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Time period and orbit radius of satellites or planets (Kepler's third law)

This type of question, asked 14 times: 2021 Paper 1, 2021 Paper 3, 2021 Paper 8, 2021 Paper 9, 2021 Paper 24, 14 Jun 2022, 29 Jun 2022, 24 Jan 2023, 29 Jan 2023, 29 Jan 2024, 5 Apr 2024, 23 Jan 2025, 24 Jan 2025, 2 Apr 2026 S1. All 14 questions below, oldest first.

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  1. Question 1

    2021 Paper 1

    2
    Consider two satellites S1S_{1} and S2S_{2} with periods of revolution 1hr1hr. and 8hr8hr. respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite S1S_{1} to the angular velocity of satellite S2S_{2} is -

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  2. Question 2

    2021 Paper 3

    7
    Two satellites A and B of masses 200 kg200\text{ }kg and 400 kg400\text{ }kg are revolving round the earth at height of 600 km600\text{ }km and 1600 km1600\text{ }km respectively. If TAT_{A} and TBT_{B} are the time periods of AA and BB respectively then the value of TB−TAT_{B}-T_{A} : [Given : radius of earth =6400 km= 6400\text{ }km, mass of earth =6×1024 kg= 6 \times10^{24}\text{ }kg ]

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  3. Question 3

    2021 Paper 8

    6
    A geostationary satellite is orbiting around an arbitrary planet ' PP ' at a height of 11R11R above the surface of ' PP ', RR being the radius of ' PP '. The time period of another satellite in hours at a height of 2R2R from the surface of ' PP ' is: ('P' rotates once about its axis in 24 hours.)

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  4. Question 4

    2021 Paper 9

    20
    The time period of a satellite in a circular orbit of radius RR is TT. The period of another satellite in a circular orbit of radius 9R9R is:

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  5. Question 5

    2021 Paper 24

    23
    Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour and 8 hours respectively. The radius of the orbit of nearer satellite is 2×103 km2 \times10^{3}\text{ }km. The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is πx rad h−1\frac{\pi}{x}\ \text{rad h}^{- 1} where xx is .....
  6. Question 6

    14 Jun 2022

    92
    The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R3R will be:

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  7. Question 7

    29 Jun 2022

    100
    The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be:

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  8. Question 8

    24 Jan 2023

    96
    If the distance of the earth from Sun is 1.5×106 km1.5 \times10^{6}\text{ }km. Then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is:

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  9. Question 9

    29 Jan 2023

    105
    The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.

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  10. Question 10

    29 Jan 2024

    104
    A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution?

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  11. Question 11

    5 Apr 2024

    109
    A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius of the orbit around the planet is : (Given: radius of the geostationary orbit for earth is 4.2×104 km4.2 \times10^{4}\text{ }km )

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  12. Question 12

    23 Jan 2025

    85
    If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon =27= 27 days and gravitational attraction between the satellite and the moon is neglected.

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  13. Question 13

    24 Jan 2025

    14
    A satellite is launched into a circular orbit of radius ' R ' around the earth. A second statellite is launched into an orbit of radius 1.03 R . The time period of revolution of the second satellite is larger than the first one approximately by :-

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  14. Question 14

    2 Apr 2026 S1

    5
    A planet ( P1P_{1} ) is moving around the star of mass 2 M in the orbit of radius R . Another planet ( P2P_{2} ) is moving around another star of mass 4 M in a orbit of radius 2R2R. Ratio of time periods of revolution of P2P_{2} and P1P_{1} is ____\_\_\_\_ .

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