Suppose there existed a planet that went around the sun eight times as fact as the earth. What would be its orbital size as compared to that of the earth ?

Explanation

If the period of revolution of the earth around the sun is T, the period of the planet is `T/8`. If the semi major axes of their elliptical orbits are `r_1 and r_2` respectively , then from Kepler.s law,
`(T/(T//8))^2=(r_1/r_2)^3`
`or, r_1/r_2=8^(2//3)=4, or, r_2=r_1/4`
so, the orbital size of the planet is 1/4 th that of the earth.