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Kepler ’s third law, which is of very great value, may hestated as follows :—
If me take the mean distance of any planet from the Sun ,and the periodic time in which it goes once round its orbit, theratio of the square of the time to the cube of the distance willbe found to be the same for all the platiets.
This may, perhaps, he best illustrated by one or two simpleexamples, although only approximately, and not so as to showthe beautiful precision with which the law holds good. Forinstance, the mean distance of the Earth is 2-6 times that ofMercury, and its period is 4-2 times. The square of the latternumber is 17-64, while the cube of the former is 17-576, bothof which, to one place of decimals, give the same result, 17-6.
Fig . XXXV.—Kepler’s Second Law: A planet describes equal areas round the Sun in equal times.
Again, the period of Uranus is close upon 84 years, and84 squared is equal to 7056. The distance of Uranus is verynearly 19-18 times the Earth ’s, which number cubed produces7055*8, the result being therefore in almost exact agreementwith the. law.
So, if a new planet were found, and its period were observedto be five times that of the Earth , we should be able, bysquaring 5 (which gives 25), and taking the cube-root ofthis square, which will be rather less than 3, to say at oncethat its distance from the Sun must be rather less than threetimes the Earth ’s distance.
In connection with this mention of the planetary distances,we may as well allude in passing to the curious relation exist-