I want to know how to correctly calculate altitude and azimuth difference, separately, between two points in the sky. The same way will be with icrs coordinates. For the altitude difference, I simply subtracted altitude values of two points, but for the azimuth, the difference has to be multiplied with the cosine of altitude of one point, right? I tried to reproduce the results with the astropy spherical_offset_to() method, which returns dAz and dAlt but get quite different results. I tried to find corresponding literature but couldn't. Can someone explain to me how it should be calculated? Thanks
Here is reproducible example for two points, a and b.
import numpy as np from astropy.coordinates import SkyCoord a = SkyCoord(az=0, alt=30, unit="deg", frame="altaz") b = SkyCoord(az=90, alt=40, unit="deg", frame="altaz") print(a.spherical_offsets_to(b)) print(b.spherical_offsets_to(a)) print("dAz:",((b.az - a.az)*np.cos(np.deg2rad(a.alt))).value, "dAlt:", (b.alt - a.alt).value) print("dAz:",((a.az - b.az)*np.cos(np.deg2rad(b.alt))).value, "dAlt:", (a.alt - b.alt).value)
And here are the results:
(<Angle 67.23952373 deg>, <Angle 33.82584497 deg>) (<Angle -69.63942512 deg>, <Angle 22.52101212 deg>) dAz: 77.94228634059948 dAlt: 10.0 dAz: -68.94399988070803 dAlt: -10.0
EDIT: More details regarding the purpose of my question/request.
Two devices, located on the earth, separated with some fixed azimuth and altitude angle between them. Both devices point in the sky. I have a series of RA & Dec coordinates(or equally AltAz) of their pointings, during some time range. Using that pointings data, I want to measure mentioned fixed angle offset between two devices.
Why? If I know the angle offset, and the coordinates of one device, I can calculate the pointing for the second device and vice versa.