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At what distance from the centre of the Earth is the net gravitational field due to the Earth and the Moon equal to zero? The mass of the Earth is 6.0 * 10²⁴ kg, the mass of the Moon is 7.4 * 10²² kg, and the centre-to-centre distance between them is 4.0 * 10⁵ km.
- 3.6 * 10⁵ km
- 36 * 10⁵ km
- 3.6 * 10⁶ km
- 3.6 * 10⁸ m
Correct answer: 3.6 * 10⁵ km
Solution
Equating the gravitational fields of Earth and Moon along the line joining them gives r / (d - r) = sqrt(Me / Mm). Solving yields r approximately 3.6 * 10⁵ km from Earth's centre.
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