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PLANETS AND THEIR SATELLITES

second. Also, four periods of Titan are almost exactly equal to three of Hyperion.

The result of the latter relation is a certain very curious action of these two satellites on each other, through their mutual gravitation. To show this we give a diagram of the orbits. That of Hyperion, the outer of the

Fig. 43.—Orbits of Titan and Hyperion, showing their relation.

two, is very eccentric, as will be seen by the figure. Suppose the satellites to be in conjunction at a certain moment; Titan, the inner and larger of the two at a point A, Hyperion at the point a just outside. At the end of sixty-five days Titan will have made three revolutions and Hyperion four, which will bring them again into

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