The size of the solar system is difficult to get

 By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

20 November 2011

Some questions appear simple and straightforward until you think twice about them and then the complexity is revealed. For example, a reader asked me this: “How big is the solar system?”

Now if some one asked you how big your house is, you would probably tell them something like “two bedrooms”. While that answer appears satisfactory, it really isn’t accurate. For one, all two-bed-roomed houses are not the same size – some have bigger rooms than others.

So, simply saying “two bedrooms” is far from enough. Real estate professionals go a little farther and give the “plinth area”, but that still doesn’t answer the question in full. Think about it; don’t some houses have “taller” rooms than others?

These are the kind of thoughts that went through my mind when I read the question: “How big is the solar system?”. Nevertheless, I will attempt to answer it.

The distance from the sun to the outermost planet, Neptune, is about 4.5 billion kilometres. Now if you missed the story in August 2006, Pluto is no longer considered a planet, thus Neptune is recognised as the farthest one.

If there was really nothing else after planet Neptune, how would we respond to the question? One might argue that since the last object is 4.5 billion km, then the area occupied by the solar system must be a circle of that radius.

But, area and circle are two dimensional concepts while the region we are talking about has three dimensions. We should really be thinking in terms of volume. It is not a flat disc, but a thin cylinder.

Knowing the radius, we can work out on the surface area (pi-r-squared) and this comes to about 64 billion square kilometres. If we knew the height of this thin cylinder, we could easily get the volume by multiplying the area by height.

Unfortunately, the sizes of the major bodies in the solar system vary greatly from the tiny Mercury at about 4,800km across to the sun which is 1.4 million km in diameter. So which of these should we use?

In addition, the orbits of the planets do not lie in the same flat surface. For that reason, the planets do go “above” and “below” the equatorial plane of the sun by different amounts. Being the outermost, Neptune goes “up” or “down” by about 500 million km.

Thus the shape of the Solar system may be visualised as a distorted cylinder measuring 4.5 billion km in radius with a height of 500 million km at the outer rim and only 1.4 million km at the centre. The volume of such a shape is simply the average of the two extremes. This comes to about 16 billion-billion cubic kilometres.

Is this a fair estimate of how big the solar system is? Perhaps not: we have left out Pluto, Sedna, Quaoar, Eris and many other known heavenly bodies (including comets) that exist much farther away than Neptune. This is why there is no simple answer to the seemingly simple question “how big is the solar system?”.