The calculation starts with a quote from Pañcavimśa Brahmana, which postdates the Rgveda
The world of heaven is as far removed from this world,
they say, as a thousand earths (literally "cows") stacked one above the
Then we suppose that the sun is halfway between heaven and earth, or 500 earth-diameters (this is supposed as there are three "planets" (Moon, Mercury and Venus) that have shorter periods and so are supposed to be closer, and three (Mars, Jupiter, Saturn) that are further, so the sun must be about half way) However, you will note that this is pure supposition, and is not accurate.
We now suppose that both Moon and sun are moving around the Earth at the same speed. This combined with the known length of the year and month imply that the moon is 40 Earth-diameters, and that the sun is about 4.6 times bigger than the Earth, while the moon is much smaller.
The Earth was taken to be about 7500 miles in diameter, probably from measurements of shadows at the solstice. And so the distances to other bodies can be calculated.
A careful reader will note that while this is an impressive attempt at calculation, the actual values obtained are very very far from the accepted modern values. 500×7500 gives 3.75million miles, or 6million km, compared to a modern value of a shade under 150 million km.
The Rgveda may contain hidden information. But there is no evidence presented in your source that the composers of the Rgveda, or later texts Pañcavimśa Brahmana had any actual ability to calculate accurate values for the distance to the sun. Indeed, this was not done until the calculations of Edmund Halley and the observations of the transit of Venus.