Gravity at surface of a planet \(=\) gravity at surface of the earth.

\(g_p=g_e\)

\(P_1=1.5 P_e\)

Radius of earth \(=R\)

\(g=\frac{G\left(P \times \frac{4}{3} \pi R^3\right)}{R^2}\)

It's given, \(P_P=1.5 P_E\)

\(\frac{ G \times \frac{4}{3} \pi R^3 \times P_e}{R^2}=\frac{G \times \frac{4}{3} \pi \times\left(R^1\right)^3 \times P_p}{\left(R^1\right)^2}\)

or, \(R_P=R^1 P_P\)

or, \(R^1=R \times \frac{P_p}{P_p}=\frac{R}{1.5}=\frac{2 R}{3}\).