Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and 458

Question

Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and 458 km above the surface of the Moon, where the acceleration due to gravity is 1.05 m/s^2. The radius of the Moon is 1.70 ✕ 10^6 m. Determine:

a. The astronaut’s orbital speed.
b. The period of the orbit.

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Sigridomena 4 years 2021-08-28T16:26:42+00:00 2 Answers 5 views 0

Answers ( )

  1. Helga
    0
    2021-08-28T16:28:10+00:00
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    Answer:

    (a) Speed v=1505.3 m/s

    (b) Time Period=9001.56s

    Explanation:

    Radius of moon r=1.70×10⁶m

    Acceleration due to gravity g=1.06m/s²

    height h=458km=458000

    For Part (a)The astronaut’s orbital speed.

    By using the centripetal equation:

    F=\frac{mv^2}{R+h}=mg\\ v^2=g(R+h)\\v=\sqrt{g(R+h)}

    Substitute the given values

    So

    v=\sqrt{1.05m/s^2(1.70*10^6m+458*10^3m)}\\ v=1505.3m/s

    For Part(b) The period of the orbit.

    Total distance=Circumference

    =2\pi (R+h)\\=2\pi (1.70*10^6m+458000m)\\=13.55*10^6m

    Speed v=1505.3m/s

    Time Period=Distance/Velocity

    =\frac{13.55*10^6m}{1505.3m/s}\\ =9001.56s

    Time Period=9001.56s

  2. dangkhoa
    0
    2021-08-28T16:28:13+00:00
    Reply

    Explanation:

    Below is an attachment containing the solution

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