[UColorado] Kepler's 3rd law: p^2 =a^3 for all planets. The period p for the earth is 1 year The distance of the earth to the sun is called 1 A. U. Suppose an asteroid is in circular orbit around the sun at a distance of 2 A. U. How long does it take the asteroid to orbit the sun once?

Explanation:

Given the Kepler's third law

p² = a³

Given that,

Period of earth

P(earth) = 1 year

Distance of earth from sun

a(earth) = 1 A.U

An asteriod that is rotating round the sun is at a distance of 2A.U for the sun

a(asteroid) = 2 A.U

So, we want to calculate period of astronaut I.e. p(asteroid)

Using the Keplers law

p²/a³ = constant

p(earth)²/a(earth)³ = p(asteriod)²/a(asteroid)³

So, p(e)²/a(e)³ = p(a)²/a(a)³

1²/1³ = p(a)²/2³

1 = p(a)/8

p(a) = 8 years

Then, the asteroid will take 8years to round the sun