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The existence of the dwarf planet Pluto was proposed based
Chapter 6, Problem 40(choose chapter or problem)
The existence of the dwarf 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, because Pluto is small and the irregularities in Neptune’s orbit were not well known. To illustrate that Pluto has a minor effect on the orbit of Neptune compared with the closest planet to Neptune:
(a) Calculate the acceleration due to gravity at Neptune due to Pluto when they are \(4.50 \times 10^{12}\) m apart, as they are at present. The mass of Pluto is \(1.4 \times 10^{22}\) kg.
(b) Calculate the acceleration due to gravity at Neptune due to Uranus, presently about \(2.50 \times 10^{12}\) m apart, and compare it with that due to Pluto. The mass of Uranus is \(8.62 \times 10^{25}\) kg.
Questions & Answers
QUESTION:
The existence of the dwarf 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, because Pluto is small and the irregularities in Neptune’s orbit were not well known. To illustrate that Pluto has a minor effect on the orbit of Neptune compared with the closest planet to Neptune:
(a) Calculate the acceleration due to gravity at Neptune due to Pluto when they are \(4.50 \times 10^{12}\) m apart, as they are at present. The mass of Pluto is \(1.4 \times 10^{22}\) kg.
(b) Calculate the acceleration due to gravity at Neptune due to Uranus, presently about \(2.50 \times 10^{12}\) m apart, and compare it with that due to Pluto. The mass of Uranus is \(8.62 \times 10^{25}\) kg.
ANSWER:Step 1 of 3
Given data:
The distance between Neptune and Pluto is \(4.50 \times {10^{12}}\;\;{\rm{m}}\) .
The mass of Pluto is \(1.4 \times {10^{22}}\;{\rm{kg}}\) .
The distance between Neptune and Uranus \(2.50 \times {10^{12}}\;\;{\rm{m}}\).
The mass of Uranus is \(8.62 \times {10^{25}}\;{\rm{kg}}\).
Step 2 of 3
(a)
Gravitational Acceleration is the acceleration of an object caused by the force of gravity from another object. Below mentioned formula calculate acceleration due to gravity at Neptune due to Pluto.
\({g_{nep/pl}} = \frac{{GM}}{{{R^2}}} \)
Here, \({g_{nep/pl}}\) is the acceleration due to gravity at Neptune due to Pluto, G is the gravitational constant, M is mass of Pluto and R is distance between Neptune and Pluto.
Substitute the values in the above expression, and we