Answer
$M = 6.3\times 10^{16}~kg$
Work Step by Step
We can find the mass $M$ of the asteroid:
$T^2 = \frac{4\pi^2~r^3}{GM}$
$M = \frac{4\pi^2~r^3}{GT^2}$
$M = \frac{(4\pi^2)(1.0\times 10^5~m)^3}{(6.67\times 10^{-11}~N~m^2/kg^2)(27\times 3600~s)^2}$
$M = 6.3\times 10^{16}~kg$
