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Math Help - Average orbital velocity of planets

  1. #1
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    Average orbital velocity of planets

    Hi,

    I'm having a bit of trouble with this problem.

    The distance D is the distance in millions of miles from the sun, and P is the period in years it takes to revolve one time around the sun.

    Earth:
    D = 92.9
    P = 1.0

    I know that the formula for angular velocity is: omega = theta/t, with t being the time
    and also that the linear speed is: v = radius*omega
    also that 1 revolution is 360 degrees or 2pi

    I think the problem I'm having though is with unit conversion. There are problems for other planets too, but if I can get help with just one, I can figure the rest of them out.
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  2. #2
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    Hello, qleeq!

    The distance D is the distance in millions of miles from the sun,
    and P is the period in years it takes to revolve once around the sun.

    Earth: . D = 92.9,\;P = 1.0

    Find the average orbital velocity of Earth.

    Assuming that Earth's orbit is a circle, its radius is 92,900,000 miles.

    The length of this orbit is: . 2\pi(92,\!900,\!000) \:=\:583,\!707,\!915 miles.

    The Earth travels that far in one year (365 days = 8760 hours).


    Therefore, its average velocity is: . \dfrac{583,\!707,\!915}{8,\!760} \;\approx \;66,\!633 mph.
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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, qleeq!


    Assuming that Earth's orbit is a circle, its radius is 92,900,000 miles.

    The length of this orbit is: . 2\pi(92,\!900,\!000) \:=\:583,\!707,\!915 miles.

    The Earth travels that far in one year (365 days = 8760 hours).


    Therefore, its average velocity is: . \dfrac{583,\!707,\!915}{8,\!760} \;\approx \;66,\!633 mph.
    Ah! I knew it. Thanks a lot. I looked in the solution manual, and it ran me through the unit conversion steps which made it a little more confusing than helpful.
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