What is the period of the space at a distance 2.4e10m from the center of mercury
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What is the period of the space at a distance 2.4e10m from the center of mercury

[From: ] [author: ] [Date: 12-01-02] [Hit: ]
which, when plugging in numbers, gives us 4.98x10^9 s as the period.......
What is the period of the space at a distance 2.4e10m from the center of mercury?

Mass of mercury is 3.303e23 kg

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mv²/ r = GMm/ r²

v²= GM/ r = 6.673e-11*3.303e23 / 2.4e10

v = 30 m/s

T = 2π R/ v = 2π *2.4e10/ 30 =

T = 5.03 e+9 second
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To use Kepler's law , the distance must be the semi major axis of the ellipse.

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We cannot use F= (mv^2)/r= GMm/r^2 because we cannot assume that the orbit is circular.
We can, however, apply Kepler's Third Law of Orbiting Satellites: T= sqrt((4pi^2)(r^3)/(GM))
which, when plugging in numbers, gives us 4.98x10^9 s as the period.
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