CHAPTER II.

Explanation of astronomical terms, &c.

1. The orbit of a planet or comet is the imaginary path or track, in which it performs its revolution round the Sun. The orbits of all the primary planets are elliptical or oval, with the Sun situated in one of the foci; as at S. This is usually called Kepler's first law.

If in two points F, S, taken in a plane, are fixed the ends of a thread, the length of which is greater than the distance between these points; and if the point of a pen or pencil applied to the thread, and held so as to keep it uniformly tense, is moved round, till it returns to the place from whence the motion began; the point of the pen or pencil, as it moves round, describes upon the plane a curve line, which is usually called the ellipse. The figure bounded by the curve line is, properly speaking, the ellipse or oval, though the term ellipse is more commonly used to imply the boundary of that figure.

The points F and S, where the ends of the thread were fixed, are called the foci of the ellipse. The point C, which bisects the straight line between the foci, is named the centre of the ellipse. The line A B is called the transverse or greater axis, and Q H the conjugate or lesser axis ; and the distance between one of the foci as S, and the centre C, is called the eccentricity of the ellipse. It is evident, that the less the eccentricity is, the nearer will the figure of the ellipse approach to that of a circle.

2. Aphelion is that point in the orbit of a planet which is farthest from the Sun, sometimes called the higher apsis.

3. Perihelion is that point in the orbit of a planet which is nearest to the Sun, sometimes called the lower apsis.

4. Apogee is that point of the earth's orbit which is farthest from the Sun, or that point of the Moon's orbit which is farthest from the Earth.

5. Perigee is that point of the Earth's orbit which is nearest to the Sun, or that point of the Moon's orbit which is nearest to the earth.

The terms Aphelion and Perihelion are also applied to the Earth's orbit.

6. Apsis of an orbit is either its aphelion or perihelion apogee or perigee; and the straight line which joins the apsides, is called the line of the ap

sides.

7. The distance of the Sun from the centre of a planet's orbit, is called the eccentricity of the orbit. 8. A straight line drawn from the centre of the Sun to the centre of any of the primary planets, is called the radius vector of that planet.

A straight line joining the centres of the Earth and Moon, is called the radius vector of the Moon.

9. As the orbits of the planets are elliptical, having the Sun in one of the foci; their motions round

that body are not equable, being greatest in the perihelion, and least in aphelion. The motion of a planet in every point of its orbit is, however, regulated by an immutable law, which is this; that the radius vector of a planet describes equal elliptic areas in equal times. This is usually called Kepler's second law.

10. It was also discovered by Kepler, and has been fully confirmed by all astronomers and mathematicians since his time, that the square of the time in which any planet revolves round the Sun, is to the square of the time in which another planet does the same, as the cube of the mean distance of the former from the Sun, is to the cube of the mean distance of the latter. This is usually called Kepler's third law.

Hence, if the distance of the Earth, or of any planet, from the Sun, and the periodical revolutions of all the planets be once ascertained; the cubes of the mean distances of the several planets from the sun may be readily found by direct proportion.

11. The true anomaly of a planet is its angular distance at any time from its aphelion, or apogee. 12. The mean anomaly is its angular distance from its aphelion, or apogee, if it had moved uniformly with its mean angular velocity.

In the tables of the Sun, Moon, and planets, the epochs ⚫ have been hitherto given for the apogee; but as they must be taken for the perigee of comets, De la Caille proposed that, for the sake of uniformity, the same should be adopted for all the bodies in the planetary system.

13. The difference between the mean anomaly and true anomaly, is called the equation of the centre.

14. The mean place of a body is the place where that body (not moving with an uniform angular velocity about the central body) would have been if the angular velocity had been uniform. Its true