Methods, Transformations, and Visualizations of Reference Frames in Orbital Mechanics

Abstract

This investigation explores planetary motion within the solar system, with a focus on
mapping these movements using principles from physics and engineering. It centers around
modeling the trajectories of planets while accounting for different frames of reference, including
the rotational effects of Earth. Concepts such as vectors, Kepler’s laws, and Newton’s laws of
motion provide the scientific basis of the research, implemented by Python, which is used to
map out these orbital dynamics. Using a two-body gravitational model and standard
moving-frame relations, coordinate shifts are implemented via rotation matrices to map
planetary motion consistently across frames. Simulations provide 2D orbit plots and 3D
visualizations employing right ascension and declination to contextualize spatial relationships
and viewing geometry. Results highlight that no single frame is universally best, each is suited to
specific questions and operations. Heliocentric perspectives align naturally with Kepler’s laws
while Earth-fixed and observer-fixed frames illuminate observational phenomena and
operational viewpoints relevant to tracking, navigation, and local sensing.