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Romer Astronomical Method

Romer observed the eclipses of the Jupiter’s satellites at times when earth was at difficult positions with respect to Jupiter. He found that while the earth in its orbital motion round the sun, receding from Jupiter, the mean period between two successive eclipses of a particular satellite is longer than that when the earth is moving nearer the Jupiter. This anomaly formed the basis for the calculation of velocity o flight. He explained when the earth is receding from Jupiter, light has to travel a greater distance at each successive disappearance of the satellite whereas when the earth is approaching the Jupiter, light has to travel a shorter distance at each successive disappearance of the satellite.

Jupiter has a number of satellites or moons revolving round it. Jupiter makes a complete revolution around the sun in 11.86 years whereas earth completes one revolution in one year. It is assumed for the sake of simplicity that the orbits of the earth and the Jupiter are circular.

The satellites which revolve round the Jupiter have their periods lying between 11 hours 58 minutes for the satellite nearest the planet and 16 days, 16 hours, 32 minutes and 11 seconds for the most remote satellite.

As the satellite revolve in orbits nearly parallel to the plane of the Jupiter’s orbit, each satellite, once in every revolution, enters the shadow of the Jupiter, and so becomes eclipsed. Romer studied the eclipses of the innermost satellite of Jupiter. At some time, Jupiter J₁ and the earth E₁ are on the same side of the sun and are in conjunction. If light were transmitted instantaneously, the actual time of eclipse and its observation on the earth should be the same. If light has a velocity c, then light from the satellite at the time of eclipse has to travel a distance J₁E₁ before reaching the earth.

Thus, the eclipse will be observed J₁E₁/c later on the earth. If the actual time of eclipse is T₀ and T₁ is the time when it is observed on the earth then

After a lapse of 0.545 of a year, when the earth is at E₂ the Jupiter will be at J₂, i.e. in opposition. Let the eclipse of the same satellite to be observed at this time. It will be observed J₂E₂/c: seconds after its actual occurrence. If t is the time for one revolution of the satellite the time actually elapsed between the first and the nth eclipse will be = (n – 1) t. If T₂ is the time of observation of the nth eclipse on the earth, then

Let I = T₂ – T₁ be the time interval elapsed between the observation of the first and the nth eclipse on the earth i.e. when the earth has moved from conjunction to opposition.

where d is the diameter of the earth’s orbit round the sun

I = (n – 1)t + d/c (iv)

Similarly, it can be proved that the time interval between the first and the nth eclipse observed on the earth when the earth moves from E₂ to E₃ will be

I’ = (n – 1)t – d/c (v)

i.e. when the earth moves from opposition to conjunction.

I – I’ = 2d/c

Romer observed that the time interval I was 32 minutes 52 seconds more than the time interval I’.

Taking the diameter of the earth’s orbit as 185.6 × 10⁶ miles and the time interval I – I’ = 1972 seconds, Romer calculated the value of c as

c = 186,000 miles/second (approx.).

This method is not very accurate due to the following reasons: (i) Orbits are not circular but they are elliptical. (ii) Correct value of the diameter of the earth is not known. (iii) It may not be possible to note the exact time when the eclipse occurs.