Fundamental to the absolute determinations of distances in astronomy is the trigonometrical parallax. Although the name is not common outside of astronomy, the principle is in constant use by us all: we are walking in a field, the grass at our feet quickly brushes past us, a tree in the distance more slowly shifts its posi¬tion, but a wooded hill on the horizon appears unmoved. Here we are playing tricks with our language. Neither the trees, nor the grass, nor the horizon has moved; we are the ones, the only ones, in motion. However, in realizing this we have stated the principle of parallax: as we change our position, objects around us appear to move. Moreover, if we want to keep an object in our view we must turn our head more quickly the closer it is to us. Here are the fundamentals of a relation between angles (the turn of our head) and distances (to the trees and the grass) which are the quantita¬tive bases of trigonometrical parallax. It is again as true for trees and cities as it is for planets and stars (figure 1.2). Consciously or subconsciously, parallax is a natural method that we all use in judging distances as we move from place to place.

Nature has also provided us with another means of judging distance, but without our moving. Of course we have another name for it, but it is again the same principle. This time it is called stereo vision. Our visual sensation of depth is a direct consequence of our having two eyes; with it we have a natural ability to judge relative distances. Stereo vision, in fact, is so natural that we seldom have consciously to look out of one eye. remember how things are arranged, and then look out of the other to compare. Often it is amusing to stop and do just this, but the brain does such a fine job of assimilating the information for us that we rarely have to think about the process.

The relative distances of objects can be adequately judged over several hundred metres using stereo vision. Shifting our head back and forth can give us some additional depth and of course changing our position bodily is even more effective. In this process we have made the subtle transition between stereo vision and general parallax. Is there any limit ? Can we see how far away the Moon is ? Can we experience the depth of space ? Surprisingly, perhaps, the answer is yes. We are forever changing our perspective: daily as the Earth rotates, yearly as we circle the Sun, over millennia as the stars proceed through space. All of the Universe is in motion and these motions can free us from our forest and actually allow us to see the depth of space.

Stars and planets constitute the first recognizable members of the Universe. The Sun itself is a star, shining by light produced deep in the hot reaches of its interior. Energized by reactions caused by the tremendous temperature and pressure exerted by its great mass, the Sun produces light by thermonuclear reactions. Many orders of magnitude smaller and less massive, the planets are found revolving around the Sun. Unable to produce tempera¬tures in their interiors sufficient to start nuclear burning, the planets are without light of their own. The Earth, like the other planets that circle the Sun (and doubtlessly circle other similar stars) is dependent on its parent star for light. In the sky we see stars by their own light; the planets are visible only by reflection.

As a reminder of the initial whirl that existed when the Earth first formed, our planet is spinning. Drawn together by gravity and bound by molecular and atomic forces, it is a rocky sphere some six thousand kilometres in radius, formed in orbit round the Sun. It required a quarter of a million years of the evolution of man to discover this dimension of our Earth. For most of that time, six thousand kilometres was conceptually large enough to encompass most of the ‘known Universe”. And yet soon after, the Earth itself gave man new eyes with which to look beyond.

Our planet turns in relative solitude in space, but it is neither unique nor totally alone in its travels around the Sun. The Earth is one of a system of planets of various sizes and distances from our star. By chance, one of these planets formed so close to us that we share the same orbit. Seen from afar, the Earth and Moon form a double planet. weaving their way carefully around the Sun, trading positions every 28 days or so.

Our satellite-planet, the Moon, is so close that in the course of an evening we can see the effects of its proximity. When the Moon appears to rise in the East as we turn with the surface of the Earth, a close inspection of its leading edge (or limb) will reveal features that slowly disappear as the evening progresses and the Earth moves us to a different point of view. This is known as daily or DIURNAL PARALLAX.

We may try the same test with the planets but to no avail. We must conclude that the planets are so much further away than the Moon that we cannot detect the effects of diurnal parallax on their images. And so the scale of our world must increase immensely as we progress beyond Earth, The discovery of horizons beyond horizons repeats over and over in the exploration of the Universe.

Let us now apply more fully our methods of geometry and analogy to the Solar System and in so doing highlight some dangers. For simplicity, let us assume (incorrectly) that all spherical objects in the Solar System are of the same diameter. This we boldly accept, for the moment, on the grounds of the uniformity of nature. Our simple assumption, right or wrong, allows us to go ahead and calculate distances to the Sun, the Moon and most of the planets. We don’t even have to have the correct absolute sizes of any one of them in order to calculate their relative distances.

One immediate consequence of our assumption is that the Sun and. Moon must be at the same distance, for in the sky they both appear to be of the same size. How confident can we be of our con¬clusion ? We may repeat our measurements, but the result would be essentially the same. Alternatively, we may attempt a different experiment, such as looking for diurnal parallax of features on the surface of the Sun. But reconsiderations may be forced upon us from other directions. Having the Moon pass in front of the Sun would certainly demand that we abandon our conclusion and look again at our assumptions and this is the case in the simple illustra¬tion we give here. Unfortunately, in contemporary astronomy few tests of simple assumptions are as compelling as a total eclipse of the Sun!

Some assumptions about the uniformity of nature, as yet, have had no tests at all. Some of our crucial assumptions may be very wrong and the discovery of such systematic errors may result in a great restructuring of our thoughts. We have created a mental picture of the Universe based on our observations and our assump¬tions. Fuelled by new observations and different assumptions, revolutions of thought about the Universe have occurred many times in our recent past, and revolutions have occurred when many thought they understood the basic structure of the world: similarly, today, we believe we understand.

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