How do you know the speed of light is 3x 10^8 m/s?

-Karthik Gurumurthy

Back in the mid-1600s, these astronomers in Paris were watching Jupiter’s moons, particularly the innermost one called Io. They tracked when it disappeared behind Jupiter, reappeared on the other side, and calculated that Io takes about 1.75 days (that’s 1 day and 18 hours) to make a complete revolution around Jupiter.

With this info, they thought they could predict exactly when Io would be eclipsed in the future. But then something weird started happening. When Earth was on the opposite side of the sun from Jupiter, Io’s eclipses happened a few minutes later than predicted. And when Earth moved to the other side of its orbit (with the sun between Earth and Jupiter), the eclipses were about 16⅔ minutes late!

This totally baffled the French astronomers until 1675 when a Danish guy named Ole Römer had a genius realization: The delay wasn’t because of anything weird happening with Jupiter or Io – it was because light itself takes time to travel! When Earth was farther away from Jupiter, the light reflecting from Io had to travel a longer distance to reach us.

Römer figured out that the delay was exactly 1,000 seconds (about 16 minutes and 40 seconds). He also knew from other astronomers that Earth’s distance from the sun was about 93 million miles, and that when the observations were made at different points in Earth’s orbit, the difference in distance was about

Back in the mid-1600s, these astronomers in Paris were watching Jupiter’s moons, particularly the innermost one called Io. They tracked when it disappeared behind Jupiter, reappeared on the other side, and calculated that Io takes about 1.75 days (that’s 1 day and 18 hours) to make a complete revolution around Jupiter.

With this info, they thought they could predict exactly when Io would be eclipsed in the future. But then something weird started happening. When Earth was on the opposite side of the sun from Jupiter, Io’s eclipses happened a few minutes later than predicted. And when Earth moved to the other side of its orbit (with the sun between Earth and Jupiter), the eclipses were about 16⅔ minutes late!

This totally baffled the French astronomers until 1675 when a Danish guy named Ole Römer had a genius realization: The delay wasn’t because of anything weird happening with Jupiter or Io – it was because light itself takes time to travel! When Earth was farther away from Jupiter, the light reflecting from Io had to travel a longer distance to reach us.

Römer figured out that the delay was exactly 1,000 seconds (about 16 minutes and 40 seconds). He also knew from other astronomers that Earth’s distance from the sun was about 93 million miles, and that when the observations were made at different points in Earth’s orbit, the difference in distance was about 299337984000 meters (the diameter of Earth’s orbit).

So he did the math: diameter # given above divided by 1,000 seconds = 3×10^8 m per second. Boom! That’s how fast light travels!

Galileo had tried to measure the speed of light earlier in the 1600s using lanterns on distant hills, but light moves WAY too fast to measure over such short distances. He could only conclude that light moves really fast. It took astronomical observations across the solar system to finally crack this mystery!