CHAPTER VII. ON THE MOTIONS OF THE PRIMARY PLANETS-THE COPERNICAN SYSTEM-THE PTOLEMAIC SYSTEM. SOLAR OR 93. HAVING stated some of the principal arguments for the motion of the earth, in an orbit nearly circular about the sun, let us now consider the planets in general. Astronomy has added much indeed to our knowledge of the creation, by enabling us to ascertain that the planets are vast bodies, revolving round the sun in orbits nearly circular, some at greater and others at less distances than the earth; that some of these bodies are smaller and others much larger than the earth: and that, according to a high degree of probability, they are bodies of the same nature as that on which we live. 94. The principal planets are always observed to be nearly in the ecliptic, the annual path of the sun on the concave surface; and for the present let us consider them as seen in the ecliptic. The most striking circumstance in the planetary motions is the apparent irregularity of those motions, the planets one while appearing to move in the same direction among the fixed stars as the sun and moon, at another in opposite directions, and sometimes appearing nearly stationary. These irregularities are only apparent, and arise from a combination of the motion of the earth and motion of the planet; the observer, not being conscious of his own motion, attributing the whole motion to the planet. 95. The planets really move, according to the order of the R circular about the sun in the centre. As the computed place always agrees with the observed place, it necessarily follows that the retrograde, stationary appearances, and direct motions, of these planets, are explained, by assigning these circular motions to them. 98. It is easy to demonstrate the retrograde and stationary appearances. To do this more clearly, it will be necessary to consider the effect of the motion of the spectator arising from the motion of the earth, in changing the apparent place of a distant body. The spectator, not being conscious of his own motion, attributes the motion to the body, and conceives himself at rest. Let S be the sun, (Fig. 15) ET the space described by the earth in a small portion of time which therefore may be considered as rectilinear. The motion is from E toward T. Let V be a planet, supposed at rest, any where on the same side of the line of the direction of the earth's motion as the sun. Draw EP parallel to TV, then while the Mearth moves through ET, the planet supposed at rest will appear to a spectator, unconscious of his own motion, to have moved by the angle VEP, which motion is direct, being the same way as the apparent motion of the sun. And because the earth appears at rest with respect to the fixed stars, the planet will appear to have moved forward among the fixed stars by the angle VEP EVT the motion of the earth, as seen from the planet supposed at rest. Thus the planet being on the same side of the line of direction of the earth's motion as the sun, will appear, as far as the earth's motion only is concerned, to move direct. Let M be a planet any where on the opposite side of the line of direction, then the planet will appear to move retrograde by the angle MER. And therefore, as far as the motion of the earth only is concerned, a planet, when the line of direction of the earth's motion is between the sun and planet, will appear retrograde. 99. To return to the apparent motion of the inferior planets. Let the earth be at E, (Fig. 14), and draw two tangents GE and ED. Then when the planet is at D or G, it is at its greatest elongation from the sun S. It is clear that the planet being in the inferior part of its orbit between D and G, relatively to the earth, and the earth being supposed at rest, the planet will appear to move from left to right, that is, retrograde and in the upper part of the orbit from right to left, that is, direct. But the earth not being at rest, we are to consider the effect of its motion. In the case of an inferior planet, the planet and the sun are always on the same side of the line of direction of the earth's motion, and therefore the effect of the earth's motion is always to give an apparent direct motion to the planet, (Art. 98). Hence in the upper part of the orbit between the greatest elongations, the planet's motion will appear direct, both on account of the earth's motion and its own motion. In the inferior part of the orbit the planet's motion will only be direct, between the greatest elongation and the points where the retrograde motion from the planet's motion becomes equal to the direct motion from the earth's motion. At these points the planet appears stationary: and between these points, through inferior conjunction, it appears retrograde. 100. Next, for the superior planets, or those planets which are farther from the sun than the earth is. The interval of time between two succeeding oppositions of a superior planet to the sun can be observed. A superior planet is in opposition, when the earth is between the sun and planet. It is known when a superior planet is in opposition, by observing when it is in the part of the zodiac opposite to the place of the sun. Let T represent the time between two successive oppositions, then viewing the planet from the sun, the earth will appear to have gained an entire revolution, or 360° on the planet, in the time T; and the earth and planet being supposed to move with uniform an gular velocities about the sun, the angle gained by the earth will increase uniformly. 101. Let TEL (Fig. 16) represent the orbit of the earth, CDOG that of a superior planet; N the place of the planet when the earth is at E. Then, in the triangle SNE, we have the angle SEN by observation, and the angle NSE by computation. For NSE is the angle at the sun which the earth has gained on the planet since the preceding opposition. This angle 360° time since opposition: T. The two angles NSE and SEN being known, the angle SNE is known, and therefore SN relatively to SE. For sin. SNE: sin. SEN: SE : SN. Having thus obtained the distance of a superior planet from the sun, we can, at any time, by help of the time T, and time of preceding opposition, compute the angular distance of the earth from the planet, as seen from the sun, and thence, by help of the earth's distance and planet's distance from the sun, we can compute the planet's elongation from the sun. Thus the planet being at R and the earth at E, we compute the angle RSE, and knowing the sides ES and SR, we can (by plane trig.) compute the angle RES, the elongation of the planet from the sun. This being compared with the observed angle, we always find them nearly agreeing, and thereby is shewn that the motions of the superior planets are explained, by those planets moving in orbits nearly circular about the sun. As the computed place nearly agrees with the observed place, it necessarily follows that the retrograde and direct motions, and the stations, of these planets are explained, by assigning to them these circular motions. 102. And it is easy to demonstrate these appearances. It is clear that the planet being in any part of its orbit, and the earth being supposed at rest at any point E, the planet will appear to move from west to east, or direct. But the earth not being at rest, we are to consider the effect of its motion. The earth being at E, draw the tangent DEG, then if the planet is in the upper part of the orbit DCG, it is on the same side of the line of direction of the earth's motion as the sun, and therefore the effect of the earth's motion is to give an apparent direct motion to the planet. The earth being at E, and the planet at D or G, the planet is said to be in quadrature; consequently from quadrature to conjunction, and from conjunction to quadrature, the planet appears to move direct, both on account of its own motion and the motion of the earth. If the planet is in the lower part of the orbit DOG, the effect of the earth's motion is to give an apparent retrograde motion to the planet; consequently from quadrature to opposition, and from opposition to quadrature, the planet moves direct or retrograde according as the effect of the planet's motion exceeds, or is less than, the effect of the earth's motion. Between quadrature and opposition their effects become equal, and the planet appears stationary, and afterward through opposition to the next station retrograde. 103. The apparently irregular motions of the planets among the fixed stars, must strike the most cursory observer, and it would not at first be expected that these motions could be explained by so simple an arrangement of the bodies. But it is not enough to establish the true arrangement and true motions of the bodies, that the general appearances are explained. It is necessary that the most minute circumstances of their apparent motions can be shewn to arise from that arrangement. We have supposed above that the orbits are accurately circular, that the planes of these orbits and that of the earth coincide, and that the angular motions were uniform; but if the planes of the orbits coincided, if the orbits were accurately circular, and were uniformly described, the planets would always appear in the ecliptic, and would always be found exactly in the places which the computation on the circular hypothesis points out; but none of these things take place exactly. The deviation however can be explained, by |