The sputnik one satellite orbiting earth mass equals 5.98×10 to the 24th power kilograms in a circle of radius 6.96×10 to the six power mete

Question

The sputnik one satellite orbiting earth mass equals 5.98×10 to the 24th power kilograms in a circle of radius 6.96×10 to the six power meters what was its orbital velocity

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Thu Thủy 5 years 2021-09-02T20:48:24+00:00 1 Answers 26 views 0

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  1. kimchi2
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    2021-09-02T20:50:06+00:00
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    Answer:

    7572 m/s

    Explanation:

    The force between two masses separated by a distance r is given as:

    F=G\frac{m_1m_2}{r^2}

    Where F is the attractive force between 2 masses, m1 and m2, r is the distance between the centres of the masses and G is the universal gravitation constant, which is 6.674*10^-11 Nm^2/kg^2

    The mass of the earth (m_1) is far greater than the mass of the sputnik (m_2). Therefore m_1m_2=m_1. The mass of the sputnik is neglected, therefore:

    F=G\frac{m_1}{r^2}=\frac{(6.674*10^{-11})(5.98*10^{24})}{(6.96*10^6)^2} = 8.2389N

    But F is actually centripetal acceleration, a = v²/r

    8.2389 = v^2 / 6.96*10^6\\v=7572m/s

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