Prerequisites for celestial coordinate conversions?

The celestial coordinate systems help identify the celestial objects in the sky for a given observer. The coordinate systems discussed previously along with their components are listed below

1. The Horizontal coordinate system
   1. Azimuth
   2. Altitude
   3. Zenith angle
2. The Equatorial coordinate system
   1. Declination
   2. Right ascension
   3. Hour angle
3. The Ecliptic coordinate system
   1. Ecliptic longitude
   2. Ecliptic latitude
4. The Galactic coordinate system
   1. Galactic longitude
   2. Galactic latitude

Below we will discuss the coordinates of each coordinate system, their relationships, and the prerequisites for performing coordinate conversion from one coordinate system to the other. The python NumPy library is extensively used which can be imported as follows

import numpy as np

Altitude (alt) and zenith angle (z)

The altitude/zenith angle pair is used in the horizontal coordinate system. This pair is used in conjunction with the azimuth angle to determine the location of a celestial object in the observer’s sky. The altitude and zenith angle being complementary angles, can be determined directly from the other one. The conversion to and fro for altitude and zenith angles is shown below

Altitude to zenith angle

Zenith angle to altitude

If the provided angle is in radians change deg=True to deg=False.