The existence of the planet Pluto was proposed based on irregularities in Neptun

Question

The existence of the planet Pluto was proposed based on irregularities in Neptune's orbit. Pluto was subsequently discovered near its predicted position. But it now appears that the discovery was fortuitous, since Pluto is small and the irregularities in Neptune's orbit were not well known. Answer the following to illustrate that Pluto has a minor effect on the orbit of Neptune compared with other planets. (a) Calculate the acceleration of gravity at Neptune due to Pluto when they are 4.20 1012 m apart. The mass of Pluto is 1.4 1022 kg. (b) Calculate the acceleration of gravity at Neptune due to Uranus, when they are 2.80 1012 m apart. The mass of Uranus is 8.62 1025 kg. cGive the ratio of this acceleration to that due to Pluto.
(acceleration from part (b) / acceleration due to Pluto)

Explanation / Answer

A) accelaration due to gravity is g1 = G*M/r^2 =(6.67*10^-11*1.4*10^22)/(4.2^2*10^24) = 5.3*10^-14 m/s^2

B) accelaration duer to gravity is g2 = G*M/r^2 = (6.67*10^-11*8.62*10^25)/(2.8^2*10^24) = 7.33*10^-10 m/s^2

C) g2/g1 = (7.33*10^-10)/(5.3*10^-14) = 13830.18

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