|78||The Solar System|
altered that commensurability of period, which depends on the major axis, ceases. Then the bodies will cease to affect each other forcibly. They will gradually meet each other elsewhere, finally oppositely to what they did at first, and the action first produced will be as gradually un-done ; but it will be very long before the major axes attain their original value again ; then they will pass rapidly through them once more in the reverse way.
If, then, the periods of the two bodies are commensurable, they will not appear to be so, since their major axes will stay commensurate but a brief time compared with the time they are out.
Gaps due to change of major axis.Now, if we have a swarm of bodies revolving at various distances round a central mass, and disturbed by a third, the third will seem, in con- sequence of this, to sweep out spaces where otherwise bodies would revolve in times commensurate with its own. Jupiter has done this very thing in the case of the asteroids, striping the zone with vacant belts. Calculation alone reveals this, asthe asteroids are too few to disclose the fact to the eye. But in the rings of Saturn we can actually see the empty places. The gaps in the rings are shown in the following table and in the accompanying picture of the ring system :—