Rømer's Measurement of the Speed of Light

Ole Rømer, a Danish astronomer, calculated the speed of light by observing the eclipses of Jupiter's moon during the years 1668–1674. A discrepancy was observed for the time between the eclipses, increasing when the Earth was moving away from Jupiter and decreasing when the Earth was approaching. In half a year, there are a total of 102 eclipses of Io, giving a maximum delay of 16.5 minutes (shown in the bottom-right plot). Rømer interpreted this as the difference in the times needed for the light to travel between Jupiter and Earth. He obtained a value of 214,000 km/s compared to the current value 299,792 km/s. The diameter of the Earth's orbit was not accurately known and there was also an error in the measurement of the delay. Nevertheless, it was a first confirmation that the speed of light is finite.

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The time delay of an eclipse of Io is given by

Δ t=(1/c)((Sqrt[((((Subscript[R, E])sin((Subscript[ω, E])i P)))^2)+((((Subscript[R, J])-(Subscript[R, E])cos((Subscript[ω, E])i P)))^2)])-(Subscript[d, 1])),

where (Subscript[R, E]) and (Subscript[R, J]) are the radii of the orbits of the Earth and Jupiter, (Subscript[ω, E]) is the angular velocity of Earth, i represents the (i^th) period of Io, and P is Io's period; finally, (Subscript[d, 1]) is the distance when the Earth is closest to Jupiter and c is the velocity of light.

[1] J. H. Shea, "Ole Rǿmer, the Speed of Light, the Apparent Period of Io, the Doppler Effect, and the Dynamics of Earth and Jupiter," Am. J. Phys., 66(7), 1988 pp. 561–569.

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