The Study of Astronomy, adapted to the capacities of youth / In twelve familiar dialogues, between a tutor and his pupil: explaining the general phænomena of the heavenly bodies, the theory of the tides, &c.

by teacher of astronomy John Stedman

Tutor. The diameter of the sun is 893552 miles, of the earth 7920 miles; how much does the sun exceed the earth in magnitude?

Pupil. The cube of 893522, the sun’s diameter, is 713371492260872648; and of 7920, the earth’s, 496793088000. And 713371492260872648 divided by 496793088000 is equal to 1435952, and so many times is the bulk of the sun greater than that of the earth.

Tutor. This one example may suffice, as I intend by and by to give you a table of diameters, &c.; you may then calculate the rest at your leisure.

Pupil. I shall now, Sir, be glad to have the other explained.

Tutor. The periods of the planets, or the times they take to complete their revolutions in their orbits, are exactly known; and the mean distance of the earth from the sun has been also ascertained. Here, then, we have the periods of all, and the mean distance of one, to find the distances of the rest; which may be found by attending to the following proportion:

As the square of the period of any one planet,

Is to the cube of its mean distance from the sun;

So is the square of the period of any other planet,

To the cube of its mean distance.

The cube root of this quotient will be the distance sought.