It is impossible to draw the solar system to scale in a newspaper

 By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

08 April 2012

Last week’s article was special in that, for the first time in its nine-year history, this column photograph accompanying the text. That picture showing the sun and eight planets left me wondering whether it is possible to draw a scale diagram of the solar system in a newspaper. Let’s find out…

The best starting point would be with the farthest planet from the Sun. At 4.5 billion kilometres, Neptune is the outermost planet in the solar system. This means that the diameter of its orbit is about 9 billion km (4.5bn x 2).

Suppose we want to draw the scale diagram as a centrespread; that is, to straddle across the two centre pages when the newspaper is opened out flat. That way, we are able to draw a complete circle touching the top and bottom of the page. This will represent the orbit of Neptune and its diameter will be 33cm.

Thus, the scale of the diagram is 33cm represents 9bn km. Now; since 33cm = 330mm, thus we can rewrite the scale as 1mm represents 27 million km (9bn divided by 330).

The next planet “inwards” from Neptune is Uranus. It lies 2.87bn km from the Sun, therefore its orbit is about 5.75bn km across. So, how many millimetres would represent 5.75bn km in our scale? Well, 1mm is 27m km, therefore, 212mm (21.2cm) will be 5.75bn km (5.75bn divided by 27m).

Using similar calculations, it turns out that the orbits of Saturn, Jupiter, Mars, Earth, Venus and Mercury will be 10.5cm, 5.7cm,1.1cm, 0.8cm (8mm) and 0.4cm (4mm), respectively.

That takes care of the orbits; the next step is to draw the Sun and the planets on this diagram. With a diameter of about 1.4m km, the Sun is the largest object in the Solar System – it is about 100 times the size of the Earth. In the scale of 27m km per millimetre, the Sun would be just a dot measuring 0.05mm! (1.4 divided by 27)

Let’s put that into some perspective: a dot printed on this newspaper is about half a millimetre (0.5mm) wide. In the scale solar system that we are drawing, the Sun would be about one-tenth of this full stop mark: “.”

Imagine that!

0.05mm is actually just about the smallest dot visible with the unaided human eye. You need a magnifying glass (or microscope) to see anything smaller than that. Therefore, if the largest object in the solar system is just barely visible, we can conclude that nothing else can be seen! Remember that orbits don’t actually exist – they are the imaginary paths followed by the planets.

And there is more: the thinnest pencil available in the market has a tip of 0.2mm. So, you we wouldn’t find anything to draw a 0.05mm dot with. In short, it is impossible to make a scale drawing of the solar system on a single sheet of a newspaper.

The natural question that arises is: what is the size of the smallest paper that can fit a scale diagram of the solar system? That is a story for another day.