Kepler's Three Laws of Planetary Motion:

I. The planets move in ellipses with the sun at one focus.

II. The radius vector of a planet (line adjoining sun and planet) sweeps over equal areas in equal times.

III. The square of the time of revolution (the year) of each planet is proportional to the cube of its mean distance from the sun.

Sir Isaac Newton discovered that the law of gravitation extends to the stars. That is, every mass in the universe attracts every other mass with an attraction directly proportional to the product of the masses and inversely proportional to the square of the distances between them.

Ocean tides are caused by the difference between the attraction of the sun and moon for the main body of the earth and their attraction for different particles of the earth's surface. The tide-raising force of the disturbing body is proportional to its mass and inversely proportional to the cube of its distance. The tides produced by the sun are, therefore, only two-fifths as great as the tides produced by the moon.

The celestial sphere is an imaginary sphere of infinite radius, with the earth at its center, upon which the celestial bodies are considered to be projected for convenience in determining their positions with respect to fixed points of reference in the heavens.

The north and south poles of the heavens are the points on the celestial sphere directly above the north and south poles of the earth.

The celestial equator is the great circle in which the plane of the earth's equator intersects the celestial sphere. It passes through the east and west points of the horizon and through the zenith—or point directly overhead—at the earth's equator.

The ecliptic is the great circle in which the plane of the earth's orbit intersects the celestial sphere. The celestial equator and the ecliptic are inclined to each other at an angle of 23½°, which is called the obliquity of the ecliptic. The two points in which the celestial equator and the ecliptic intersect are called respectively the vernal equinox and the autumnal equinox.

The vernal equinox is an important point of reference on the celestial sphere.

As the position of a point on the earth's surface is determined by its longitude and latitude so the position of an object on the celestial sphere—star, sun, planet—is determined by its Right Ascension and Declination.

The Declination of a celestial object is its distance north or south of the celestial equator, measured in degrees, minutes and seconds of arc, on a great circle of the celestial sphere passing through the object and north and south poles of the heavens. These great circles are called hour circles and they correspond to the meridians or circles of longitude on the earth's surface. The declination of an object in the heavens corresponds to the latitude of a point on the earth's surface. The Right Ascension of a point on the celestial sphere corresponds to the longitude of a point on the earth's surface. It is measured—as longitude is measured—in degrees, minutes and seconds of arc or in hours, minutes and seconds of time—eastward along the celestial equator from the hour circle passing through the vernal equinox to the foot of the hour circle passing through the object. The hour circle passing through the vernal equinox is the zero meridian for the celestial sphere just as the meridian of Greenwich is the zero meridian on the earth's surface.

The mean distance of the earth from the sun is 92,900,000 miles and is called the astronomical unit.

The sun with its satellites advances through the universe at the rate of 4 astronomical units in a year or approximately one million miles a day.

The parallax of a star is the angle at the star subtended by the radius of the earth's orbit, 92,900,000 miles, or the astronomical unit. It is, in other words, the angular distance between the earth and sun as viewed from the star. The larger the parallax the nearer the star. The largest known stellar parallax is that of Alpha Centauri and its value is 0".75.

The light-year is the distance that light travels in one year. It is equal to about 63,000 astronomical units or nearly six trillion (6,000,000,000,000) miles. The velocity of light is 186,000 miles per second.

The parsec is equal to 3.26 light-years. It is the distance of a star that has a parallax of one second of arc.

The apparent magnitude of a star is its apparent brightness estimated on a scale in which a difference of one magnitude corresponds to a difference in brightness of 2.51, or the fifth root of one hundred. A difference of five magnitudes corresponds to a difference one one hundredfold in brightness, of ten magnitudes to ten thousandfold in brightness. In exact measurements on this scale magnitudes are estimated to tenths.

Stars that are one magnitude brighter than stars of the standard first magnitude are of the zero magnitude and stars still brighter are of negative magnitudes.

Sirius is a star of the -1.6 magnitude. Jupiter at opposition is of -2.0 magnitude and Venus at greatest brilliancy of -4.0 magnitude. The sun on this scale of comparative brightness is of the -26.7 apparent magnitude. The faintest stars visible in the most powerful telescope in the world—the 101-inch Mt. Wilson Hooker telescope—are of the twentieth magnitude.

The absolute magnitude of a star is its apparent magnitude at the standard distance of ten parsecs or 32.6 light years. The absolute magnitude of the sun is five. That is, the sun would be a fifth-magnitude star at the standard distance of 32.6 light-years. The absolute magnitudes of stars indicate how bright they would be relatively if they were all at the same standard distance. Apparent magnitudes indicate how bright the stars appear to be at their true distances.

The mean distance of the moon from the earth is approximately 240,000 miles or sixty times the earth's radius.

The sun is four hundred times farther away than the moon and its diameter is about four hundred times greater than the moon's diameter.

The nearest star is about 275,000 times more distant than the sun, and the most distant known object, the globular star cluster, N.G.C. 7106, is about fourteen billion times more distant than the sun.

The earth is a spheroid flattened at the poles and its polar diameter is about twenty-seven miles shorter than its equatorial diameter. An object weighs less at the poles than at the equator.

The earth's interior is as rigid as steel and probably consists of a core of magnetic iron surrounded by an outer stony shell.

Eclipses of the sun occur when the moon passes between the earth and sun. They can only occur at the time of new moon. There must be at least two solar eclipses every year separated by an interval of six months and there may be as many as five solar eclipses in a year. Eclipses of the moon occur when the earth comes between the sun and moon, and the moon passes into the earth's shadow. Eclipses of the moon can only occur at full moon. There may or may not be eclipses of the moon every year. The greatest number of eclipses than can occur in any one year, solar and lunar combined, is seven and the least number is two and in that case they are both solar eclipses.

The sun is a yellow, dwarf star of a density of one and one-fourth that of water and with a surface temperature of about 12,000° F. except in sun-spot regions where the temperature is about 6,000° F. It is probably gaseous throughout.

The sun, as well as the planets, rotates on its axis and different portions of the surface rotate at slightly different rates. The average period of the rotation of the sun on its axis is about twenty-six days.

The sun is a variable star with a twofold variation. One is of long period during the eleven-year sun-spot cycle with a range of from three to five per cent. The other is a short irregular variation with a period of a few days, weeks or months and a range of from three to ten per cent.

Sun-spots are solar cyclones and appear black only by contrast with their hotter and brighter surroundings. They come in eleven-year cycles (approximately) with periods of maximum and minimum appearance.

The brightness and blue color of the sky is due to the scattering of sunlight by the molecules of oxygen and nitrogen in the earth's upper atmosphere. If there were no atmosphere the skies would appear black except in the direction of the heavenly bodies, which would be visible by day as well as by night.

The solar corona is the rare outer envelope of the sun and it is visible only during a total eclipse of the sun. It is partly of an electrical nature and it varies in form during the sun-spot cycle. It often extends to a distance of several solar diameters on either side of the sun.

The warmth and the habitability of the earth's surface is due to the presence of water-vapor and carbon-dioxide in the atmosphere. Without these substances in the atmosphere life on the earth's surface would be impossible.

Half of the earth's atmosphere and all clouds lie within seven miles of the earth's surface, and at high elevations above the earth the temperature is many degrees below zero.

The temperature of space approaches the absolute zero of -459° F.

The only planets in the solar system with the exception of the earth that might possibly support life are Venus and Mars.

Stars shine by their own light but planets shine only by reflected light from the sun.

If the earth were represented by a six-inch school globe the sun would be on the same scale a globe fifty-four feet in diameter. Mercury would be a small ball two and a third inches in diameter. Venus would be another six-inch globe. Mars would be a ball about the size of a baseball, three and a fifth inches in diameter. The moon would be about the size of a golf ball, one and a half inches in diameter. The largest asteroids would be the size of marbles. Average-sized asteroids would be the size of shot and the smallest would be merely grains of sand.

Jupiter would be a huge globe standing as tall as a man five feet six inches in height. Saturn would be a smaller globe four and a half feet in diameter and its ring system would extend to a distance of five and a half feet on either side of the globe. Uranus would be represented by a globe almost exactly two feet in diameter and Neptune would be a slightly larger globe with a diameter of two feet two and a half inches.

The satellites of the outer planets would range in size from tennis and golf balls for the largest, to marbles for the smaller and grains of sand for the smallest.

On the same scale of measurement the distance of the six-inch globe of the earth from the fifty-four foot globe representing the sun would be one and one-tenth miles. The moon would be placed fifteen feet from the earth-globe and the diameter of the solar system on the same scale measured across the orbit of Neptune would be sixty-six miles. The nearest star on this scale would be three hundred thousand miles away.

If the distance from the earth to the sun is taken as one inch so that the scale of the universe is reduced six trillion times, the diameter of the solar system across Neptune's orbit is five feet and the distance of one light-year comes out almost exactly equal to one mile. The nearest star to the five-foot solar system would be four and a third miles away; the most distant known object would be two hundred and twenty thousand miles away, and the extent of the visible universe would be three hundred thousand miles. On the same scale the diameter of our sun would be about one hundredth of an inch and the diameters of the giant stars Antares and Betelgeuze would be four inches and two and three-fourth inches respectively. To see the earth we would need a microscope.