Rømer revisited: A modern estimation of the speed of light from observations of Jupiter’s Galilean satellites

2016 May 22

James Appleton

Ole Rømer (1644–1710) is one of the key figures of astronomy, remembered nowadays for establishing that the velocity of light is finite. He based the conclusion on nine years (1668–’76) of observations of the Galilean satellites of Jupiter, made at Uraniborg and Paris, and communicated it to the Académie Royale des Sciences in Paris in 1676.
The four Galilean satellites (Io, Europa, Ganymede and Callisto, in order outwards from Jupiter) present a fascinating spectacle. Their orbits are approximately coplanar with that of Jupiter and, as a result, they can transit in front of the planetary disk, are subject to occult-ations when they pass behind the planet, and may enter its shadow and be eclipsed. For Io and Europa, prior to opposition, eclipse disappearance events are visible but corresponding reappearance events occur when the satellite is occulted and hence are invisible. After opposition, the situation is reversed; eclipse disappearance events occur in occultation and are invisible, but corresponding reappearance events are visible.
Ganymede, orbiting further from the planet, follows essentially the same pattern but occasionally both disappearance and reappearance phenomena of an eclipse are visible. Callisto, orbiting even further from Jupiter, exhibits behaviour similar to Ganymede and, in addition, throughout lengthy periods during each apparition of the planet, passes consistently above or below the shadow cone, missing eclipse altogether.
Rømer’s approach was based on an assumption that eclipse disappearances and reappearances of Io, observed by a hypothetical Jovicentric1 observer, follow a regular periodicity. From this, he developed an argument to conclude that light does not travel instantaneously; there is, however, no record that he estimated its velocity.
It is a comparatively simple matter to repeat his approach and, using modern information about the scale of the solar system, to take a step further and estimate the speed of light (denoted c), but surprisingly, few modern amateur astronomers have reported tackling the challenge. However, in early 2012, members of the Orwell Astronomical Society, Ipswich (OASI), began the project. Independently, in late 2013, members of the Hampshire Astronomical Group (HAG) began a similar project and in 2014, the organisers of National Astronomy Week (NAW 2014) encouraged widespread participation and reporting of results to add to the observations obtained by members of OASI and HAG.
This paper describes the observations and their analysis to estimate c.        

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