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 QH 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

place is the place where the body actually is at any time.

Illustrations of the above articles.

1. Let APQBH, (see fig., page 239,) be the elliptical orbit of a planet, S the Sun in one of the foci; the planet in revolving round that luminary in the direction of the letters APRQ, &c. cannot be always at the same distance from the focus S, but will be farthest from it at the extremity A of the greater axis, and nearest to it when in B. The point A is mamed the higher apsis, or the aphelion; and the point B the lower apsis, or perihelion; these two points vary, and their motion in a century is called the secular motion. The distance between the centre C and the sun, or focus S, is the eccentricity of the orbit. The greater axis AB is the line of the apsides. The straight line SQ, drawn from the extremity of the lesser axis QH to the sun, is the mean distance of the planet from the sun.

The mean distance added to the eccentricity is equal to the aphelion distance SA. And the mean distance minus The eccentricity is equal to the perihelion distance SB.

2. A planet does not proceed in its orbit with an equal motion; but in such a manner that the Radius Vector describes an area proportional to the time: for instance, suppose a planet to be in A, when in a certain time it arrives at P, the space, or area, ASPA is equal to the space, or area, PSQP, described in the same time from P.

3. If the angular motion of the planet about the sun were uniform, the angle described by the planet in any interval of time, after leaving the aphelion, might be found by simple proportion, from knowing the periodic time in which it describes 3600; but as the angular motion is slower near aphe lion, and faster near perihelion, to preserve the equable de scription of areas, the true place will be behind the mean place in going from aphelion to perihelion; and from peri helion to aphelion, the true place will be before the mean place. For instance, suppose P be the true place of a planet at the end of a certain time after leaving the aphelion A; then, its mean place would be in some part of the orbit between P and B. Now, let R be the mean place of the planet, when P is its true place; then the angle ASR is the mean anomaly; the angle ASP, the true anomaly; and the angle PSR, the difference between the mean anomaly and ne true anomaly, is the equation of the centre.

Or, if a planet is supposed to move in a circle, in the centre of which is the sun, the portion RO of the circle bears the same ratio to the whole circumference, that the time since the planet passed its aphelion does to the time of its whole revolution; the arc RO is termed the mean anomaly.

Again, if the elliptical orbit of a planet be so divided that the area ASP shall have the same ratio to the area of the whole ellipse AQBH, which the time since the planet passed its aphelion has to its whole period, then is the angle ASP the measure of the planet's distance from the aphelion, at the time the planet is in P. This angle is also the true anomaly; and the difference between the mean anomaly and the true anomaly, is the equation of the centre, as before.

4. The arc AD of the circle AGBK intercepted between the aphelion A, and the point D, determined by the perpendicular DPE to the line of the apsides, drawn through the true place P of the planet, is called the eccentric anomaly, or of the centre. Or, the angle ACD at the centre of the circle, is usually called the eccentric anomaly.

5. Equations, in Astronomy, are corrections which are applied to the mean place of a body, in order to get its true place; and argument is also a term sometimes used to denote a quantity upon which another quantity or equation depends; or, it is the arc, or angle, by means of which another arc may be found, bearing some proportion to the first: thus, the argument of the equation of the centre, is the distance of a planet from the aphelion or apogee, because it is upon that the equation of the centre depends.

15. The Nodes are the two opposite points where the orbit of a primary planet intersects the plane of the ecliptic, or where the orbit of a secondary planet cuts that of its primary. The straight line joining these two points is called the line of the

nodes.

Ascending node is that point where the planet ascends from the south to the north side of the ecliptic; and the opposite point where the planet descends from the north to the south side of the ecliptic, is called the descending node. The ascending node is denoted by the character U, and the descending node by. The inclinations of the planes of the orbits of all the planets, except Pallas, to the plane of the Earth's orbit are small. small