Meridian Transits

Consider a celestial object, of declination $\delta$ and right ascension $\alpha$, which is viewed from an observation site on the earth's surface of terrestrial latitude $L$. According to Eq. (55), the object culminates, or attains its highest altitude in the sky, when $\alpha_0=\alpha$. This event is known as an upper transit. Furthermore, the object attains its lowest altitude in the sky when $\alpha_0=180^\circ + \alpha$. This event is known as a lower transit. Both upper and lower transits take place when the object in question lies in the meridian plane.

According to Eq. (55), the altitude of a celestial object at its upper transit satisfies $\sin a_{\rm +} = \cos (L-\delta)$, implying that

$$a_{\rm +} = 90^\circ - \vert L-\delta\vert.$$ (59)

Likewise, the altitude at its lower transit satisfies $\sin a_{\rm -} =- \cos (L+\delta)$, giving

$$a_{\rm -} = \vert L+\delta\vert - 90^\circ.$$ (60)

The previous two expressions allow us to group celestial objects into three classes. Objects with declinations in the range $90^\circ \geq \delta > 90^\circ -L$ never set: i.e., their lower transits lie above the horizon. Objects with declinations in the range $L-90^\circ > \delta \geq -90^\circ$ never rise: i.e., their upper transits lie below the horizon. Finally, objects with declinations in the range $90^\circ -L\geq \delta \geq L - 90^\circ$ both rise and set during the course of a day. It follows that all celestial objects appear to rise and set when viewed from an observation site on the terrestrial equator (i.e., $L=0^\circ$) . On the other hand, when viewed from an observation site at the north pole (i.e., $L=90^\circ$), objects north of the celestial equator never set, whilst objects south of the celestial equator never rise. All three classes of celestial object are present when the sky is viewed from an observation site on the earth's surface of intermediate latitude.