Rømer calculated that the eclipses were observed 17 minutes earlier when Jupiter was in opposition compared to when it was close to conjunction. This was attributed by Rømer to the finite speed of light. From Rømer’s data, compute the speed of light, first inAU min−1, and then inm s−1.

When earth and Jupiter is in the position of opposition and conjunction then the Speed of light is the ratio between the distances from the earth to the Jupiter, to the difference in times taken by light to reach the earth in these two situations.

$v = \frac{∆x}{∆t}$

Here $∆x$ is the difference in the distance from the Earth to Jupiter when it is at opposition and conjunction, and $∆t$ is the difference in time taken by light in these two situations to reach the Earth.

Orbital radius of the Earth = 1 AU

Orbital radius of Jupiter = 5.2 AU

At opposition, distance between earth and jupiter is

(5.2 - 1) AU = 4.2 AU

At conjunction, distance between them

(5.2 + 1)AU = 6.2

so the difference in the distance in these two positions is 

$$\begin{gathered} ∆x = 6.2 -4.2 AU \\ = 2 AU \end{gathered}$$