Relativity Science Calculator - Olaf Roëmer and the speed of light

Olaf Roëmer and the speed of light

"... light takes some time to come from the satellite to us; and it takes approximately ten or eleven minutes to traverse a distance equal to the semi-diameter of the Earth's orbit" - Giovanni Cassini ( 1625 – 1712 )
( but this astronomical insight was quickly rejected by Cassini only to be proven correct later by Olaf Roëmer! )

Almost from ancient times, light has been acknowledged as the transmitter of information to human eyes. Without light hardly anything is known about the "external world". Aristotle ( 384 - 322 BC ) conceived of light as ubiquitous and instantaneous whereas Empedocles of Acragas ( 492 - 432 BC ), Sicilian philosopher-physician-poet and Socrates contemporary, philosophized that the time of transit of light thru an intervening space while bringing information to an observer's eye is finite.

More recently, however, the first acknowledged quantitative determination of the finite speed of light was performed by Danish Olaf Roëmer ( 1644 - 1710 )


Olaf Roëmer

in December 7, 1676 and officially published in "Philosophical Transactions of the Royal Society, No. 136; June 25, 1677, by Olaf Roëmer". He observed that Jupiter had a transit orbit equivalent to 12 Earth-years and that between an Earth-winter and -summer Jupiter moved slightly [ 1/24th in its total transit orbit ] and hence remained relatively aligned with Earth during any 6 - month period. Further, by observing the satellite motions of Jupiter's Io moon as Io entered and then exited from behind Jupiter's shadow when Earth and Jupiter were closest [ Earth summer position at H, see below ], it took approximately 42 hours and 28.6 minutes or ≈ 42.5 hours.


Roëmer's explanation, published June 25, 1677


source: NASA, December 7, 2002 with Io casting

its own shadow to its left. Io was first discovered by

Galileo Galilei on January 7, 1610.

Now as days passed and further observations were made, Roëmer calculated additional minutes to observe Io's reemergence from behind Jupiter's shadow as Earth and Jupiter moved further apart in their respective solar obits [ Earth's relative movement from position G to F. See above. ] In fact, at position F, the period of Io's reemergence was approximately 14 seconds longer! Contrariwise, the time elapses for Io's appearance from behind Jupiter's shadow would shorten as Earth moved relatively closer to Jupiter as from position K to L. At winter position E, the time neither shortened nor lengthened but however there was a delay of approximately 22 minutes as compared to summer position H. Interestingly winter position E represents 2.0 AUs or the diameter of Earth's solar transit which Giovanni Cassini calculated as ≈ 140,000,000 km in 1672. Roëmer therefore astutely calculated the finite speed of light as


[ note: the speed of light is denoted by    from the Latin celeritas meaning speed or swiftness. ]

These numbers which Roëmer used were of course best estimates and approximations calculated by him over several years. Nevertheless Danish Olaf Roëmer did indeed first demonstrate that , speed of light, is finite and calculable. The modern transit time over 2.0 AUs for Io's reemergence is now accepted as ≈ 16 minutes 40 seconds.

The historical record in determining   :