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March 29, 2017

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While visiting Planet Physics, you toss a rock straight up at 13.6 m/s and catch it 3.50 s later. While you visit the surface, your cruise ship orbits at an altitude equal to the planet's radius every 340.0 minutes.

What is the mass (in kg) of the planet?

  • Physics help please - ,

    The time of flight of the tossed rock is T = 2 Vo/g = 3.50 s.
    Therefore the local value of g is
    2 Vo/T = 7.77 m/s^2

    The value of g is related to the radius R and mass M of the planet by
    g = G*M/R^2

    From the period of the orbit, you know that the orbital velocity is
    V = 2*pi*R/P
    where P is the known period, 20,400 s.
    Since m V^2/R = m g,
    4*pi^2*R/P^2 = 7.77 m/s^2
    That equation can be solved for the orbit radius, R.
    Then use g = G*M/R^2 for M

    G is the universal constant of gravity,
    6.67*10^-11 N m^2/kg^2

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