• #### Roemer velocity of light.

From carl eto@21:1/5 to All on Sun Nov 26 09:14:54 2023
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§ 2. Roemer

Roemer describes a method to measure the velocity of light in "A Presentation Concerning the Propagation of Light Determined" (1676) where Roemer uses the eclipse of Io (fig 3).

"Hence, if light would travel the diameter of the Earth in one second, it would travel each interval FG and KL in 3 1/2 minutes. This should lead to a deviation of about half an hour between two revolutions of this satellite observed in FG and KL
respectively. On the other hand, nothing of such a substantial difference has been found." (Roemer, p. 276).

Roemer's measurement of the velocity of light is reliant on the Earth’s yearly velocity that is derived using the Earth’s orbital circumference (9.4 x 108 km) and the Earth's yearly orbital time of 364 days (3.154 x 107s),

(9.4 x 108 km) / (3.154 x 107s) = 30 km/s……………………………………………......……………..1

The distance of each interval FG and KL is equal to,

d = (152,853.5047 s/r) (40 r) (30,000 m/s) = 1.831 x 1011 m.........................................................2

The distance d (equ 2) corresponds with 40 rotations of Io around Jupiter where Io has a period of 42.5 h (152,853.5047 s) and the Earth is said to be orbiting the Sun at a velocity of 30 km/s. On the evening of November 9, Roemer observed a 10-minute (
600 s) time delay of Io's eclipse that Roemer attributed to light propagating the distance d which is used to calculate the velocity of light,

c = (1.831 x 1011 m) / (600 s) = 3.05 x 108 m/s.................................................................................3

The measurement of the velocity of light (equ 3) is reliant on viewing the eclipse of Io at a specific time but the time at which Io is being viewed requires the initial time at dusk and the time when Io is viewed at night but using a hourglass, the time
measurement uncertainty would be greater than the 10-minute time delay that is used to measure the velocity of light.

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