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Math

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The period of revolution of a planet around the sun is the time it takes for the planet to complete one orbit of the sun. The period, P years, is give by Kepler's third law P^2=D^3, where D is the average distance from the sun in astronomical units (AU). One AU is the average distance f the Earth fromt he sun. Use the average distance formt he sun to find the period of revolution for Jupiter; 5.20 AU to the nearest tenth of a year.

I don't get that, the teacher said the answer was 11.9 I think. Anyone care to explain how?

Thanks

  • Math - ,

    Easy.

    5.20 AU is the distance so:

    P^2=D^3 is equivalent to:
    P^2=5.20^3
    5.20^3 is 140.608, 140.608 is the period.
    So the new equation would be:
    P^2=140.608
    Since you now know that 140.608 is the period squared, the opposite of squaring is square rooting. So this is how you would write it.
    ã140.608=11.85782442
    It asked for the nearest tenth of the year so rounding up would make the answer 11.9
    So the period of revolution for Jupiter is 11.9 years.

    -Don

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