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By Richard Fitzpatrick

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Now, λ and α satisfy Eq. 39), as well as the above equation. Thus, eliminating α between these two equations, we obtain sin λ sin ǫ . 43) cos L This expression gives the azimuth, A, of the ascending point of the ecliptic as a function of its ecliptic longitude, λ, and the latitude, L, of the observation site. For instance, suppose that we wish to find the azimuth of the point at which the sun rises on the eastern horizon at an observation site of terrestrial latitude +60◦ , on a day on which the sun’s ecliptic longitude is 08PI00.

The symbols S and N indicated that the upper transit of the sun occurs to the south and north of the zenith, respectively. 5: Right ascensions of the ecliptic for latitude 0◦ . 6: Oblique ascensions of the ecliptic for latitude +10◦ . 7: Oblique ascensions of the ecliptic for latitude +20◦ . 8: Oblique ascensions of the ecliptic for latitude +30◦ . 9: Oblique ascensions of the ecliptic for latitude +40◦ . 10: Oblique ascensions of the ecliptic for latitude +50◦ . 11: Oblique ascensions of the ecliptic for latitude +55◦ .

A great circle passing through the zenith) drawn through it. 12: Parallactic angle in the case where increasing altitude corresponds to decreasing ecliptic latitude. SCBE is the southern horizon, with S and E the south and east compass points, respectively. DYB is the ecliptic. ZDS the meridian, and Z the zenith. ZYC is an altitude circle. altitude a ≡ CY of point Y, as well as the angle µ ≡ ZYB. Note that µ is defined such that it lies between the ecliptic in the direction of increasing ecliptic longitude and the altitude circle in the direction of increasing altitude.

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