substitute values:

\[ g = 10,\quad R_E = 6×10^6,\quad m=100 \]

\[ \Delta E = \frac{10 × 6×10^6 × 100}{6} \]

\[ \Delta E = 10^9 \text{ J} \]

\[ = 1000 × 10^6 \text{ J} \]

Final Answer = 1000

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