From Kepler’s third law, an asteroid with an orbital period of 8 years lies at an average distance from the Sun equal to: A. 2 astron

Question

From Kepler’s third law, an asteroid with an orbital period of 8 years lies at an average distance from the Sun equal to:
A. 2 astronomical units.
B. 4 astronomical units.
C. 8 astronomical units.
D. 16 astronomical units.
E. It depends on the asteroid’s mass.

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Vodka 4 years 2021-08-14T16:34:07+00:00 1 Answers 1439 views 0

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  1. mocmien2
    2
    2021-08-14T16:35:16+00:00
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    Answer:

    The correct option is (B).

    Explanation:

    The Kepler’s third law of motion gives the relationship between the orbital time period and the distance from the semi major axis such that,

    T^2\propto a^3\\\\T^2=ka^3

    It is mentioned that, an asteroid with an orbital period of 8 years. So,

    (8)^2=ka^3\\\\64=ka^3\\\\a=(64)^{\dfrac{1}{3}}\\\\a=4\ AU

    So, an asteroid with an orbital period of 8 years lies at an average distance from the Sun equal to 4 astronomical units.

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