How can I calculate the angle of tilt for moon phase at my location?

[snorkeler]

I have an iPad app almost complete that displays live weather data from my home weather station here in Hawaii for community use.

I'm showing a picture of the moon phase, and a UPS freight pilot friend who flies at night pointed out that the conventional vertical phase orientation is inaccurate.

In order to rotate the pictures, I would need a formula to calculate the angle of tilt for our 20° latitude at time of moonrise, and I suppose time of moonrise also. This is outside my area of expertise...can someone point me in the right direction?

 

[Bill_K]

snorkeler, This is going to be a bit messy, but I guess you knew that! I can point you in the right direction, but you will have to fill in the details. You will need to do some spherical trigonometry. The formulas for right spherical triangles are called Napier's Rules, which can be found for example on Wikipedia. Note that in spherical trig, everything is an angle. Even the sides of triangles are angles.

Definitions:
Zenith - the point directly overhead
Meridian - the line on the sky passing through the Zenith and going directly North-South
Ecliptic - the path on the sky followed by moon, sun and planets (approximately).

Ok, the vertices of the triangle are Z = Zenith, M = Moon and E = intersection of Ecliptic and Meridian. First, what is the side ZE? This will vary during the year. In spring and fall at the time of the equinoxes it will be your colatitude, 90 - 20 = 70 degrees. In summer and winter it will differ from this up to 23.5 degrees in either direction, varying sinusoidally.

Second, what is the side EM? This will increase at a constant rate, being 0 when the moon crosses the meridian and going all the way around 360 degrees in a 24-hour period.

Given ZE and EM you can use Napier's rules to calculate the angle at the vertex M, which is the angle of tilt you want.

To find the time of moonrise, set ZM = 90 degrees and solve for t.