How Romer calculated Speed of Light

Pavitra Kanetkar |


... and that's how Rømer calculated Speed of Light 

Rømer found differences in Jupiter's Eclipses of Io.

The confusion here is, the total time of a eclipse will always be same regardless the earth's position around the sun so how did he get the time difference.

Jupiter is so large that eclipses occur at regular intervals. Every time Io completes a revolution around Jupiter, the appearing time and disappearing (behind Jupiter) time can be observed by a telescope.

Rømer predicted all of Jupiter's eclipses for the next year. But as the Earth was moving away from Jupiter, there was the time difference between predicted starting time of eclipse and actual starting time of Eclipse.

The maximum difference was 22 minutes.

Rømer concluded that Io's Orbital Period cannot be changed. The only possibility is Speed of Light is not infinite. He noticed that when Earth moved away from Jupiter, the observed eclipses of Io were delayed by up to 22 minutes compared to when Earth was closer. 

Over six months, Earth moves from a position where it is closest to Jupiter to a position where it is farthest away. The extra distance light must travel in this time is approximately the diameter of Earth’s orbit around the Sun.

Rømer reasoned that if light takes 22 minutes (1320 seconds) to travel 300 million km, then the speed of light (cc) can be estimated using:

c=distancetime=3×108 km1320 sc = \frac{\text{distance}}{\text{time}} = \frac{3 \times 10^8 \text{ km}}{1320 \text{ s}}

The modern value of the speed of light is 299,792 km/s.

Rømer’s estimate was lower due to imprecise measurements of Earth’s orbit at the time, but it was still a groundbreaking achievement.


 

Following table shows the differences in the observed eclipse times that Rømer would have noticed due to Earth's changing distance from Jupiter. This table is based on the idea that as Earth moves away from Jupiter, the observed eclipse times are delayed, and as Earth moves toward Jupiter, the eclipse times are observed earlier than expected.

 

Position of Earth Eclipse Observation (Relative to Expected Time) Reason Time Difference Accumulated
Earth approaching Jupiter Eclipse observed earlier than expected Light has to travel a shorter distance -11 minutes
Earth closest to Jupiter Eclipse observed on time Minimum light travel distance 0 minutes
Earth receding from Jupiter Eclipse observed later than expected Light has to travel a longer distance +11 minutes
Earth farthest from Jupiter Eclipse observed most delayed Maximum light travel distance +22 minutes

Explanation:

  • Earth Approaching Jupiter: As Earth moves toward Jupiter, the distance light has to travel decreases, so the eclipses are observed earlier than expected.

  • Earth Closest to Jupiter: When Earth is closest to Jupiter, the distance is minimized, so eclipses are observed exactly on time.

  • Earth Receding from Jupiter: As Earth moves away from Jupiter, the light has to travel farther, causing the eclipses to be observed later than expected.

  • Earth Farthest from Jupiter: When Earth is at its farthest point from Jupiter, the delay is at its maximum (about 22 minutes).

 

-- Pavitra Kanetkar

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