VCA 1.F. The Size of the Universe

In the Srimad-Bhagavatam a figure of 500 million yojanas is given for the diameter of the universe. On the basis of 8 miles per yojana, this comes to 4 billion miles, a distance that can accommodate the orbit of Saturn (according to modern distance figures), but that is smaller than the orbital diameters of Uranus, Neptune, and Pluto. Since this figure for the diameter of the universe seems to be quite small, it is interesting to note the purport given by Srila Prabhupada to CC ML 21.84:

In his Anubhasya commentary on this verse of Caitanya-caritamrta, Srila Bhaktisiddhanta Sarasvati quotes from Sūrya-siddhanta 12.90, "The circumference of the sphere of the Brahmandee in which the sun's rays spread is 18,712,080,864,000,000 yojanas" (SS, p. 87). Then he quotes Siddhanta-siromani, Goladhyaya Bhuvana-kosa: "Some astronomers have asserted the circumference of the circle of heaven to be 18,712,069,200,000,000 yojanas in length. Some say that this is the length of the zone binding the two hemispheres of the Brahmanḍa. Some Pauranikas say that this is the length of the circumference of the Lokaloka Parvata [adrsya-drsyaka-girim] (SSB1, p. 126).

Here the circumference of 18,712,069,200,000,000 yojanas corresponds to a diameter of 5,956,200,000,000,000 yojanas. This number is much larger than the 500,000,000-yojana diameter given in the Bhagavatam, and we might ask how it relates to it. According to the Bhagavatam (5.20.37),

This verse reconciles the statement that the 18-quadrillion-yojana circumference is the limit of distribution of the sun's rays with the statement that it is the circumference of Lokaloka Mountain. We also note that in SB 5.20.38 the diameter of Lokaloka Mountain is stated to be half the diameter of the universe. This is consistent with the statement in Srila Prabhupada's purport that "according to some, this is only half the circumference." We are thus left with a picture of the universe in which the rays of the sun and other luminaries spread to a radial distance of 2,978,100,000,000,000 yojanas, and are there blocked in all directions by an enormous mountain. This mountain lies halfway between the sun and the beginning of the outer coverings of the universe. This means that the distance from the sun to the coverings of the universe is some 5,077 light-years, where a light-year is the distance traveled in one year by a beam of light moving at 186,000 miles per second and we use the Sūrya-siddhanta's 5-mile yojanas.

In Chapters 3 and 4 we will say more about the possible relation between this very large universal radius and the much smaller figure given in the Bhagavatam. At present we will consider what the jyotisa sastras have to say about the radius of the universe. It turns out that the Siddhanta-siromani, the Sūrya-siddhanta, and many other jyotisa sastras give a simple rule for computing this number.

The Sūrya-siddhanta gives the following rule: "Multiply the number of ... revolutions of the moon in a kalpa by the moon's orbit...: the product is equal to the orbit of heaven (or the circumference of the middle of the brahmanḍa): to this orbit the sun's rays reach" (SS, p. 86). If we perform this calculation, we find that the circumference of the brahmanḍa, or universe, is:

In The Aryabhatiya of Aryabhata we find the statement that the circumference of the sky (akasa-kaksa) in yojanas is equal to 10 times the number of minutes of arc covered by the moon during one divya-yuga (AA, p. 13). This comes to:

When interpreting this figure, we should keep in mind that Aryabhata used a yojana of about 7.55 miles rather than 5 miles. If we convert Aryabhata's figure to 5-mile yojanas, we obtain a universal circumference that is almost exactly one thousandth of the figure cited in Sūrya-siddhanta and Siddhanta-siromani. The reason for this is that Aryabhata used the number of revolutions of the moon in a divya-yuga rather than the number of revolutions in a kalpa. (There are 1,000 divya-yugas per kalpa.)

We mention Aryabhata's calculation for the sake of completeness. There are a number of ways in which Aryabhata differs from other Indian astronomers (AA). For example, he is unique in making the four yugas equal in length, and he also suggests that the earth rotates daily on its axis. (All other Indian astronomers speak of the kala-cakra rotating around a fixed earth.) Our main point here is that very large figures for the size of the universe were commonly presented in the jyotisa sastras, and such figures have been accepted by Srila Bhaktisiddhanta Sarasvati Thakura and Srila Prabhupada.