How astronomical distances are measured

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

19 September 2021

Last week, I described an experiment that helps in estimating how far a person should be in order to view the sun and the farthest planet (Neptune) without turning the head or the eyes from side to side. I started out by shrinking the actual distance between the two heavenly bodies to fit on the length of an A4 sheet of paper – about 30cm.

Since the true distance is about 4.5 billion kilometres, the scale on paper comes to 1cm representing 150 million km. I found that the closest I can be and still be able to see the whole paper was about the length of a pen – about 15cm. This translates to 2.25 billion kilometres “above” or “below” the plane of the solar system in reality.

The purpose of that experiment was not just to find out an answer, but, more importantly, to illustrate how astronomers (and scientists, in general) are able to find out some seemingly impossible things. When we read that the moon is 384,000km from the Earth, some may wonder who stretched out a tape-measure all that way? And this distance was known many centuries before the first man-made object was landed on the moon!

The truth is that astronomical distances are not measured directly in kilometres. The direct measurements are in degrees of angles. To determine how far the moon is from the Earth, it is observed from two different places simultaneously and then the angle between the two lines of sight is measured. This yields an isosceles triangle with two equal, but unknown, sides (from Earth to moon) and a third one (that between the places) that is known.

With a little secondary-school geometry (remember sines, cosines and tangents of angles?), the distance to the moon can be evaluated from the angle between the lines of sight. Once this has been determined, it can be used to evaluate the distance to the Sun; this way:

Imagine the scenario at half-moon. The three bodies – sun, moon and earth – must be in an arrangement that forms a right-angled triangle, with the moon at the 90-degree corner. So, if we measure the angle between the line of sight of the moon and that of the sun, we can use it (with the help of a little geometry) to determine the distance to the sun. it comes to about 150 million kilometres. And, with that, the sky is no longer the limit: we can go to the other stars!