Calculating the rotation angle of the moon's surface features for a given date and location on earth

[sepw]

Hi

First, thank you for the excellent Astronomy project! During the development of my iOS app I have attempted to use several different projects but none have been as well-designed, well-documented and simple to build/integrate as yours.

My project's requirements are simple: render a two-dimensional representation of the moon, as observed from a given date and location on earth, with the correct

• illumination (% and angle);
• rotation of surface features.

Representing the moon's libration is not a requirement.

I have the illumination % and angle working correctly, as discussed by @sihil and @cosinekitty in #292. The discussion surrounding that issue and the code in camera.c were extremely helpful. Thank you for that!

However, I am stuck on the rotation of the moon's surface features. @cosinekitty provides some helpful tips to @sihil in #292 (comment), suggesting use of the Astronomy_RotationAxis() function (I'm using the C interface) in combination with "the longitude correction from the libration function". I have investigated the source code of the Astronomy_Libration() function but am unable to see how this might help me.

I have no experience with astronomical algorithms and would greatly appreciate some more information. In addition, it would be great if the missing steps could be added to the camera demo programs such that this information would also be available to others.

Many thanks.

[cosinekitty]

For the Moon's surface features, I would have to sit down and study it carefully. You are right that libration is a secondary concern, to get a little extra realism. Getting the Moon's axis orientation correct for a given observer is the most important part. I believe using the RotationAxis function is the correct first step. Its return value includes the north vector, expressed in EQJ (equatorial J2000) coordinates.

The tricky part is how to re-orient this vector. I believe you would use a similar rotation matrix approach as in camera.c, only you would have to calculate the rotation matrix that converts EQJ (not EQD - equator of date) to the observer's HOR (horizontal) orientation. But then you have to project that vector from the Moon's apparent center to find out where its north pole is, as seen by the observer, and figure out the angle to rotate the Moon's image.

This is not obvious to me right now. Furthermore, it would be good to find known correct answers from a reliable source before writing any code. I have found it doesn't make sense to write code to calculate an answer if you don't already have at least one test case where you know what the right answer is.

I don't have time to devote to this kind of research right now. Maybe Stellarium source code would give some clues. I don't know if the JPL Horizons online calculator can calculate apparent orientation of the Moon. I don't remember seeing that there, but it's worth a look, just to see if there is good test data.

I hope this helps at least a little bit...

[sepw]

Hi @cosinekitty

Many thanks for the input. I'll take a look at the Stellarium source code...