A satellite orbiting Earth at an orbital radius r has a velocity v. Which represents the velocity if the satellite is moved to an orbital ra

Question

A satellite orbiting Earth at an orbital radius r has a velocity v. Which represents the velocity if the satellite is moved to an orbital radius of 5r?

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Thạch Thảo 4 years 2021-07-26T16:52:52+00:00 1 Answers 44 views 0

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  1. huyenthanh
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    2021-07-26T16:54:50+00:00
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    Answer: The new velociry is v/√5

    Explanation:

    The orbital velocity of something that orbits the planet is:

    v = √(G*M/r)

    where G is the gravitational constant, M is the mass of the earth, and r is the orbital radius.

    If we now have a radius equal to 5r, then the new velocity will be:

    v2 = √(G*M/5r)

    we can take the 1/√5 out, and get:

    v2 = √(G*M/5r) = √(G*M/r)*(1/√5)  

    The first part is equal to the initial velocity, so we can write this as:

    √(G*M/r)*(1/√5) = v/√5

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