Question

According to Kepler's Third Law, a solar-system planet that has an orbital period of 8 years would have an orbital radius of about ________ year(s)

Answer 1

Answer:

Orbital period, T = 1.42 years

Explanation:

It is given that,

Orbital period of a solar system planet, $T=8\ years=2.52\times 10^{8}\ s$

The orbital period of the planet can be calculated using third law of Kepler's. It is as follows :

$T^2=\dfrac{4\pi^2}{GM}r^3$

M is the mass of the sun

$r^3=\dfrac{T^2GM}{4\pi^2}$

$r^3=\dfrac{(2.52\times 10^{8})^2\times 6.67\times 10^{-11}\times 1.989\times 10^{30}}{4\pi^2}$    

$r^3=2.134\times 10^{35}$

$r=5.975\times 10^{11}\ m$

r = 1.42 AU

So, the solar-system planet that has an orbital period of 8 years would have an orbital radius of about 1.42 AU.