A planet of mass m moves around the Sun of mass M in an elliptical orbit. The maximum and minimum distance of the planet from the Sun are r1

Question

A planet of mass m moves around the Sun of mass M in an elliptical orbit. The maximum and minimum distance of the planet from the Sun are r1 and r2, respectively. Find the relation between the time period of the planet in terms of r1 and r2.

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Sapo 3 years 2021-07-15T12:56:27+00:00 1 Answers 16 views 0

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  1. minhkhang
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    2021-07-15T12:58:20+00:00
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    Answer:

    the relation between the time period of the planet is

    T = 2π √[( r1 + r2 )³ / 8GM ]

    Explanation:

    Given the data i  the question;

    mass of sun = M

    minimum and maximum distance = r1 and r2 respectively

    Now, using Kepler’s third law,

    ” the square of period T of any planet is proportional to the cube of average distance “

    T² ∝ R³

    average distance a = ( r1 + r2 ) / 2

    we know that

    T² = 4π²a³ / GM

    T² = 4π² [( ( r1 + r2 ) / 2 )³ / GM ]

    T² = 4π² [( ( r1 + r2 )³ / 8 ) / GM ]

    T² = 4π² [( r1 + r2 )³ / 8GM ]

    T = √[ 4π² [( r1 + r2 )³ / 8GM ] ]

    T = 2π √[( r1 + r2 )³ / 8GM ]

    Therefore, the relation between the time period of the planet is

    T = 2π √[( r1 + r2 )³ / 8GM ]

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