Answer
The new radius is 0.44 r
Work Step by Step
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.
