Orbit

ORBIT, in astronomy, is the path of a heavenly body revolv ing around an attracting centre (from Lat. orbita, a track, orbis, a wheel) ; in particular, it denotes the path of a planet or comet around the sun, or of a satellite around its controlling planet.

Kepler's Laws.

In 1609 Johann Kepler announced two laws of planetary motion, and by 1619 he added a third. Kepler's first law is as follows:—A planet moves around the sun in an elliptic orbit, the sun being situated in one focus of the ellipse. If the straight line joining any two points S and T is produced equal distances beyond S and T to A and B, and if P is any point such that the sum of the distances P S and P T is equal to the distance A B, then the aggregate of all such points as P is the curve known as the ellipse. The points S and T are the foci. The curve passes through A and B and A B is called the major axis of the ellipse. if C is the mid-point of A B, the ratio of the length of C S to the length of C A is called the eccentricity. The ellipse then is specified by means of (i) the semi-major axis and (ii) the eccentricity. If the eccentricity happens to be zero, the two foci must coincide at the centre C and the resulting curve is simply a circle; if the eccentricity is precisely unity, then the curve is known as a parabola. Kepler's first law simply states that if the sun is supposed situated at the focus S, the planet's path around the sun—in other words, its orbit—is an ellipse such as is represented in the diagram above. The time required for a complete revolution in the ellipse is the planet's revolution period ; for example, the earth's period of revolution is a little over 365 days; Mercury describes its orbit in 88 days, and Neptune requires 165 years. At A—the point of the ellipse nearest S—the planet is said to be in perihelion, and when it reaches B, the most remote point of the ellipse from S, it is said to be in aphelion.

Kepler's second law states that the straight line joining the sun to the planet (the radius vector) sweeps out equal areas in equal times. In the preceding figure let D be the position of the planet in its elliptic orbit a month after it reached perihelion (A) ; similarly let E F be two positions of the planet separated by an interval of a month; the pair of points X, Y are defined in the same way. The shaded area S D A, for example, is the area

swept out by the radius vector in one month and by the second law the three shaded areas are equal. Now it is clear from the figure that the arc A D is greater than the arc X Y, for the areas S D A and S X Y are equal and S A and S D are less than S X and S Y; consequently, the velocity of the planet in its orbit must be greater between A and D than between X and Y. More definitely, the velocity of the planet is greatest at peri helion, decreasing gradually until aphelion is reached and there after increasing to a maximum again at perihelion.

The figure also shows that the angles described in equal inter vals of time by the radius vector vary throughout the orbit ; for example the angle D S A is clearly greater than the angle X S Y. The angular velocity is greatest at perihelion and least at aphelion. In one complete revolution around the sun, the radius vector sweeps out 36o° and as the period of revolution is accurately known, the average angular velocity is easily deduced. This is known as the "mean motion" and is expressed as so many degrees (or seconds of arc) per day.

Kepler's third law is a relation connecting the semi-major axes of the several planets with their periods of revolution. In Kepler's time, the mean distance of any one planet from the sun was not known in miles but it was known fairly accurately in terms of the earth's mean distance from the sun regarded as the unit of the distance ; in other words, the planetary system had been fairly correctly mapped out but the scale of the map was lacking. Also, the periods of the several planets were known with considerable accuracy. The third law expressed in words is : the cube of the semi-major axis of any planetary orbit divided by the square of the period of revolution is the same whatever planet is con sidered. If the year is regarded as the unit of time and the earth's mean distance from the sun as the unit of distance (this is known as the astronomical unit of distance) the quotient above for the earth is plainly unity and consequently by the third law the cube of the semi-major axis of any other planet (expressed in terms of the astronomical unit) must be equal to the square of the planet's period (expressed in years).