Explore BrainMass

Explore BrainMass

    Gravitation: Radius and Period of Orbits

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Question: Calculate the period of a satellite in an orbit just above the Earth's atmosphere (whose thickness may be neglected). Find also the periods for close orbits around the Moon and Jupiter.

    © BrainMass Inc. brainmass.com September 27, 2022, 3:59 pm ad1c9bdddf
    https://brainmass.com/physics/orbits/gravitation-radius-period-orbits-214154

    SOLUTION This solution is FREE courtesy of BrainMass!

    Please see the attachment file.

    Thanks for using BrainMass.

    When a satellite orbits a planet just above its surface, the gravitation force on it acts as the centripetal force.
    Let the mass of the satellite is m, radius of orbit is equal to the radius of planet is R and mass of the planet is M. Then the force of gravitational attraction on the satellite will be

    Now if the angular velocity of rotation of the satellite is w, then the centripetal force required on it will be

    As the gravitational force is the centripetal force we have

    Or
    Or
    Hence the time period of rotation of the satellite will be

    Now for earth
    M = kg
    R = 6.37*106 m
    Substituting we get

    Thus the time period of the satellite of radius nearly equal to earth will be
    5058 s = 1.405 hr.
    Now for Moon
    M = 7.36 kg
    R = 1.74*106 m
    Substituting we get

    Thus the time period of the satellite of radius nearly equal to moon will be
    1036 s = 17.27 min.
    Now for Jupiter
    M = 1.90 kg
    R = 7.0*107 m
    Substituting we get

    Thus the time period of the satellite of radius nearly equal to moon will be
    2.70*106 s = 748.95 hr = 31.21 earth days.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com September 27, 2022, 3:59 pm ad1c9bdddf>
    https://brainmass.com/physics/orbits/gravitation-radius-period-orbits-214154

    Attachments

    ADVERTISEMENT