Question

***Answer for a medal***

Planet A takes 1 year to go around its star at an average of 1 A.U. distance. Planet B is 4 A.U. from the star. Calculate how long Planet B takes to orbit.

______________ years

512
64
23
8

Answer 1

can i get some help please :'(

Answer 2

I guess the answer is 8.
by kepler's third law,
\[T ^{2} \alpha A^{3}\]
T=time in years
A=Astronomical Unit.
as A=4 therfore \[A ^{3}=64\]
and \[T ^{2}=64 \]
hence T=8

But it is not the correct answer you should try the formula\[T^{2}=\left( \frac{ 4\pi ^{2} }{ GM } \right)A ^{3}\]
where M=mass of the Sun=\[2\times10^{30}kg\]
and G is gravitational constant=\[6.67\times10^{-11}Nm ^{2}/kg ^{2}\]
1AU=\[1.5\times10^{8}km\]

I tried it but there must some calculation error, Best of luck for you.

Answer 3

\[T^2 \to a^3\] - kepler's law of planetary motion.

so around the same star, let orbital parameters for planet A be T1 , a1
and for Planet B, T2, a2
hence,
\[T2^2/T1^2 = A2^3/A1^3\]
T1 = 1, A1 = 1, A2 = 4
hence,
\[T2 = \sqrt{64} = 8\]
in years