​[UColorado] Kepler’s 3rd law: p^2 =a^3 for all planets. The period p for the earth is 1 year The distance of the earth to the sun is called

Question

​[UColorado] Kepler’s 3rd law: p^2 =a^3 for all planets. The period p for the earth is 1 year The distance of the earth to the sun is called 1 A.U. Suppose an asteroid is in circular orbit around the sun at a distance of 2 A.U. How long does it take the asteroid to orbit the sun once?

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Thanh Hà 2 days 2021-07-22T00:01:13+00:00 1 Answers 0 views 0

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    2021-07-22T00:02:53+00:00

    Answer:

    Explanation:

    Given the Kepler’s third law

    p² = a³

    Given that,

    Period of earth

    P(earth) = 1 year

    Distance of earth from sun

    a(earth) = 1 A.U

    An asteriod that is rotating round the sun is at a distance of 2A.U for the sun

    a(asteroid) = 2 A.U

    So, we want to calculate period of astronaut I.e. p(asteroid)

    Using the Keplers law

    p²/a³ = constant

    p(earth)²/a(earth)³ = p(asteriod)²/a(asteroid)³

    So, p(e)²/a(e)³ = p(a)²/a(a)³

    1²/1³ = p(a)²/2³

    1 = p(a)/8

    p(a) = 8 years

    Then, the asteroid will take 8years to round the sun

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