Many spacecraft have visited Mars over the years. Mars is smaller than the earth and has correspondingly weaker surface gravity. On Mars, th

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Many spacecraft have visited Mars over the years. Mars is smaller than the earth and has correspondingly weaker surface gravity. On Mars, the free-fall acceleration is only 3.8 m

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Thu Thủy 4 years 2021-09-03T11:19:54+00:00 1 Answers 315 views 0

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  1. Latifah
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    2021-09-03T11:20:56+00:00
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    Incomplete question.The complete one is here

    Spacecraft have been sent to Mars in recent years. Mars is smaller than Earth and has correspondingly weaker surface gravity. On Mars, the free-fall acceleration is only 3.8m/s2. What is the orbital period of a spacecraft in a low orbit near the surface of Mars?

    Answer:

    T=5900s=99min

    Explanation:

    Given

    r_{satelite}=r_{mars}=3.37*10^{6}m\\ g_{mars}=3.8m/s^{2}\\

    To find

    orbital period of a spacecraft T

    Solution

    An the initial calculating is computing the angular velocity of satellite :

    w=\frac{2\pi }{T}\\ w=\frac{2\pi }{110min}(1min/60s)\\ w=9.52*10^{-4}rad/s

    Computing T

    T=\frac{2\pi }{w}\\ as\\w=\sqrt{\frac{a}{r} }\\ So\\T=\frac{2\pi }{\sqrt{\frac{a}{r} }} \\T=\frac{2\pi }{\sqrt{\frac{3.8m/s^{2} }{3.37*10^{6} m} }}\\T=5900s=99min

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