The tiny Saturnian moon, Atlas, is locked into what is known as an orbital reson

Question

The tiny Saturnian moon, Atlas, is locked into what is known as an orbital resonance with another moon, Mimas, whose orbit lies outside that of Atlas. The ratio between periods of these orbits is 3:2, that is, for every 3 orbits of Atlas, Mimas completes 2 orbits. Thus, Atlas, Mimas and Saturn are aligned at intervals equal to two orbital periods of Atlas. If Mimas orbits Saturn at a radius of 169,260 km, what is the radius of Atlas's orbit?

I know the answer has to be something like 1.44e+05.

THANKS!

Explanation / Answer

The Circumference of Mimas orbit is pi x diam
= pi * 169260* 2 km
= 1,075,179 km

2 orbits of mimas = 2,150,357 km
= 3 orbits of Atlas
so i orbit of Atlas = 2,150,357 / 3
= 716,785 km
C = pi x D
D = C / pi
= 716,785 / pi km
= 228,160 km
Radius is half diameter
= 114,080 km

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