From Kepler's third law, there relationship between the period and average distance between the earth and the sun is expressed as
P^2 = a^3
where
P = sidereal period in years
a = average distance between the earth and the sun
From the information given,
P = 84
By subsituting the value into the formula, we have
84^2 = a^3
7056 = a^3
Taking the cuberoot of both sides,
[tex]\begin{gathered} a\text{ = }\sqrt[3]{7056} \\ a\text{ = }19.2 \end{gathered}[/tex]The distance is 19.2 AU
