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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.

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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

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