Problem 6. Rings around the moon The mass of the Earth is 5.97 × 1024 kg. Our moon has a mass of 7.35 x 1022 kg and a radius of 1.74 × 106 m. (a) At what point directly between the centers of the Earth and the moon will a small body experience zero net gravitational force due to these two bodies? (b) A spacecraft is maintaining a circular orbit around the moon, near its surface. How much more mechanical energy per unit mass of the spacecraft must it gain in order to reach the point in (a)?

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Chapter1: Units, Trigonometry. And Vectors
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Problem 6. Rings around the moon
The mass of the Earth is 5.97 × 1024 kg. Our moon has a mass of 7.35 × 1022 kg and a radius of
1.74 × 106 m.
(a) At what point directly between the centers of the Earth and the moon will a small body
experience zero net gravitational force due to these two bodies?
(b) A spacecraft is maintaining a circular orbit around the moon, near its surface. How much more
mechanical energy per unit mass of the spacecraft must it gain in order to reach the point in
(a)?
Transcribed Image Text:Problem 6. Rings around the moon The mass of the Earth is 5.97 × 1024 kg. Our moon has a mass of 7.35 × 1022 kg and a radius of 1.74 × 106 m. (a) At what point directly between the centers of the Earth and the moon will a small body experience zero net gravitational force due to these two bodies? (b) A spacecraft is maintaining a circular orbit around the moon, near its surface. How much more mechanical energy per unit mass of the spacecraft must it gain in order to reach the point in (a)?
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