# What is $\omega$ and $\tau$ in this celestial sphere

In the celestial sphere below, what is the $\omega$ and $\tau$ physically? I mean, In the normal world, how do we see them? for example, we can see the altitude of the sun (a) by examining the shadow of a pillar and comparing it with its height, How do we see $\omega$ and $\tau$ in real world?

S is the sun and W is the west.

Also I want to know how do they effect on the shadow of wall which is built in direction of "$SCP$ to $NCP$".

• What is the source of this image? To remind you, homework (or similar) problems must be acknowledged as such. – James K Apr 13 '17 at 21:00
• @JamesK It is from the answer of National Olympiad of an Asian country. about shadow of a wall which is built in direction of SCP to NCP in arbitary point on the north of the equator. – titansarus Apr 14 '17 at 5:45

The lines SW, WP and PS are curved. This may be to indicate that they are great circles on the celestial sphere. If so then $\omega$ is the spherical angle SWP and $\tau$ is the great circle distance SW, perhaps given as an angle with vertex at the centre of the sphere. Given three points on a sphere (in alt-az coordinates), it is a small exercise in spherical geometry to find the spherical distance and angles between them.
I'm not sure why you are being coy about the source of this. If you could link to the question from which this is taken the meanings of $\delta$ and H could be clearer. I guess the solution is an exercise in spherical angles, and projections from a circle to the plane