Estimate the length of the neptunian year using the fact that the earth is 1.50Ã108km from the sun on average.

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Estimate the length of the neptunian year using the fact that the earth is 1.50Ã108km from the sun on average.

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Orla Orla 5 months 2021-08-03T09:41:36+00:00 1 Answers 6 views 0

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    2021-08-03T09:42:36+00:00

    Answer:

    Explanation:

    We know that,

    Neptune is 4.5×10^9 km from the sun

    And given that,

    Earth is 1.5×10^8km from sun

    Then,

    Let P be the orbital period and

    Let a be the semi-major axis

    Using Keplers third law

    Then, the relation between the orbital period and the semi major axis is

    P² ∝ a³

    Then,

    P² = ka³

    P²/a³ = k

    So,

    P(earth)²/a(earth)³ = P(neptune)² / a(neptune)³

    Period of earth P(earth) =1year

    Semi major axis of earth is

    a(earth) = 1.5×10^8km

    The semi major axis of Neptune is

    a (Neptune) = 4.5×10^9km

    So,

    P(E)²/a(E)³ = P(N)² / a(N)³

    1² / (1.5×10^8)³ = P(N)² / (4.5×10^9)³

    Cross multiply

    P(N)² = (4.5×10^9)³ / (1.5×10^8)³

    P(N)² = 27000

    P(N) =√27000

    P(N) = 164.32years

    The period of Neptune is 164.32years

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