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Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and 720 km above the surface of the Moon, where the acceleration due to gravity is 0.839 m/s2. The radius of the Moon is 1.70 106 m.
(a) Determine the astronaut's orbital speed.

(b) Determine the period of the orbit.

  • physics -

    (a) First you need the value of the acceleration of gravity at the orbit location. Call it g. Here are the steps.

    Moon radius = Rm = 1.7*10^6 m
    Orbit height = H = 7.2*10^5 m
    Orbit radius = R = Rm + H
    = 2.42*10^6 m
    R/Rm = 1.424
    gm (at moon's surface) = 0.839 m/s^2
    g(at orbit radius location) =
    gm/(1.424)^2 = 0.414 m/s^2

    Now set M g = M V^2/R

    Satellite mass M cancels out.
    V^2 = (R*g)
    V = 1000 m/s

    (b) orbit period = 2*pi*R/V
    = 15,210 s
    = 4.2 hours

  • physics -

    The acceleartion due to Gravity is already given at the orbital height. Proceed to use to value of gravitational acceleration given of 0.839m/2^2. The rest of the strategy is all good.

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