What the work claims
Light does not propagate instantaneously. Its travel time is measurable across astronomical distances. The observed variations in Io’s eclipse timings are due to changes in the light-travel distance as Earth orbits the Sun.
How it was done
Rømer observed Io’s immersions at point C from Earth positions F and G, avoiding confusion with eclipses and occultations. He worked by trial and error over eight years of observations at the Royal Observatory in Paris. He reasoned that light’s finite speed explained delays in Io’s emergence from Jupiter’s shadow — for example, a ~3½-minute delay when Earth moved from point L to K.
What holds up
The core claim holds: light travels at a finite speed. This was demonstrated in 1676 using systematic, repeated observations of Io’s orbital timing against Earth’s changing position. Cassini announced the inference on 22 August 1676, citing ten to eleven minutes for light to cross half the terrestrial orbit — consistent with Rømer’s estimate of ~11 minutes for the full Earth–Sun distance.
What does not
Rømer did not calculate the speed of light. He gave no numerical value for it. He did not compute the ratio of light’s speed to Earth’s orbital speed. He did not claim to measure light’s speed directly — only to demonstrate its finitude and estimate light’s travel time across the Earth–Sun distance.
Why it matters beyond the lab
It ended the ancient assumption of instantaneous light — a precondition for Newtonian mechanics, Maxwell’s equations, and Einstein’s relativity. It showed that astronomical observation could yield fundamental physical constants — not just positions or periods — inaugurating astrophysics as a quantitative science.
Is it worth your time
Yes. It is the first empirical demonstration that light has a finite speed — not inferred from theory, but measured through celestial timing. It redefined causality in astronomy and forced revision of ephemerides. You need only grasp one orbital geometry and one delay to see how it works.