Physics: Principles with Applications (7th Edition)

The gravitational force provides the centripetal force for the asteroid as it orbits the sun. Let $M_s$ be the mass of the sun. Then, $m\frac{v^2}{r} = \frac{GM_s~m}{r^2}$ $r = \frac{GM_s}{v^2}$ In the new orbit: $r_2 = \frac{GM_s}{v_2^2}$ $r_2 = \frac{GM_s}{(1.5v)^2}$ $r_2 = \frac{1}{2.25}\frac{GM_s}{v^2} = 0.44 ~r$ The new radius is 0.44 r.