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 Examples of the Calculation by Both Methods. by Sir Henry Englefield
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 Examples of the Calculation by Both Methods. by Sir Henry Englefield,
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 ...
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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....
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