Masses and Densities of the Stars.
THE spectroscope shows that, although the constitution of the stars offers an infinite variety of detail, we may say, in a general way, that these bodies are suns. It would perhaps he more correct to say that the Sun is one of the stars and does not differ essentially from them in its constitution. The problem of the physical constitution of the Sun and stars may, therefore, be regarded as the same. Both consist of vast masses of incandescent matter at so exalted a temperature as to shine by their own light. All may be regarded as bodies of the same general nature.
It has long been known that the mean density of the Sun is only one-fourth that of the earth, and, therefore, less than half as much again as that of water. In a few cases an approximate estimate of the density of stars may be made. The method by which this may be done can be rigorously set forth only by the use of algebraic formulæ, but a general idea of it can be obtained without the use of that mode of expression.
Let us in advance set forth an extension of Kepler's third law, which applies to every case of two bodies revolving around each other by their mutual gravitation. The law in question, as stated by Kepler, is that the cubes of the mean distances of the planets are proportioned to the squares of their times of revolution. If we suppose the mean distances to be expressed in terms of the earth's mean distance from the Sun as a unit of length, and if we take the year as the unit of time, then the law may be expressed by saying that the cubes of the mean distances will be equal to the squares of the periods. For example, the mean distance of Jupiter is thus expressed as 5.2. If we take the cube of this, which is about 140, and then extract the square root of it, we shall have 11.8, which is the period of revolution of Jupiter around the Sun expressed in the same way. If we cube 9.5, the mean distance of Saturn, we shall have the square of a little more than 29, which is Saturn's time of revolution.
We may also express the law by saying that if we divide the cube of the mean distance of any planet by the square of its periodic time we shall always get 1 as a quotient.
The theory of gravitation and the elementary principles of force and motion show that a similar rule is true in the case of any two bodies revolving around each other in virtue of their mutual gravitation. If