Astronomy Astrophysics

Bahnbestimmung der Planeten und Kometen by Prof. Dr. G. Stracke (auth.)

By Prof. Dr. G. Stracke (auth.)

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H n: + ... )2- .. ·]2 (b - az) 'YJ: . . . . . . . + b 'YJ: + .. ·) 2 + ··· • • • • • Weiter ist secyz =(I- zsin~y:)-r= I+ zsin~r: + ··· secy~ =I+ 6 sin~r: + · · · Setzt man alle diese Reihen, von denen hier nur die Anfangsglieder hingeschrieben sind, in Gl. (46) ein, so erhält man links und rechts nach Potenzen von 'Yfz fortlaufende Reihen, in denen die Koeffizienten gleicher Potenzen übereinstimmen müssen. Führt man die Berechnung der einzelnen Koeffizienten a, b, c, ... - -~~ sin~y~ kz 'Y/2 + /i693 k4 n:) kz 'Yfz + ....

Q) = r sin u cos i r sin b = r sin u sin i also LI cos ß cos (A. Q) LI cos ßsin (A. Q) LI sin ß = r sin u sin i - R sin B. (8) (9) Vernachlässigt man die heliozentrische Erdbreite B, die den Betrag von etwa r" nicht übersteigt, so gehen die GI. (6) und (9) über in und r cos b cos (l-L) =LI cos ß cos (A. -L) + R r cos b sin (l-L) =LI cos ßsin (A. -L) r sin b = LI sin ß (ro) LI cos ß c;os (A. Q) = r cos u-R cos (L -~) LI cos ßsin (A. Q) LI sin ß = r sin u sin i . (n) b) Beziehungen im äquatorialen System.

E. Durch die Beobachtung erhalten werden die äquatorialen geozentrischen Polarkoordinaten Rektaszension oc und Deklination b. Man zählt oc vom Frühlingspunkt aus im Sinne wachsender Längen von oh bis 24h, oder von 0° bis 360°, b vom Äquator aus von 0° bis ± 90°, ± je nachdem P nördlich oder südlich des Äquators liegt. Zwischen den geozentrischen Koordinaten ~,, r/, C' und LI , oc, ö bestehen die Beziehungen f =LI cos b cos oc rj' =LI cos b sin oc C' =LI sin ö. (13) Die heliozentrische und die geozentrische Bewegung.

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