Planet

(3) The squares of the periodic times (the times required for the orbital revolutions of the planets) are proportional to the cubes of the mean distances (the semi-major axes of their orbits). This is known as the harmonic law and defines the relationship between a planet's orbital motion and its distance from the sun.

From these laws of planetary motion Newton deduced his law of universal gravitation which has achieved such remarkable suc cesses and prepared the way for Einstein's relativity theory.

The dimensions, form and aspect of a planet's orbit as well as the position of the planet in the orbit at any time are defined by what are known as its elements. These are :— ( r) Half the major axis, or mean distance (generally denoted by a). This defines the size of the orbit.

(2) The eccentricity (e) or the ratio of the distance of the sun from the centre of the orbit to the mean distance. This defines the shape of the orbit.

(3) The inclination (i) of the orbit plane to the ecliptic, i.e., to the plane of the earth's orbit.

(4) The longitude of the ascending node (a), i.e., the direc tion at the sun of the point on the orbit (measured from the vernal equinox or "first point of Aries") at which the planet crosses the ecliptic from its south to its north side. This defines the aspect of the orbit.

(5) The longitude of the perihelion (JO. This defines the direction of the major axis in the plane of the orbit.

(6) The period (P), i.e., time the planet takes for a revolution.

(7) The longitude of the planet at the epoch (L) or time (T) of the planet's perihelion passage. These elements are given for the several planets in Table I.

Since the orbits of Mercury and Venus lie within that of the earth these two planets when observed telescopically will show phases similar to those presented by the moon. When on the far side of the sun, i.e., near the time of superior conjunction, each of them will appear like a small full moon. As the angle earth planet-sun increases a proportionally diminishing fraction of the illuminated surface will be presented to view, and when the angle reaches 9o° the planet will appear half illuminated like the moon at first quarter. Following this a crescent form of steadily diminish ing breadth will be assumed as the planet moves toward inferior conjunction, at which point it passes between the earth and the sun.

Subsequently to this the phases described will be repeated in the reverse order up to superior conjunction when the planet will again be "full." The phases of a planet revolving outside the earth's orbit differ from those of Mercury and Venus in as much as the angle earth-planet-sun can never increase to 9o°. Thus Mars, although at times presenting a markedly gibbous aspect like a nine or ten days' old moon, is always more than half illuminated. In the case of Jupiter the defect of illumination is so small as to be almost imperceptible, but during the occultation of a satellite the planet's dark limb is seen across the satellite's disk, and a nar row black space separates the latter from the bright part of the planet's surface. In the cases of the planets revolving outside

Jupiter the phase is quite imperceptible even in powerful tele scopes. The variations in apparent diameter and brightness will, of course, also be small in the cases of the remoter planets.

Physical Condition and Atmospheres.

There is a broad distinction between the two groups of the major planets on either side of the zone of the asteroids. The planets of the inner group are of relatively small mass and high density and possess solid surfaces. Those of the outer group, especially Jupiter and Saturn, are of much larger mass but of very low density. The density of Saturn is actually less than that of water. The masses of the planets possessing satellites are derived from the distances and periodic times of the satellites by an application of Kepler's third law. The masses of Mercury and Venus are deduced from their gravitational effect on other bodies.

There is for each of the planets a certain critical velocity de termined by the force of gravity at its surface, and a particle of matter travelling at a speed in excess of this value will escape from the planet in question and revolve in an independent orbit round the sun. These critical values for the several planets are given in column 12 of Table II. Now according to the kinetic theory of gases every molecule of a gas is an independent particle and is in constant motion. Its velocity will depend on the atomic weight and the temperature and may attain to thousands of feet per second. A molecule with such a high speed in the upper part of a planet's atmosphere where it will be comparatively free from collision with other molecules cannot be retained by a body with low surface gravity but will escape into space. It might be ex pected, accordingly, that only the large and massive planets are enveloped in dense atmospheres, and that those of small mass and low surface gravity have atmospheres which are of greater rarity and tenuity. Observation shows that this is in general the case. The spectra of the planets of the outer group contain strongly marked absorption bands due to their atmospheres, while those of the inner group—Mars, Venus and Mercury—show but little de viation from the ordinary solar spectrum. It may be that the light received from Venus is almost entirely reflected from the upper part of the atmosphere, but in the cases of Mars and Mercury most of it has passed through the planetary atmosphere twice. As a matter of fact the atmosphere of Mercury seems to be almost negligible. It is known that the moon which is still smaller has none at all that is appreciable, and it cannot be supposed that an atmosphere exists on any of the minor planets, the largest of which (Ceres) has a mass only and a surface gravity only as great as the corresponding values for the earth.