The average distance of the planet mercury from the sun is 0.39 times the average distance of the earth from the sun. How long is a year on

Question

The average distance of the planet mercury from the sun is 0.39 times the average distance of the earth from the sun. How long is a year on mercury in units of earth years?

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Adela 3 years 2021-09-03T08:00:23+00:00 1 Answers 9 views 0

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  1. trucchi
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    2021-09-03T08:01:33+00:00
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    Answer:

    T_1=0.24y

    Explanation:

    Using Kepler’s third law, we can relate the orbital periods of the planets and their average distances from the Sun, as follows:

    (\frac{T_1}{T_2})^2=(\frac{D_1}{D_2})^3

    Where T_1 and T_2 are the orbital periods of Mercury and Earth respectively. We have D_1=0.39D_2 and T_2=1y. Replacing this and solving for

    T_1^2=T_2^2(\frac{D_1}{D_2})^3\\T_1^2=(1y)^2(\frac{0.39D_2}{D_2})^3\\T_1^2=1y^2(0.39)^3\\T_1^2=0.059319y^2\\T_1=0.24y

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