## Scaling the universe down to size

One of the greatest difficulties in astronomy is that of getting a feel for the relative size of celestial bodies and the distances between them. The problem arises because the objects are tiny—minute, even—compared to the distances which separate them. This is true even of such a cosy little corner as our Solar System. For example, the Earth is 11,730 times its own diameter from the Sun, but this figure has no intuitive meaning for us. Presented with a golf ball and asked to point out, not calculate, a spot 11,730 times its diameter away, we would be completely flummoxed. Ten times we could manage easily, one hundred times maybe, but with multiplication of sizes much beyond a hundred our estimates would be no better than wild guesses.

Almost every general introduction to astronomy offers tables of solar and planetary diameters, radii of orbits, distances to the nearest stars and so on. These measures are large, typically expressed in thousands of kilometres (km x 10^{3}) for planetary diameters, millions of kilometres (km x 10^{6}) for solar system distances, and light years or parsecs for interstellar distances. Such expressions are easy enough to grasp and manipulate mathematically, but for most of us they have no tangible reality.

To get around this difficulty we are often offered ratios rather than absolute measurements, e.g. the diameter of the Sun is 109 times that of the Earth; Pluto is 40 times the distance from the Sun that the Earth is; alpha Centauri, the nearest naked-eye star, is 6800 times the radius of Pluto’s orbit away, or 272,000 Astronomical Units (the radius of the Earth’s orbit = 1 AU).

However, such figures can tell only part of the story, because of the different units of measurement which are used. The raw figures are of hardly any use if you are trying to grasp the overall picture: the size of the bits *and *the size of the space between them.

Some authors offer similes, a favourite being motes of dust. In my house, however, dust motes fly as thick as winter raindrops, and so suggest that the stars almost jostle one another. This is not the case at all. To bridge the gap between the reality and its abstraction we need models that we can both comprehend and bring to mind as required.

Even such everyday concepts as the size of a million and a billion (one thousand million) cause trouble, for both are figures so large as to be beyond intuitive grasp. What sort of heap do a million peas make? A billion grains of sand? In an attempt to grasp these magnitudes, try taking a sheet of metric graph paper ruled in millimetre squares and blacken in just the top left square. Let that be one.

Now outline the top left square centimetre and you have enclosed one hundred. Next mark out a square 10 cm x 10 cm to get an impression of 10,000, and, you’ve guessed it, mark out 1 m x 1 m to *get *a million squares. To carry the exercise on to one billion you will need 1000 tn^{2} of graph paper, which is enough to completely paper all the walls, both inside and out, together with the floors and ceilings of a 200 square-metre villa.

If wallpapering is not your thing, then recall that there are 1,000,000 mm in one kilometre and that the journey from Kaitaia to Wellington is only 17 km short of the 1000 km which equates to a billion millimetres.(For South Islanders, Invercargill to Nelson is the equivalent road trip.)

Turning to the Solar System, we face an immediate difficulty because the difference in the size of the solid objects and the distances between them is so extreme. Any model at a scale allowing the Solar System to be fitted into a decent-sized living room or even a school hall reduces Jupiter to little better than a pinhead, and leaves the position of the nearest stars several streets away. Also, cramping such a model indoors denies the three-dimensional nature of space, for although the planets all orbit pretty well in the plane of the ecliptic, the system exists in three dimensions.

In order to get some sort of grasp of the spacial realities of the Solar System we need to model it at a scale where the relative sizes of the Sun and planets are easily apprehended, and yet the distances can be visualised. A scale of 1:1,000,000,000 meets these requirements nicely, and the table below gives the object diameters in millimetres and their distances from the Sun in metres.

To “make” this model, ideally one needs a hilltop with a clear all-round view and plenty of identifiable landmarks at the appropriate distances. I chose the summit of Mount Eden in Auckland for my version, simply because it is the only location with which I am sufficiently familiar to plot the positions of the planets using readily recognisable landmarks. One would have thought that in a city as extensive as Auckland any number of locations would have been possible, for the city abounds in prominent features, both natural and built. However, a surprisingly high proportion lie at the wrong distances or, if prominent in their own suburb, are inconspicuous when seen from the summit. (Readers in other places need only a street map and a scale to identify appropriate objects to mark the orbits in their “patch.”)

As an aside, the speed of light (approximately 300,000 kilometres per second) is just over 1 kilometre per hour at the scale of this model. You can see why a radio transmission from Earth to Pluto takes so long to get there—nearly five-and-a-half hours.

Between alpha Centauri and Sirius there are only four small, faint stars, none of which are visible to the naked eye. Just inside alpha Centauri, itself a bright double, is its faint companion proxima Centauri, which, at about 0.1 light years nearer the Sun, is the closest substantial body to the Solar System.

With this model, when you stand on the summit of Mt Eden you are at the centre of a sphere the radius of which is the distance to the Bombay Hills and which extends around you, over you and under you. In all that volume beyond the Solar System there is virtually nothing: just a little congealed ice and grit.

Go out again, to the distance of Great Barrier lying hull down on the horizon, and all you have managed to net are the alpha Centauri system (triple), the Sirius system (double) and five faint dwarves.

It is sobering to think that the Sun, embedded in the Orion Arm of the Milky Way, is in a relatively dense part of the galaxy’s disc. If our model gives us a picture of a stellar crowd, then how lonely are the stellar deserts? And, over all, how significant is solid matter as a component of the universe?

It scarcely rates a mention!