Has the Sun any other real motion, besides that on its axis ?

What are the apparent motions of the Sun ? What is the cause ?

What is the zodiacal light?

CHAPTER IV

Of the Geocentric motions of the Planets, &c.

1. 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 to the planet. The planets really move, as has already been observed, according to the order of the signs, in orbits nearly circular, and with motions nearly uniform, round the Sun in the centre, at different distances, and in different periodical times. The periodical time is greater or less, according as the distance is greater or less. Upon the hypothesis hyp that the planets thus move, we can ascertain, by help of observation, their distances from the Sun, and thence compute for any time the place of a planet, which is always found to agree with observation. As the principal planets are always observed to be nearly in the ecliptic, and as they revolve round the Sun in orbits nearly circular; in order to simplify the illustration of their geocentric motions, we may, for the present, without any material error, consider them as moving uniformly in circular orbits, which coincide with the plane of the ecliptic.

2. The inferior planets, Mercury and Venus, are limited in their elongations from the Sun; the greatest elongation of Mercury being about 28°, and that of Venus 47°.

The interval of time between two successive inferior conjunctions can be observed; for, in inferior conjunction, the planet being nearest to the earth, appears largest, and may be observed with a good telescope, even a very short time before the conjunction. For our purpose here it is not necessary that the time of conjunction should be observed with great accuracy. Let T represent the time between two successive inferior conjunctions; then, to a spectator in the Sun, in the time T', the inferior planet, (moving with a greater angular velocity) will appear to have gained four right angles, or 360° on the Earth; and the planet and Earth being supposed to move with uniform velocities about the Sun, the angle gained (that is, the angle at the Sun be tween the Earth and planet, reckoning according to the order of the signs,) will increase uniformly.

Let TEL represent the orbit of the Earth, DPGON that of an inferior planet, each being supposed circular, S the Sun in the centre, and P the place of the planet when the Earth is at E. Then in the triangle SEP we obtain the angle SEP the elongation by observation, and the angle PSE by computation; for it is the angle the planet has gained on the Earth since the preceding inferior conjunction. There

fore, this angle PSE: 360°:: the time from inferior conjunction: T. The two angles SEP and PSE being known, the angle SPE is known, and hence SP relatively to SE; for sine angle SPE: sine ang. SEP::SE: SP. Having thus obtained the distance of the planet from the Sun, we can, at any time, by help of the time T and the time of the preceding inferior conjunction, compute the angular distance of the planet from the Earth, as seen from the Sun, and thence, by help of the distances of the planet and Earth from the Sun, compute the planet's elongation from the Sun. Thus the planet being at O, and the Earth at E, we can compute the angle ESO; and having the sides SE and SO, we can, by trigonometry, compute the angle SEO, the elongation of the planet from the Sun. This being compared with the observed angle, we always find them nearly agreeing, and thereby is shown that the motions of the inferior planets, Mercury and Venus, are explained by those planets moving in orbits nearly circular about the Sun in the centre.

Now, in order to find the greatest elongation of the inferior planets, upon the supposition of circular orbits, at their mean distances, we have this trigonometrical proportion; as ES: SG:: radius: to sine angle SEG, because EG is a tangent to the orbit of the planet at the time of its greatest elongation, and the angle SGE, is therefore a right angle. Hence, the greatest elongation of an inferior planet is ex

R. a

pressed by this formula; the sine of the angle SEG=-,

b

b being equal to the distance of the Earth from the Sun, a the distance of the planet, and R radius or sine 900. Or, the greatest elongation may be expressed by this formula, sine ang. SEG=ax radius, a being the relative distance of the planet from the Sun, that of the Earth being unity or 1. For instance, let us take Venus: in this case, b may be taken 69 X radius

equal to 95, and a=69; then, sine angle SEG

95

9.86113=46°35′. Again, b being taken equal to 1, a will be equal to 70526, and sine ang. SEG=radius X.70526; therefore, the angle SEG is equal to 46° 35', the same as before.

The variations in the greatest elongations of the inferior planets, Mercury and Venus, is owing to the elliptical figure of their orbits, and that of the Earth, which also causes a

variation in the stationary points, and in the conjunctions. The ancients observed the places of the fixed stars and planets with respect to the Sun, by the assistance of the Moon, or planet Venus. In the day time they very frequently could observe the situation of the Moon, with respect to the Sun. Venus also being occasionally visible to the naked eye in the day time, they used that planet for the same purpose. Now we can, owing to the convenience of our instruments, without the intervention of a third object, obtain the angular distance of a planet from the Sun, by observing the declinations of each, and the difference of their right ascensions. By which we have, in the triangle formed by the distances of each from the pole of the equator and from each other, two sides and the included angle, to find the third side, the angular distance of the planet from the sun.

3. The motion of an inferior planet is direct from its stationary point, before its superior conjunction, to its stationary point, after the same conjunction; and it appears retrograding from the stationary point, before its inferior conjunction, to the stationary point, after its inferior conjunction.

As the computed place of an inferior planet always agrees with the observed place, (see the preceding Art.) it necessarily follows that the retrograde, stationary appearances, and direct motions of the planets, Mercury and Venus, are explained, by assigning circular motions to them, in orbits which coincide with the plane of the ecliptic.

In order to demonstrate the retrograde and stationary appearances in a clear manner, 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 to be at rest.

P

S*

T

E

M

Fig.2.

R

Illustrations. 1. Let S be the Sun, ET the space described by the Earth in a small portion of time, which therefore may be considered as rectilinear; the motion being from E towards T.

Let V be a planet, supposed at rest, any where on the same side of the line of direction of the Earth's motion, as the Sun. Draw EP parallel to TV; then, while the Earth 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