Question

as seen by earth based observers, the intervals between successive edge on presentations of Saturn's rings alternate between 13 years 9 months and 15 years 9 months. Why are these two intervals not equal?

Answer 1

Saturn is the sixth planet in the solar system. Because it travels in an elliptical path rather than a circular one, it doesn't always lie the same distance from the sun as it wanders through the sky.

The distance to Saturn from our planet is constantly changing as both of the planets travel through space. When the two are closest, they lie approximately 746 million miles (1.2 billion kilometers) apart, or eight times the distance between the Earth and the sun. At their most distant, when they lie on opposite sides of the sun from one another, they are just over a billion miles (1.7 billion km) apart, or 11 times the distance between the Earth and the sun.

If the Saturn is closer, it takes less time to reach the light to us. If it is far away, it takes more time to reach the light to us.

That's why the intervals between successive edge on presentations of Saturn's rings are different.