g Two planets are in circular orbits around a star of with unknown mass. One planet is orbiting at a distance r1=150×106 km and has an orbit

Question

g Two planets are in circular orbits around a star of with unknown mass. One planet is orbiting at a distance r1=150×106 km and has an orbital period T1=240 days. The second planet has an orbital radius r2=230×106 km. Find the orbital period of the second planet T2.

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Đan Thu 4 years 2021-07-19T01:47:50+00:00 2 Answers 19 views 0

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  1. Verity
    0
    2021-07-19T01:48:50+00:00
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    Answer:

    Time period of second planet will be 126.40 days

    Explanation:

    We have given radius of first planet r_1=150\times 10^6km=150\times 10^9m

    Orbital speed of first planet T_1=240days

    Radius of second planet r_2=230\times 10^6km=230\times 10^9m

    We have to find orbital period of second planet

    Period of orbital is equal to T=2\pi \sqrt{\frac{r^3}{G(M_1+M_2)}}

    From the relation we can see that T=r^{\frac{3}{2}}

    \frac{T_1}{T_2}=(\frac{r_1}{r_2})^\frac{3}{2}

    \frac{240}{T_2}=(\frac{150\times 10^9}{230\times 10^9})^\frac{3}{2}

    T_2=126.40 days

    Time period of second planet will be 126.40 days

  2. thienan
    0
    2021-07-19T01:49:38+00:00
    Reply

    Answer:

    456 days.

    Explanation:

    Given,

    r₁ = 150 x 10⁶ Km

    r₂ = 230 x 10⁶ Km

    T₁ = 240 days

    T₂ = ?

    Using Kepler’s law

    T^2\ \alpha \ r^3

    Now,

    \dfrac{T_2^2}{T_1^2}=\dfrac{r_2^3}{r_1^3}

    T_2=\sqrt{T_1^2\times \dfrac{r_2^3}{r_1^3}}

    T_2=\sqrt{240^2\times \dfrac{(230\times 10^6)^3}{(150\times 10^6)^3}}

    T_2 = 455.68\ days

    Time taken by the second planer is equal to 456 days.

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