ART. 28. _Kepler's Third Law._--The Third Law of Kepler gives the relation between the periodic time of a planet, and its distance from the sun. The periodic time of any planet is the time which it takes to go once round the sun. Thus the periodic time of the earth is 365-1/4 days. The periodic time of Venus is 224.7 days, while that of Mars is 686.9 days. Kepler had found out that different planets had different periodic times; he also found out that the greater the mean distance of the planet, the greater was the time which the planet took to perform its journey round the sun, and so he set to work to find out the relationship of the periodic time to the planet's mean distance. After many trials and many failures he arrived at the right conclusion, and at last discovered the true law which is known as Kepler's Third Law, which states that for each and every planet, the squares of their periodic times are proportional to the cubes of their mean distances. For purposes of illustration let us take the earth and the planet Venus and compare these two. The periodic time of the earth is 365 days, omitting the quarter day. The periodic time of Venus is 224 days approximately. Now, according to Kepler's Third Law, the square of 365 is to the square of 224, as the cube of the earth's mean distance is to the cube of Venus's mean distance, which are 92.7 millions of miles and 67 millions of miles respectively. The problem may be thus stated-- As 365^2: 224^2:: 92.7^3: 67^3: This worked out gives-- 133,225: 50,176: 796,597.982: cube of Venus's mean distance. So that by Kepler's Third Law, if we have the periodic time of any two planets, and the mean distance of either, we can find out the mean distance of the other by simple proportion. In making astronomical calculations, the distances of the planets are generally obtained by means of Kepler's Third Law, as the periodic time of the planet is a calculation that may be made by astronomers with great certainty, and when once the periodic times are found, and the mean distance of a planet, as our earth for example, is known, the mean distances of all the other planets in the solar system may soon be obtained. In like manner this Third Law of Kepler's is equally applicable to the satellites of any planet. For example, when the periodic time of both of Mars' satellites, Phobos and Deimos, are known, being about 8 hours and 30 hours respectively, and the distance of either is known, as Phobos with a mean distance of 5800 miles, then the mean distance of Deimos can easily be calculated by this law, and is found to be 14,500 miles.