It is impossible to draw solar system to scale, but…

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

07 June 2020

Eight years ago (April 2012), I demonstrated in this column that it is impossible to draw the solar system to scale. The reason is that the sun is too big compared to the planets and too small compared to the distances between planets.

Therefore, if you drew a dot with the thinnest pencil to represent the smallest planet, you won’t find a paper large enough to fit the other seven at the right distances. On the other hand, if you use the larges paper ever manufactured, and fitted the entire solar system on it, you won’t find a pencil thin enough to make a dot for the smallest planet.

Take the sun and the earth, for instance: the distance between them is about 150 million kilometres; the sun is about 1.4 million km in diameter while the earth is just under 13,000km.

The approximate ratios of those measurements are 1:100:10,000. In other words, If the earth was just one metre in diameter, the sun would measure 100m across and be located 10km away! And, if we scale the size of the earth to just 1mm diameter; the sun would be 10cm wide and at a distance of 10m.

Now think about the whole solar system. The outermost planet, Neptune, is 4.5 billion kilometres from the sun. This is about 30 times the earth-sun distance. So, in the scale drawing where the earth is just a 1mm dot, Neptune would be 300m from the sun! A paper that big has never been made.

What if we ignored the sizes of the sun and the planets and focused only on their orbits: would we be able to fit them on an ordinary piece of paper?

The nearest planet to the sun is Mercury at about 58 million km while Neptune, the farthest, is 4.5 billion, or, 4,500 million km away. The ratio of these two distances is about 78. That is, Neptune is 78 times as far from the sun as Mercury is.

Now, the regular A4 paper measures 210mm by 297mm. The biggest circle we can draw on it would have a diameter of 210mm; that is, a radius of 110mm.

Imagine that the sun is at the centre of that circle and Neptune is on the edge. What then would be the size of Mercury’s orbit? We simply divide 110mm by 78. The answer is 1.4mm.

In other words, on this scale, the orbit of Mercury would be a tiny circle measuring just 1.4mm in radius, or 2.8mm in diameter. Remember: that’s the orbit, not the planet!

What about the orbit of the Earth? Well: 4,500 million divided by 150 million is 30. 110 divided by 30 is about 3.7. Therefore, our orbit would be a circle measuring about 3.7mm in radius, or 7.4mm in diameter.

I think this makes an interesting project for primary school children. Give them the distances of the planets and ask them draw a scale diagram on a normal piece of paper. It will help erase the false impression created by the picture found in atlases.