Saturn is 9.57 au far from the sun
What is third law of Kepler ?
Kepler's third law, also called the law of periods, states that the square of the orbital period is proportional to the cube of its mean distance R.
Let time period of earth = T (e)
Time period of Saturn will be = T(s) = 29.5 T(e)
(since , it is given that Saturn orbits every 29.5 years )
distance of earth from sun = r(e) = 1.5 * [tex]10^{11}[/tex] m
distance of Saturn from the sun = r(s) = ?
using Kepler's third law
[tex]T^{2}[/tex] is directly proportional to [tex]r^{3}[/tex]
[tex]T(s)^{2}[/tex]/[tex]T(e)^{2}[/tex] = [tex]r(s)^{3}[/tex] / [tex]r(e)^{3}[/tex]
r(s) = r(e) [tex](T(s) / T(e))^{2/3}[/tex]
r(s) = 14.32 * [tex]10^{11}[/tex] m = 9.57 au
learn more about Kepler's third law
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