A satellite A of mass m is at a distance of r from the centre of the earth. Another satellite B of mass 2m is at distance of 2r from the earth’s centre. Their time periods are in the ratio of : 

\([\frac{1}{2\sqrt{2}}]\)

Time period does not depend upon the mass of satellite, it only depends upon the orbital radius. According to Kepler's law :

\(\frac{T_1}{T_2} = [\frac{r_1}{r_2}]^{3/2}\)

\(\frac{T_1}{T_2} = [\frac{r}{2r}]^{3/2}\)

\(\frac{T_1}{T_2} = [\frac{1}{2\sqrt{2}}]\)