g question, An asteroid is discovered in a nearly circular orbit around the Sun, with an orbital radius that is 3.83 times Earth’s. What is

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g question, An asteroid is discovered in a nearly circular orbit around the Sun, with an orbital radius that is 3.83 times Earth’s. What is the asteroid’s orbital period T , its “year,” in terms of Earth years

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Kiệt Gia 4 years 2021-08-06T14:03:26+00:00 1 Answers 39 views 0

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  1. Eirian
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    2021-08-06T14:05:14+00:00
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    Answer:

    Therefore the asteroids’s orbital period is 7.45 years.

    Explanation:

    Kapler’s third law:

    The orbital period of a planet squared is directly proportional to  the average distance of the planet from the sun cubed.

    T^2\propto r^3

    T = orbital period of the planet

    r = orbital radius of the planet

    \therefore \frac{T_1^2}{T_2^2}=\frac{R_1^3}{R_2^3}

    Here T_1 = Orbital period of the asteroid

    R_1= Orbital radius of the asteroid

    T_2=  Orbital period of Earth = 1 year

    R_2 =Orbital radius of Earth

    Given that the orbital radius of asteroid is 3.83 times of orbital radius of Earth.

    R_1 = 3.83R_2

    \frac{R_1}{R_2}=3.83

    Therefore

    \therefore \frac{T_1^2}{T_2^2}=\frac{R_1^3}{R_2^3}

    \Rightarrow ( \frac{T_1}{T_2})^2=(\frac{R_1}{R_2})^3

    \Rightarrow ( \frac{T_1}{T_2})^2=(3.83)^3

    \Rightarrow \frac{T_1}{T_2}=(3.83)^\frac32

    \Rightarrow {T_1=(3.83)^\frac32\times T_2

    \Rightarrow T_1= 7.45\times (1 \ year)    [T_2= 1 year]

    \Rightarrow T_1= 7.45 \ years

    Therefore the asteroids’s orbital period is 7.45 years.

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