From Rømer
To Black Holes
And Beyond
Introduction
This document serves as the foundational entry in a new series on the role of geometry in shaping our understanding of astronomical observations, from the earliest recorded experiments to modern black hole imaging. The focus is on the positional relationship between observer and observed, and the decisive role angular geometry plays in what we perceive as light, shadow and motion in space.
Core Principle
Observation is Geometry
Across history, pivotal astronomical claims, from Ole Rømer’s speed of light estimation to the Event Horizon Telescope’s black hole imagery, have hinged on geometry. The angle, position and relative motion of observer and target determine what is seen, how it is interpreted and whether it appears as bright, dark, moving or still.
Historical Milestones
in Geometric Observation
• Ole Rømer (1676) used the timing of Jupiter’s moon Io to suggest a finite speed of light. His conclusion was based entirely on angular timing differences caused by Earth’s orbital position, geometry dictating perception.
• James Bradley (1728) discovered stellar aberration, attributing it to the motion of Earth combined with light’s travel. The effect is geometric: the observer’s motion changes the apparent position of the star, producing a predictable circular trace.
• François Arago (1810s) and Augustin-Jean Fresnel used light interference and refraction to explain variations in starlight. The patterns depended entirely on alignment and angular displacement, geometry again at the core.
• Modern spacecraft navigation uses precise angular measurements to determine position and velocity, demonstrating that geometry remains the fundamental tool in deep space observation.
Persistent Role of Geometry
in Modern Astronomy
From lunar libration making hidden terrain visible, to gravitational lensing magnifying distant galaxies, to the interpretation of Sagittarius A*’s central shadow, geometry defines visibility. Shifts in observer position or orientation can turn a bright region into darkness, or reveal light where none was thought to exist.
The Lilborn Equation Perspective
Within the Lilborn Equation framework (E = mℓ), light is not traveling through space but is present and interacts only when conditions align.
Geometry dictates these interactions:
The angle of exposure relative to the electromagnetic field structure determines whether light is encountered and thus visible. This reframes “black hole shadows” not as one-way traps, but as zones of non-interaction specific to the observer’s location.
Need for Geometric Literacy
in Astronomy
Misinterpretations often persist when geometric factors are underappreciated or overlooked. Historical observations once attributed to light speed delays or relativistic effects have later been explained by geometric positioning, yet the original claims often remain entrenched in public and academic narratives. A renewed emphasis on geometry could correct these misconceptions.
The Road Ahead
This series will explore, in detail, landmark cases where geometry has determined observational outcomes, including:
Rømer’s light timing, Bradley’s aberration, black hole imaging, gravitational lensing, planetary transits, lunar librations and spacecraft navigation. Each will be re-examined in light of modern understanding, highlighting the decisive role of angular geometry from Earth-based observation to deep space imaging.
Produced by The Lilborn Equation Team:
Michael Lilborn-Williams
Daniel Thomas Rouse
Thomas Jackson Barnard
Audrey Williams