# calculating paralax angle from observations

Say I have 2 records, in horizontal coordinates of the azimuth ($A_z,A_z^{'}$) and altitude ($\alpha,\alpha^{'}$) of the moon at the same time in two different places that are $\theta$ degrees apart (taking the angle from the centre of the earth and assuming the earth is a perfect sphere). Is it possible to calculate the parallax angle of the moon between these two points with only the values above? if so how and if not what other values would I need?

• My intuition is that you need the latitude and longitude of the two places, not the angle between them. With that information, you can construct vectors from each observer to the Moon, from which you can calculate where they intersect (or more likely where they are closest to each other). – JohnHoltz Jan 4 '18 at 23:55
• Seems like a geometry problem. Try to make a sketch of the situation: Earth, two positions at different latitudes connecting their lines of sight with the moon. Mark the angles represented by the coordinates you know, and the solution should become clear. – AtmosphericPrisonEscape Jan 5 '18 at 13:15
• en.wikipedia.org/wiki/Parallax explains how to calculate parallax, but you want the straight line distance between the two points, ie, the line going through the center of the Earth, not the great circle distance between the two points. Also, as @JohnHoltz notes, it does depend on where on Earth you are relative to the moon, since the moon is close enough that this makes a difference. – user21 Jan 6 '18 at 12:22
• Assuming the Earth is a sphere, you could easily calculate the baseline from $\theta$, and you have your two vector angles. – Mick Jan 9 '18 at 1:44