Microcosmology: Sun

Domingos Soares

October 23, 2015

The Moon is a hole in the sky
whereby I watch the Sun.


D. Soares, Astrocosmic Poems

Cosmology is the science of the largest scales of space and time, namely, those of the whole universe. The conceptual incorporation of these scales benefits from the apprehension of large local scales. Accordingly, I discuss here the size scale of the Sun.

1. Introduction

One way to reach cosmological scales is to act like astronomers do in the determination of distances in the universe, that is, climbing up a distance ladder step by step. To begin in the lower scales and gradually rise, supported by the previous steps, to larger distances or higher steps. The investigation of the lower steps of such a cosmic ladder is what I call “microcosmology”. Anyway, rigorously, one can state that the whole universe inhabits the interior of our minds. Microcosmology is the conceptual foundation of cosmology properly said.

Let's start by the dimensions of the Sun. What is the Sun's size? How to conceptually apprehend such a size instead of just citing an enormous figure expressed in some units of length, area or volume?

In order to get a more concrete notion of the size of the Sun, I inspire myself in the Sagan Planet Walk, a solar system reduced to the scale of 1/5,000,000,000, situated in the city of Ithaca, state of New York, US (www.sciencenter.org/sagan-walk.html, Soares 2015). There sits also Cornell University, where the astronomer Carl Sagan (1934-1996) worked until his death in December, 1996 (Soares 2015). In the reduced scale of the Planet Walk the Earth is at 30 m from the Sun.

Briefly, the Sagan Planet Walk is formed by 11 stations, one for the Sun, 9 for the planets, Pluto included, and one for the asteroid belt (situated between Mars and Jupiter). Each station is a sculpture in cement and contains several information and photographs about the object in question. It shows in the upper part a circular hole representing the circumference of the solar disc. Planet dimensions appear in scale in the center of this disc. Figure 1 shows the station of Sun and the station of Earth.

Figure 1
On the left, the Sun station, the beginning of Sagan Planet Walk in Ithaca, New York. On the right, the author of this article next to the Earth station. These stations are located in the Commons mall, the heart of downtown Ithaca. The pictures were taken on 08/28/2015, in the reopening of the Commons after the renovation works. Compare with the pictures taken on 11/08/1997, the opening date of the Planet Walk, in the article Carl Sagan, the praise of scepticism. The circular openings at the top of the stations represent the solar circumference and serve for a comparison with the planetary circumferences (right photo: Lu Soares).

The Planet Walk was inaugurated on November 8, 1997, almost one year after the death of the astronomer. The pictures in figure 1 were taken on August 28, 2015, when the Commons, where the Walk begins, was reopened after works of renovation. The site of the station of the Sun was changed as can be verified by comparing the picture shown above with the picture that appeared in Soares (2015).

In section 2 I use the station of the Earth for the concrete presentation of the Sun size. I finish with some additional remarks in section 3.

2. The size of the Sun

• R_Sun: 695,000 km

• d_EM: 384,000 km ≅ R_Sun/2

• R_E: 6,371 km ≅ R_Sun/100

• R_M: 1,737 km ≅ R_Sun/400

Look now at figures 2 and 3, where all of these dimensions appear in scale.

Figure 2
The Earth, presented by the terrestrial disk in scale in the center of the Sun, and the Moon at approximately half of the solar radius. To locate the lunar disk, draw a circumference centred in the center of the solar disk, with radius equal to half the solar radius and find a luminous little spot, the Moon. Check in figure 3. The caption below the Sun window starts with “In the Sun size window above is a model of Earth and the Moon”.

Figure 3
A representative diagram of the yellow disk shown in figure 2. This disk is the one in the Earth station, figure 1 on the right.

From now on, when we look at the sky and wonder at a bright Moon, we may put ourselves, at least for a moment, in the center of the Sun. Then let us make the following reflection: the Sun, this great ball of energetic plasma, extends itself to almost the double of my distance to such a beautiful Moon that I watch high in the sky. That will be already an excellent start to begin our learning about the true dimensions of the universe.

3. Final remarks

In the previous section we showed that R_M ≅ R_Sun/400. According to the discussion made in the previous paragraph we may conclude that there must be the same ratio between the distance of the Earth to the Sun (d_ES) and d_EM. This is the only way that the Sun and the Moon would have the same apparent sizes. And that is true indeed since d_ES = 150,000,000 km and therefore d_EM ≅ d_ES/400.

The universe is great. But how great is the universe? The Sun is great. But how great is the Sun? As we saw, trying to answer the latter we can grasp the answer to the former. That is the idea: start from the microcosmos to achieve the cosmos.

Acknowledgement – Figure 3 was made in one of the computers of the Kapteyn Astronomical Institute, Groningen, The Netherlands, under the auspices of Prof. Reynier Peletier.

References

D. Soares, Carl Sagan, the praise of scepticism (www.fisica.ufmg.br/~dsoares/sagan/sagan-e.htm, 2015).