Calculate the mass of Pluto in terms of the Earth’s masses if its satellite Charon is at a distance of 19,600 km

bystudin | November 15, 2020 | Education

Calculate the mass of Pluto in terms of the Earth’s masses if its satellite Charon is at a distance of 19,600 km, and its sidereal period is 6.4 days. Take the Moon as the second body, the sidereal period of which is 27.3 days, the distance to the Earth is 384,000 km.

a1 ^ 3 / a2 ^ 3 = T1 ^ 2 * M / T2 ^ 2 * M2; M1 = a1 ^ 3 * T2 ^ 2 / a2 ^ 3T1 ^ 2; M1 = (1.96 * 10 ^ 4) ^ 3 * 27.32 ^ 2 / (3.84 * 10 ^ 5) ^ 3 * 6.4 ^ 2 = 2.4 * 10 ^ -3
Mpluton = 2.4 * 10 ^ -3M earth

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