The planet neptune travels around the sun with a period of 165 yr. What is the radius of the orbit approximately, if the orbitt is considered as circular ?

Explanation

As, `T_(1)=T_("Earth")=1 "yr" and T_(2)=T_("Neptune")=165 "yr"`
Let `R_(1) and R_(2)` be the radii of the circular orbits of the earth According to Kepler's third law
`(T_(1)^(2))/(T_(2)^(2))=(R_(1)^(3))(R_(2)^(3))/(R_(2)^(3))rArr R_(2)^(3)=(R_(1)^(3)T_(2)^(2))/(T_(1)^(2))rArrR_(2)^(3)=(R_(1)^(3)xx(165)^(2))/(1^(2))`
`rArr R_(2)^(3)=165^(2)R_(1)^(3)rArrR_(2)~~30R_(1)`.