Using triangulation to measure distance to the stars

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

21 January 2024

Last week we saw how the height of a mountain can be measured by triangulation. Similar principles may be applied in the determination of the distance of astronomical objects. The nearest of these is the moon. The earliest measurements distance to the moon were done over 2,000 years ago.

The idea was fairly simple – in principle. Two people simultaneously look at the moon from two different locations (a few hundred kilometres apart) and make careful observations of its location in the sky relative to the stars. This forms a triangle with the moon at the apex. The angle at the moon can be determined and, knowing how far apart the two observers are, the distance to the moon can be calculated – about 380,000km.

Once we have the distance to the moon, we can use it to measure the distance to the sun. Now, at the half-moon phase, the angle between the earth-moon line and the moon-sun line must be 90 degrees. So, in this position, the three form a right-angled triangle.

If we measure the angle between the earth-sun line and the earth-moon line, we can easily determine the remaining angle of the triangle. Since the distance to the moon is already known, we can calculate how far the sun is – it comes to about 150 million km. And, once we have the distance to the sun, the entire universe is opened!

We can now measure distances to the stars. All we need is to observe them in 6-month intervals. In 6 months, the earth has done half the journey round the sun. Therefore, the straight-line distance between the two positions is 300 million km. When observing a star, that distance forms the base of a triangle. All we need are the angles between the earth-sun line and the earth-star line.

It turns out that the stars are very, very far away – many trillions of kilometres. So far out that light, traveling at 300,000km per second takes many years to get to earth. How we know the speed of light is another long story. The nearest star from the sun is about 40 trillion km away. Light from there takes about four years and three months to reach us!

Clearly, the greater the distance the farther backward in the history of the universe we see. So, this question arises: can we see so great a distance away that the light we see is the one that was emitted at the beginning of the universe?