Radicals Help!?

The time in years, T, for one complete orbit of a planet around a star can be calculated from the equation:

T=√ Kr3

The average radius, in kilometres, of the planet’s orbit is r, and K is a constant that changes depending on the mass of the star.

(1) Rearrange the equation to isolate K.

Then calculate for K for Earth’s solar system knowing that Earth takes one year to go around the sun and that the radius of Earth’s orbit is 1.49 x 10^8 km from the sun

(2) Calculate how many Earth years it takes Neptune to complete an orbit. Neptune’s average orbital radius is 4.5 x 10^9 km.

2 Answers

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  • Bryce
    Lv 7
    3 months ago

    1. T^2= Kr^3; K=T^2/r^3

    K= [1.49*10^(-8)]^3

    2. r =1.49*10^8/4.5*10^9≈ 30.2

    T= (30.2)^(3/2)≈ 166 years

  • Alan
    Lv 7
    3 months ago

    if you meant

    T = sqrt(Kr^3) and not sqrt( Kr*3)

    square both sizes

    T^2 = Kr^3

    (1)

    K = T^2/r^3

    K = (1 year)^2/ (1.49 X10^8)^3

    K = 3.02302E-25

    (2)

    T= sqrt( 3.02302E-25*( 4.5 x 10^9)^3 ).= 165.9737353 years

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