A spaceship of mass m travels from the Earth to the Moon along a line that passes through the center of the Earth and the center of the Moon. At some point along the journey, the gravitational force on the spaceship due to the Earth is twice the magnitude of the corresponding force due to the Moon. Calculate the ratio of the distance between the Moon and the spaceship to the distance between the Earth and the spaceship at that point, r_M-s/r_E-s. You can use M_E = 5.97 x 10^24 kg and m_M = 7.35 x 10^22 kg. If the distance between the Earth and Moon is 3.84 x 10^8 m, what is the distance between the spaceship and the Earth in units of 10^8 m at that point?
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We are given: - Mass of the Earth, \( M_E = 5.97 \times 10^{24} \) kg - Mass of the Moon, \( M_M = 7.35 \times 10^{22} \) kg - The gravitational force due to the Earth is twice the gravitational force due to the Moon at a certain point. Show more…
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