Density = Mass/Volume; Volume = Mass/density

Volume (V) of the hypothetical satellite:

A mass of 1.00 × 10^{19} × 10^{3} g of ice has a volume of 1 x 10^{22}cm^{3} = (1 x 10^{22})/10^{15}km^{3}

V = 1 x 10^{7}km^{3}

v = 4/3πr^{3}

r = (3v/4p)^{1/3} = ((3 x 10^{7})/(4 x 3.14))^{1/3} = (0.2388 x 10^{7})^{1/3}

r = 133.6km or 134km