Question

Calculate the radius of a hypothetical satellite of Uranus that has a mass of 1.00 × 10¹⁹ kg (i.e.,  equal to the mass of its ring particles) assuming that these particles are composed to water ice having a density of 1.00 g/cm³.

Answer 1

Density = Mass/Volume; Volume = Mass/density

Volume (V) of the hypothetical satellite:

A mass of 1.00 × 10¹⁹ × 10³ g of ice has a volume of 1 x 10²²cm³ = (1 x 10²²)/10¹⁵km³

V = 1 x 10⁷km³

v = 4/3πr³

r = (3v/4p)^1/3 = ((3 x 10⁷)/(4 x 3.14))^1/3 = (0.2388 x 10⁷)^1/3

r = 133.6km or 134km