If there was no gravity, we could hold the Moon in orbit around the Earth by giv

Question

If there was no gravity, we could hold the Moon in orbit around the Earth by giving the
Earth a positive charge and the moon an equal but opposite (negative) charge. What
would be the magnitude of the required charge? What would be the surface charge
density of this charge at the Moon? What would be the electric field just above the
Moon’s surface along a line between the Earth and the Moon. What would be the voltage
between the Earth and Moon? You may assume that the charges on both bodies are
uniformly distributed over their surfaces.

Explanation / Answer

m1 * m2 = q^2 mass of Earth = 5.9742 × 1024 kilograms mass of the Moon = 7.36 × 1022 kilograms radius of the moon = 1 737.4 kilometers 5.9742 × 10^24 * 7.36 × 10^22 = q^2 charge , q = 6.629 * 10 ^(23) C charge density on moon = - 6.629 * 10 ^(23) / 4 * pi* r^2 = -1.7477*10^(10) C/m2

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