Chapter 42: Problem 6

Question: In 1676, Ole Roemer deduced that the speed of light is finite by observing the time of the eclipse of one of Jupiters satellites, Io (see Fig. 10 Chap 42). Based on the known orbital properties of Io, it was predicted to emerge from Jupiters shadow at a particular time, corresponding to the earth at position x in its orbit. When the earth was actually at position y, Io emerged from Jupiters shadow about $\Delta t~=~10~{\rm min.}$late. Roemer concluded that the discrepancy must be due to the additional time required for the light from Io to travel the additional distance of the radius of the Earths orbit. What value can be calculated for the speed of light from this observation.

Solution: The radius of the earths orbit about the sun is $R~=~1.50\times 10^{11}~{\rm m}$, and therefore, the speed of light estimated from this observation is $C_{\rm obs}~=~R/\Delta t~=~2.5\times 10^8~{\rm m/s}$. This is reasonable close to the true value.