Answer
The orbital radius of the planet which orbits Vega is 18.5 R
Work Step by Step
We can write an expression for the orbital radius $R$ of the earth. Let $M_s$ be the mass of the sun.
$T^2 = \frac{4\pi^2~R^3}{G~M_s}$
$R^3 = \frac{G~M_s~T^2}{4\pi^2}$
$R = (\frac{G~M_s~T^2}{4\pi^2})^{1/3}$
We then write an expression for the orbital radius $R_p$ of the planet which orbits Vega.
$(55~T)^2 = \frac{4\pi^2~R_p^3}{G~(2.1~M_s)}$
$R_p^3 = \frac{G~(2.1~M_s)~(55~T)^2}{4\pi^2}$
$R_p = (\frac{G~(2.1~M_s)~(55~T)^2}{4\pi^2})^{1/3}$
We can divide the orbital radius $R_p$ of the planet orbiting Vega by the orbital radius $R$ of the earth.
$\frac{R_p}{R} = [(2.1)(55)^2]^{1/3}$
$R_p = 18.5~R$
Therefore, orbital radius of the planet which orbits Vega is 18.5 R
