Uranus, the seventh planet in the solar system, was first

Chapter , Problem 95

(choose chapter or problem)

Uranus, the seventh planet in the solar system, was first observed in 1781 by William Herschel. Its orbit was then analyzed in terms of Keplers laws. By the 1840s, observations of Uranus clearly indicated that its true orbit was different from the Keplerian calculation by an amount that could not be accounted for by observational uncertainty. The conclusion was that there must be another influence other than the Sun and the known planets lying inside Uranuss orbit. This influence was hypothesized to be due to an eighth planet, whose predicted orbit was described independently in 1845 by two astronomers: John Adams (no relation to the former president of the United States) and Urbain LeVerrier. In September of 1846, John Galle, searching in the sky at the place predicted by Adams and LeVerrier, made the first observation of Neptune. Uranus and Neptune are in orbit about the Sun with periods of 84.0 and 164.8 years, respectively. To see the effect that Neptune had on Uranus, determine the ratio of the gravitational force between Neptune and Uranus to that between Uranus and the Sun, when Neptune and Uranus are at their closest approach to one another (i.e., when aligned with the Sun). The masses of the Sun, Uranus, and Neptune are 333,000, 14.5, and 17.1 times that of Earth, respectively.