There are a lot of internet 'stories' and 'posters' talking about Rg veda indicating the speed of light. Here is my analysis of it.
Rk Veda sloka 1.50
ud u tyaM jÀtavedasaM devaM vahanti ketavaH dRZe vizvÀya sUryam
apa tye tÀyavo yathÀ nakSatrÀ yanty aktubhiH sUrÀya vizvacakSase
adRzram asya ketavo vi razmayo janÀM anu bhrÀjanto agnayo yathÀ
taraNir vizvadarzato jyotiSkRd asi sUrya vizvam À bhÀsi rocanam
TranslationIndeed agni deva (jatavedasam deva) carry (vahanti) the brightness (ketavaH), the sight of the suryas of the Universe (drze visvaya suryam), away (apa) the progression as if/like naksatras (tayavo yatha naksatras) by the night (aktubhih), the Universal sight of surAs (surAya vizva caksase) seen of the brightness (adrzam asya ketava) reins of the janA (vi razmayo janAm) nearly burn (anu bhrajanta) as if in agni (agnayo yatha) moving forwards (taraNi) conspicious/visible universally (vizva darsata) creating the flames (jyotis krd) exists (asi) sun (surya) universe (vizam) appear/manifest (a bhasi) pleasing (rocanam)
The suryas of the Universe including all the stars that progress at night, burn the janA (particles) as if in agni/fire and their brightness is carried by this agni deva moving forward, the created jyoti/flames cross over the universe (causing) visibility, manifesting a pleasing Universe.
sAyana's translationsAyana translates sUrya as 'Our Sun', which is not surprising. He understands Rg veda 1.50.4 sloka as "Surya produces the jyoti which crosses over swiftly the Universe. Universe is illuminated by Sun's radiance".
He explains it as (5)
"tvam dharaNi taritA anyena gantum zakyasya mahato dhvanao gantasi tathA cha smaryata yojanAnAM sahasram dve dve shate dve cha yojane | ekena nimiShArdhena kramamANa namo.astu te"
Hey surya, you leader of others in earth, possible/capable of greatly enveloping it and as you go, it is to be remembered 2202 yojanas by one/by itself, by half nimiSa progress, salutations be to you".
Surya is the leader of others in the dharaNi, the earth. It is capable of greatly enveloping the earth. It progresses 2202 yojanas in half nimesha. sAyana (not rig veda) gives this figure.
Since the Rg veda sloka talks about 'Surya' jyoti switfly crossing the Universe, sAyana remembers the speed at which sun envelopes the earth by crossing 2202 yojanas in 0.5 nimisha.
Irrespective of what its value is, this shows that there was a 'specific' value assigned for light to reach the earth.
'Curve fitting' with Artha sAstra alone
There are various definitions of Yojana and nimisha in various scriptures. Instead of taking one measurement from one text and another from another text, let's stick to Kautilya's artha sAstra. It has definitions of space and time in Chapter 20 (4).
Since space and time are related, the idea is definition of space and time from a single scripture will be consistent.
ArthasaAstra's space measurement
Kautilya's arthasastra says in Chapter 20 (3), '4 aratnis are equal to 1 danda, 1 dhanus, 1 nAlika and 1 paurusha', thus equating danda and dhanus.
Then says in Chapter 20 (6) " 192 angulas are 1 danda, used in measuring such lands as are gifted to equal to Bráhmans" and "1000 dhanus is 1 goruta, 4 gorutas are 1 yojana".
It also says "14 angulas are equal to sama, sala, pariraya or pAda". From these we can say 1 Yojana is equal to 768,000 angulas.
Since pAda continues to be used and used as 30 cms, 1 angula is 30/14 = 2.14 cms. This means 1 Yojana = 768000 *2.14 cm = 16.4 kms.
ArthasaAstra's time measurementWith respect to time artha sAstra says "5 nimesa is 1 kAstha, 30 kAsthas are 1 kAla, 40 kAla are 1 nAlika, 2 nAlikas are 1 muhurta, 15 muhurta is 1 day or 1 night".
1 day is 12 hours. So 1 muhurta is 12/15 = 48 minutes. 1 nAlika is 24 minutes or 1440 seconds.
1 kAla is 1440/40 = 36 seconds. 1 kAstha is 1.2 seconds. 1 nimisha is 1.2/5 = 240 milliseconds. So half nimisha is 120 milliseconds..
From arthasAstra alone Yojana is 16.4 kms, nimisha is 120 milliseconds.
Using that data to fit 2202 yojana in 1/2 nimisha, we get 36,112 kms in 120 milliseconds. This leads to a value of 300,933 kms per second.
From artha sAstra alone, the values of Yojana and nimisha seem to match the modern value of speed of light.
Why I call it curve-fitting..?Though my entire definition of Yojana and nimiSha is from artha sAstra and straight forward, I termed it as curve-fitting. The reason is 1 pAda, I assumed as 30 cms. Now this is my mapping, based on how we use pAda now (as 30 cms).
Artha sAstra defines angula as equal to the breadth of middle-finger of an average man or 8 yavas, where 1 yava is size of a barley. These are difficult to translate into current metric measurements. The only nearest measurement I could get is pAda which is used till now as 1 foot or 30cms. This could be wrong.
Points to be notedsAyana uses the phrase 'smaryata yojanAnAm", which means it is to be remembered/recollected.. So somehow in some text sAyana got the information that surya jyoti travels 2202 yojanas in ardha nimisa. He recollects it when talking about the Rg veda sloka which talks about surya jyoti swiftly spreading in the Universe.
Thus sAyana does not define the yojana or nimisha or the numbers 2202 and 0.5 nimisha. He is merely recollecting that number from somewhere he read. So it should have been in some scripture which we lost.
So yes, sAyanA seems to indicate a right number for speed of light, if we correlate it with measurements of artha-sastra, as I defined here. Even if it is a right or wrong number it is 100% certain he indicates that light travels at a 'finite' speed.
But it is not from Rg veda, but probably some scripture that we might have lost.