On the Determination of the Orbits of Comets, According to the Methods of Father Boscovich and Mr. de La Place. with New and Complete Tables; And Exam

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1793 Excerpt: ...arithmetical complement of twice the Logarithmic Cosine of the half Anomaly, and the Logarithm of the Perihelion Distance. § 2. The rest of the operation for Comets is the same as for Planets. We have the distance from the Node to the Perihelion, which is the Arch N V, Figure 13; we have found the Anomaly, which is the Arch V C; and if the Comet's motion is direct, and the time follows the arrival at the Perihelion; or both these conditions are changed, V C, will follow the order of the Signs; otherwise it will not. By the two Arches N V, V C, with their direction, we obtain the Arch N C, which is the Co U F1c. 13. met's distance from the Node; which with the Angle N, which is the Inclination of the Orbit, will give the Arch C P, the Comet's Heliocentric Latitude; and N P, which is the distance from the Node N, to the place of the Comet on the Ecliptic; and the Longitude of the Node being known, the Comet's Heliocentric Longitude is found from it. The Theorem for the Latitude C P, is; Sin. N C X Sin. N = Sin. C P. And for the Arch N P, the Theorem is, Tangent N C X Cosine N = Tangent N P. UA. § 3. This might have been done from Figure 1, by Plane Trigonometry only; but the method above given is very simple, and generally used for the Planets. Transferring these Elements to Figure 1, we have the direction of the Line S P, which is the Heliocentric Longitude; the Radius S C; the Heliocentric Latitude C S P: from whence may be deduced the Curtate Distance S P, = SC X Cosine C S P. From the Ephemera we find the Earth's place and distance from the Sun. The difference of the Heliocentric Longitude of the Comet, and the Earth, is the Angle TSP; which with the Sides S T, S P, will give the Angle S T P; and the Comet's curtate distance from the Earth, T P....