Planet (Gr. , to wander; , a wandering star), a name formerly used to distinguish the seven celestial bodies which seem to move from the seemingly fixed stars, and now applied to the eight primary members of the solar system, and by some astronomers to the asteroids. The planets of the ancient systems of astronomy were the sun, the moon, Mercury, Venus, Mars, Jupiter, and Saturn; and there can be no doubt that the week of seven days had its origin in this circumstance. (See Week.) The solar system may be divided into three distinct families: 1, the four planets, Mercury, Venus, the earth, and Mars, commonly called the terrestrial planets; 2 (in order of distance), the asteroids or minor planets; 3, the four giant planets, Jupiter, Saturn, Uranus, and Neptune. In this classification we regard the moon, and the various satellites which attend on the four major planets, as so intimately associated with the planets to which they belong as not to need separate consideration.
Nevertheless, it may be questioned whether our moon ought not to be regarded as a fifth member of the innermost family of planets, seeing that she differs much less from Mercury in size than Mercury differs from the earth. - The first point to be noticed in the general survey of the sun's family is the scale of the various parts of the planetary system. It is the more necessary to dwell on this relation because in ordinary pictures of the orbits the point is overlooked. In fact, any picture professing to show the whole of the sol^r system must necessarily be inexact, simply because the scale suited to show properly the orbits of the four outer planets is too small to show the paths of the four inner planets; and a scale suited to these smaller orbits would be such that the paths of the outer planets could not be included within a sheet of reasonable compass. The relative distances of the eight primary planets are as follows, the earth's being taken as 1,000:
The distances of the asteroids range between 2,200 and 3,400 in this scale. There is a certain uniformity in the progression of these distances (omitting Neptune), which led astronomers to recognize as real the empirical law of Bode or Titius, at least until the discovery that Neptune's orbit does not correspond with the law. The law may be thus presented: Under the names of the planets in order set the number 4; then write down in succession the numbers 0, 3, 6, 12, 24, 48, and so on, setting the 0 under Mercury, the 3 under Venus, and so on. Adding the columns thus obtained, we get the following result:
The real distances given in the former table correspond very closely with these results. Divided severally by 100, they give the series:
22 - 34
The statement of the law can be simplified, if we take the orbit of Mercury as an inner limit from which to measure the distances of the several planets. These distances, so measured, form a geometrical progression, doubling as we proceed outward; only in the case of Neptune the multiplier suddenly changes from 2 to l-§. When we consider the dimensions and masses of the planets, we no longer find any uniformity of progression. The middle family or zone of asteroids is the least in point of mass; the innermost familv comes next in order; and the outermost is by far the most massive. Taking the mass of the earth at 1,000, the combined mass of the outer family amounts to 419,975, that of the innermost to 2,068; and probably the combined mass of the zone of asteroids does not amount to 100 on this scale. The following table presents the relative masses of the eight primary planets, the earth's mass being taken as 1,000, and brings prominently into view the irregular distribution of matter within the solar system:
The earth and moon
To which add the sun's mass, 315,000,000, and the asteroidal family, less than 100. - A relation not commonly dealt with in treatises on astronomy may next be considered. Every orb in space bears sway, so to speak, over a certain region around it, in such sort that matter within that region is more completely under the influence of the orb's attractive power than under any other attractive influence. It would not be easy to assign a perfectly satisfactory criterion for the extent of any orb's domain in this respect, simply because the control exercised by it depends to a great degree on the velocity of the attracted matter. But as a convenient statical measure of the controlling power of each planet, we may take the attraction exerted on a body at rest at any point, as compared with the sun's attraction on a body at that point; and we may assign as the limit of a planet's domain the surface determined by the law that at any point of it the planet's attraction is exactly equal to the sun's. It is easy to determine this surface for any given planet. Thus let M be the sun's mass, D the distance of a planet, m the mass of the planet, which may be supposed collected at the planet's centre, so far as such an inquiry as the present is concerned.
Now take a point at distance d from the centre of the planet, and on the line joining the centres of the sun and planet; then the attractions exerted by the planet and the sun on a particle placed at this point are respectively proportional to m/d2 and M/(D-d)2 and in order that these may be equal we must manifestly have [d/(D-d)]=√ m/√ M, or d=-√m/(√M+√m)D. Again, if d' be the distance of a point on the line joining the centres, but beyond the planet, then clearly we must have, for the attractions to be equal, the relation d1=√m/(√M+√m)D.Hence d+ d'=2√Mm/(M-m).D;or, since m is very small compared with M, d + d' =2 √(m/M).D, very nearly. This is in reality the diameter of the spherical domain of the planet; for it is easily shown by a geometrical construction that the surface where the sun's influence and the planet's are exactly equal is a sphere. Thus let P be the planet, S the sun, Q a point where the planet's influence and the sun's are equal.
Then m/(PQ)2 = M/(SQ)2 or PQ:
SQ:: √M: √m, a constant ratio. But QA, the bisector of the angle PQS, divides PS so that PA: AS:: PQ: QS; hence A is a point where the planet's attraction equals the sun's; and QB, the bisector of the angle PQF, divides PS produced so that BP: BS:: PQ: QS. Therefore B is another point where the planet's attraction equals the sun's. And the angle BQA is a right angle, because its parts BQP and AQP are respectively the halves of the angles FQP and SQP, which together make up two right angles. Hence Q is a point on a circle with BA as diameter, and is therefore a point on a spherical surface having BA as diameter. Also manifestly PB is the d', and PA is the d, of the above demonstration. Accordingly the radius of the planet's spherical domain is 77b = √(m/M).D, or varies as the square root of the planet's mass and the distance of the planet from the sun, jointly. It is easy therefore to calculate the value of this radius, for the several planets. The following table presents the results as calculated by the writer, where the column of velocities is added to illustrate a relation referred to above:
Radius of spherical domain.
Velocity of bodies attracted to the sun from great distances when at distance of these planets.
41.4 m. per second.
The earth and moon.....
It will be noticed that the domain ascribed to the earth and moon does not really extend so far as the moon, and in making the calculation the mass of the moon should perhaps not have been added. It is easy to make the necessary correction; for the mass of earth and moon being 1,012 where earth's mass = 1,000, the square root of the mass is greater in the ratio 1,006: 1,000, or by less than the 160th part; 162,880 represents the radius thus reduced with sufficient approximation. The mass of the moon being about the 81st part of the earth's, the moon's attraction sphere, estimated solely with reference to the sun, has a radius equal to one ninth of the earth's, or to about 18,100 m. The case is quite different with Jupiter's satellites and Saturn's, seeing that the outermost satellite of Jupiter travels at a distance of only 1,150,000 m. from the placet's centre, and the outermost of Saturn's at a distance of 2,368,000 m. from Saturn's centre, and both these distances are far less than the radius of the spherical domain of either planet. The near equality of these domains, notwithstanding the great disparity between the two planets as to their mass, illustrates the effect of distance in diminishing the energy of the sun's action.
This is still more strikingly shown in the case of Neptune, whose domain enormously exceeds that of any other planet. When we consider further that matter which has been drawn sunward from interstellar space travels with a velocity proportioned to the square root of the distance from the sun, and therefore moves much more slowly at Neptune's distance than at that of any other planet, we perceive that our estimate of Neptune's relative power must be still further increased; and perhaps in such considerations as these we may find an explanation of the anomalous position of Neptune in several respects. We have seen that Bode's law is not fulfilled in his case. Moreover, the largeness of Neptune's mass compared with that of Uranus is remarkable. A certain law could have been recognized in the arrangement of the masses had the mass of Neptune been less than that of Uranus. For in the inner family of planets we perceive that the masses increase with distance from the sun to a maximum and then diminish, an explicable arrangement; and in the outer family we should have had in the case supposed a continuous decrease outward; but the decrease down to a minimum followed by increase is very difficult to interpret.
In this connection we may note an empirical law which Prof. Kirkwood of Bloomington, Ind., has recognized as seemingly connecting the rotation periods of the planets with their masses and distances. It is as follows: " If through the sun a line be drawn cutting the orbits of all the planets (supposed to be projected on the invariable plane of the solar system), and the intercepts between each consecutive pair of orbits be divided in the proportion of the square roots of the masses of the corresponding planets; and if the distances between these points of division be D, D', D", and n be the number of sidereal revolutions which the planet makes on its axis in its periodic time, then will the following relation hold for two consecutive planets, n2: n'2:: D3: D/3. This supposes the existence of a planet between Mars and Jupiter, corresponding to the aggregate of the asteroids, and having a mass equal to one third of the earth's." We venture to express some doubt whether the rotation periods of the planets have been determined with sufficient accuracy to support this ingenious theory. But Prof. Walker considers that Kirk-wood's law may be legitimately deduced from the nebular hypothesis.
The position of the axes of the several planets might be expected to indicate the existence of some law or relation resulting from the nebular hypothesis; but it is difficult to recognize any in the following table, which includes all the planets whose rotation has been accurately ascertained:
Inclination of equator to orbit.
Longitude of rising node of equator on orbit.
23h. 56m. 4s.
23° 27' 24"
24 37 23
28 27 00
9 55 26
3 5 30
10 29 17
26 48 40
167° 4' 5"
It is supposed that the equator of Uranus is inclined about 75° to the planet's orbit, while the axis of Neptune is so abnormally posited (if the planet's rotation corresponds with the motion of his satellites) that the inclination of his equator must be described as exceeding 160°. In other words, the inclination measured as a plane angle amounts to less than 20°, but the planet rotates from east to west instead of from west to east.- - The orbital motions of the planets present certain features of uniformity; thus each of the chief planets travels in an orbit very nearly circular (though in some cases notably eccentric in position), all the planets travel the same way round, and the planes in which they travel are little inclined to the ecliptic, and (on the average) still less to the medial plane of the system. The following table presents the eccentricities (the mean distance of each planet being unity) and the inclinations of the orbits to the ecliptic, in the arrangement of which it is difficult to recognize any law in respect of magnitude:
7° 0' 8.2"
3. 23 30.8
0 0 0
1 51 51
1 18 40.3
2 29 28.1
0 46 29.9
1 46 59.0
Some of the asteroids have orbits of much greater eccentricity and inclination. Thus the eccentricity tif Polyhymnia is no less than 0.339119, and the inclination of Pallas amounts to 34° 45'; so that the excursions of Polyhymnia on either side of its mean distance, and the excursions of Pallas on either side of the plane of the ecliptic, exceed when taken together the mean distance of either planet. It has been remarked that " there are few more interesting chapters in the history of astronomy than those which treat of the mathematical relations presented by the planetary eccentricities and inclinations." Seeing these elements, as we do, undergoing gradual processes of increment and decrement continuing for long periods in the same direction, astronomers were in doubt until mathematics solved the difficulty whether the planetary system was in truth stable, or whether processes might not be in action which would go on with gradually increasing effects until at length the whole system would be destroyed. Gradually the progress of analysis revealed the true interpretation of these processes, and showed them to belong, not to changes tending continually in one direction, but to oscillatory variations proceeding in orderly sequence within definite and not very wide limits.
We owe to Lagrange the first enunciation of the laws relating to the stability of the solar system; but to Laplace must be ascribed the credit of establishing the important theorems which have been justly called the Magna Charta of the solar system. He proved in 1784 that in any system of bodies travelling in one direction around a central attracting orb, the eccentricities and inclinations, if small at any one time, would always continue inconsiderable. His two theorems may be thus stated: 1. If the mass of each planet be multiplied by the square of the eccentricity, and this product by the square root of the mean distance, the sum of the products thus formed will be invariable. 2. If the mass of each planet be multiplied by the square of the tangent of the orbit's inclination to the medial or fixed plane, and this product by the square root of the mean distance, the sum of the products thus formed will be invariable, Thus is the stability of the solar system secured for periods which, compared with all known units of time measurement, appear to us absolutely infinite.
Every orbit will undergo continual changes of eccentricity and of inclination, now one, now another having a maximum amount of either form of apparent irregularity; but in the midst of this continual flux, the eccentricity and the inclination of the solar system regarded as a whole remains constant. Not the star sphere itself is more unchanging than the position of that circle upon it which marks the position of the well named " fixed plane " of the planetary system.