The first successful measurement of the speed of light was conducted by Danish astronomer Ole Rømer in 1676. Rømer's method was based on observations of the moons of Jupiter.
At the time, astronomers knew that Jupiter had four largest moons, now known as the Galilean moons, discovered by Galileo Galilei in 1610. These moons, Io, Europa, Ganymede, and Callisto, regularly orbit Jupiter. Rømer focused on Io, the closest of these moons to Jupiter.
Rømer noticed that the timing of Io's eclipses by Jupiter seemed to vary depending on the Earth's position in its orbit around the Sun. He made this observation while he was studying the motion of Jupiter's moons to improve the accuracy of predicting their positions for the Royal Observatory in Paris.
Rømer correctly hypothesized that the variations in the timing of Io's eclipses were due to the finite speed of light. When the Earth was closer to Jupiter, the observed eclipse times were ahead of their predicted times, and when the Earth was farther from Jupiter, the observed eclipse times were behind their predicted times.
He realized that light takes time to travel the vast distance between Jupiter and Earth, and the observed time discrepancies were a result of this light travel time. The speed of light was affecting the apparent timing of Io's eclipses as seen from Earth.
Using his observations and some mathematical calculations, Rømer estimated the speed of light to be about 225,000 kilometers per second, which is remarkably close to the actual value of around 299,792 kilometers per second.
Rømer's groundbreaking work not only provided an initial measurement of the speed of light but also offered strong evidence that light traveled at a finite speed, contrary to the previously held belief that light propagated instantaneously. His work laid the foundation for future experiments and measurements to refine the value of the speed of light, and it became a crucial milestone in the development of modern physics.