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A spaceship of mass 1000 kg is to be launched from the Earth's surface into free space (to infinity). Taking g = 10 m/s² and Earth's radius R = 6400 km, calculate the energy required.

1. 6.4 * 10¹⁰ J
2. 6.4 * 10¹¹ J
3. 6.4 * 10⁸ J
4. 6.4 * 10⁹ J

Correct answer: 6.4 * 10¹⁰ J

Solution

To just reach free space (zero total energy at infinity), the energy supplied must equal the binding energy, which is m*g*R when written using g at the surface.

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