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Kepler's third law: period or orbit radius from the ratio of the other

This type of question, asked 3 times: 9 May 2023 S1, 20 Apr 2025 S2, 19 Apr 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    9 May 2023 S1

    23
    The period of a planet around the sun is 8 times that of Earth. The ratio of radius of planet's orbit to the radius of the Earth's orbit is

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  2. Question 2

    20 Apr 2025 S2

    16
    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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  3. Question 3

    19 Apr 2026 S1

    108
    A geostationary satellite is orbiting the earth at a height of 4R4R above the surface of the earth, where RR is the radius of the earth. Another satellite is orbiting the earth at a height 1.5R1.5R from the surface of the earth with periodic time 'T' in hour. The value of 'T' in hour is

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