Orbiton’s sun tracking system employs a multi-step process rooted in celestial mechanics and vector calculus to establish the sun’s position in real-time with exceptional accuracy. This methodology is essential for maximizing observational effectiveness and ensuring alignment across spatial and temporal scales. The three key stages of the tracking process are as follows:

1. Extraction of Real-Time Azimuth and Altitude (Az/Alt) Values via Astropy Library
Using the Astropy library, a comprehensive Python package for astronomy calculations, we continuously retrieve the sun’s azimuth (Az) and altitude (Alt) values in real time. The azimuth denotes the sun’s compass direction relative to the observer, while altitude signifies the angular distance above the horizon. These values are calculated based on precise geographic coordinates and synchronized with Universal Time (UT) to ensure consistency with international standards.

2. Conversion to Cartesian Coordinates (x, y, z) Based on Az/Alt Angles
To model the sun's position in three-dimensional space, we convert the Az/Alt values into relative Cartesian coordinates (x, y, z). This involves a spherical-to-Cartesian transformation, where azimuth and altitude angles are interpreted to produce normalized vectors along three orthogonal axes. Mathematically, given the altitude Alt and azimuth Az, we calculate the components as:

• x=cos(Alt)×sin(Az)
• y=cos(Alt)×cos(Az)
• z=sin(Alt)

3. Inferred Orientation: Calculating Pitch and Roll Using Arctangent Functions
With the Cartesian coordinates established, we deduce the required adjustments in orientation—pitch and roll—for our instrument alignment. By applying inverse trigonometric functions, specifically the arctangent, to these x, y, z lengths, we resolve the required pitch (elevation angle adjustment) and roll (horizontal rotation) values that enable the apparatus to lock onto the sun’s position. This step ensures the apparatus dynamically adapts to variations in the sun's path throughout the day.