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Gravitational Perturbation1

# Gravitational Perturbation1 - 1 The Sun is so massive...

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Gravitational Perturbations and the Prediction of New Planets Computing the orbit of the Earth as an ellipse around the center of mass for the Earth-Sun system assumes that they are the only two masses in the Universe. In reality, the Universal Law of Gravitation implies that the Earth interacts gravitationally not only with the Sun, but with every other mass in the Universe: the Moon, the other planets, asteroids and comets, the distant stars. The Two-Body Approximation However, from the form of the gravitational force we see that the interactions are largest when two situations are fulfilled: (1) the product of the masses of the two objects is large, which maximizes the numerator of the expression for the strength of the gravitational force, and (2) the objects are near each other, which minimizes the denominator of the force equation. The two-body approximation that the orbits of the planets are determined only by the gravitational interaction between the Sun and the planet is possible because

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Unformatted text preview: 1. The Sun is so massive compared with every other object in the Solar System, 2. Objects outside the Solar System such as stars are so distant that the distance squared factor in the denominator renders their gravitational interactions with the planets negligible. For example, the Sun is about 300,000 times more massive than the Earth, and about 1000 times more massive than the largest planet. Thus, the product of the mass of a planet and the mass of the Sun is always much larger than the product of the masses of any two planets, and it is a good initial approximation to neglect all interactions except that of the planet and the Sun. EXERCISE: use the Astrophysical Calculator to compare the products of the masses of the Sun and Mars with the product of the masses of Mars and the Earth. The answer is the ratio of the masses of the Sun and the Earth, which is about 300,000, as noted above....
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Gravitational Perturbation1 - 1 The Sun is so massive...

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