grocery asked in Science & MathematicsMathematics · 3 months ago

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.

Relevance
• 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