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Order of magnitude[edit] Rømer starts with an order of magnitude demonstration that the speed of light must be so great that it takes much less than one second to travel a distance equal to Earth's diameter. The point L on the diagram represents the second quadrature of Jupiter, when the angle between Jupiter and the Sun (as seen from Earth) is 90°.[note 6] Rømer assumes that an observer could see an emergence of Io at the second quadrature (L), and also the emergence which occurs after one orbit of Io around Jupiter (when the Earth is taken to be at point K, the diagram not being to scale), that is 42½ hours later. During those 42½ hours, the Earth has moved further away from Jupiter by the distance LK: this, according to Rømer, is 210 times the Earth's diameter.[note 7] If light travelled at a speed of one Earth-diameter per second, it would take 3½ minutes to travel the distance LK. And if the period of Io's orbit around Jupiter were taken as the time difference between the emergence at L and the emergence at K, the value would be 3½ minutes longer than the true value. Rømer then applies the same logic to observations around the first quadrature (point G), when Earth is moving towards Jupiter. The time difference between an immersion seen from point F and the next immersion seen from point G should be 3½ minutes shorter than the true orbital period of Io. Hence, there should be a difference of about 7 minutes between the periods of Io measured at the first quadrature and those measured at the second quadrature. In practice, no difference is observed at all, from which Rømer concludes that the speed of light must be very much greater than one Earth-diameter per second.[5]

However Rømer also realised that any effect of the finite speed of light would add up over a long series of observations, and it is this cumulative effect that he announced to the Royal Academy of Sciences in Paris. The effect can be illustrated with Rømer's observations from spring 1672. Jupiter was in opposition on 2 March 1672: the first observations of emergences were on 7 March (at 07:58:25) and 14 March (at 09:52:30). Between the two observations, Io had completed four orbits of Jupiter, giving an orbital period of 42 hours 28 minutes 31¼ seconds. The last emergence observed in the series was on 29 April (at 10:30:06). By this time, Io had completed thirty orbits around Jupiter since 7 March: the apparent orbital period is 42 hours 29 minutes 3 seconds. The difference seems minute – 32 seconds – but it meant that the emergence on 29 April was occurring a quarter-hour after it would have been predicted. The only alternative explanation was that the observations on 7 and 14 March were wrong by two minutes.

Ole Christensen Rømer (Danish pronunciation: [o(ː)lə ˈʁœːˀmɐ]; 25 September 1644, Århus – 19 September 1710, Copenhagen) was a Danish astronomer who in 1676 made the first quantitative measurements of the speed of light.

Rømer and the speed of light