Just looking at stars in the night sky seems as if every star is equally far away. Feels like we are bound by some spherical ball with stars on the sphere. Any star seems to be as far as any other and this led the ancient Greeks to believe that all the stars were the same distance away. Distance is one of the most important and difficult parameters which has to be measured in Astronomy. Astronomers use some smart methods to measure stellar distances. These distances are really too huge to be determined using traditional methods as they are beyond the scale of any physical instrument we use.

People started to think about ways to measure stellar distances but there were no instruments before Galileo built a refracting telescope in 1609 which would aid in measuring distances with sufficient accuracy.

Here’s a list of methods used to measure Stellar distances:

1. Parallax Method.
2. Using Variable Stars.
3. Using Colour of Stars.
4. Using expansion of Universe.

Parallax Method

Parallax is definitely observed by everyone. When we look out the window of a car or train we see objects closer to us pass by rapidly as compared to objects far away from us. Objects very far away from train/car like mountains in-fact appear stationary. A driver looking at the speedometer observes speed as 80 kmph but at the same time a person looking at the speedometer observes the speed over 90 kmph. So we define parallax as difference between the apparent position of object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines.

For stars, the distance between the two viewing points needs to be large, as they are so far away. The best we can do is to use the opposite sides of the Earth’s orbit (Annual Parallax). A photo of an area of sky is compared with one taken six months previously. Robert Hooke outlined in 1674 the problems of looking for annual motion of stars and Isaac Newton tried to calculate the distance of Sirius by comparing its brightness to that of the Sun. However, until the 19th century, telescopes were not sensitive enough to detect the very tiny parallax motions. The first person to succeed was F. W. Bessel who in 1838 measured the parallax angle of 61 Cygni .

There are two sub-types:

Annual Parallax : It is caused by the Earth’s yearly orbit around the sun. The measurements are taken 6 months apart i.e from two opposite points on the orbit.

Geocentric or diurnal parallax : Our observations are made from the surface of the Earth, not its centre. This is irrelevant when observing distant objects such as stars. But for closer objects (e.g. within the Solar System), a correction must be made. This is geocentric parallax, or diurnal (daily) parallax
(since it varies daily as the Earth spins around its axis).

Here is an example of calculation of Parallax. If anyone’s interested in the detailed geometric treatment of parallax, this is a good reference.

Even with recent telescope technology, the smallest parallax angle measurable from Earth has been about 0.01″. Only approximately 3000 stars have been observed with a reasonable degree of accuracy. In order to improve this figure, ESA has launched a satellite designed specifically to measure the tiny angles involved to excellent accuracy. Parallaxes as small as 0.002″ are possible.

Named HIPPARCOS (HIgh Precision PARallax COllecting Satellite) in honour of the Greek astronomer Hipparchus , the satellite was put into orbit by the European Space Agency in 1989.

Variable Stars

As the name suggests, variable stars are those whose brightness varies (fluctuates) as seen from earth. There are different reasons of why the brightness of these stars varies.

They are classified as:

• Intrinsic Variables: Whose luminosity changes periodically. For eg. the star might shrink or swell up periodically.
• Extrinsic Variables: Whose apparent change in brightness is due to the change in amount of light that reaches Earth, or the star might get eclipsed due to other companion or planetary system orbiting around it.

It does sound weird, that variable stars aid us in measuring huge distances.One particular type of variable star has proved invaluable for helping to determine the stellar distances. This is a type known as a Cepheid Variable.

So what are these Cepheid Variables? They are named Cepheid Variables because the first star of it kind (The Delta Cephei) was discovered in the constellation Cepheus. All stars, late in their lifetime, change from being average stars for their mass ( main sequence stars ) to becoming swollen red giants . Most stars change from the swollen red giant phase to pulsating variable stars before they finally die, all reactions ceasing. These are Cepheid Variables, which expand and contract, glowing brightly and fading every so often.

Cepheid Variables are very large, luminous, yellow stars. They change in brightness very regularly with periods of 1 to 70 days between peaks.

Extrinsic variables have variations in their brightness, as seen by terrestrial observers, due to some external source. One of the most common reasons for this is the presence of a binary companion star, so that the two together form a binary star. When seen from certain angles, one star may eclipse the other, causing a reduction in brightness.

So how is it that we determine distances using these type of stars? Well the answer is very smart. The important feature of a Cepheid Variable that allows it to be used for distance measurements is that its period is related directly to its luminosity . This relation allows us to work out how much brighter than the Sun the star is. From there we can calculate how much further away the star must be than the Sun to make it the brightness we see from Earth!!

Colour of Stars

I don’t know how people sometimes claim they see a “reddish” star just by looking at it through naked eyes, but personally through naked eyes I see stars as white dots. But when you click a long exposure photo or see a star through Prism you can see that star’s do have different colours. By obtaining the spectrum using prism or diffraction grating and analysing it we can even determine the surface temperature of the star!!

Astronomers divide stars into seven types according to their spectrum: O,B,A,F,G,K,M. The order of these letters can be easily remembered by the mnemonic – Oh be a fine girl kiss me! O stars are the hottest (50 000 degrees C) and are blue. M stars are the coolest (3 000 degrees C) and are red.

Now we are able to determine the surface temperature of a star. So how is distance measured using this parameter? Well we use Stefan’s Law which relates the star’s surface temperature to its luminosity. Once we know the luminosity, the absolute magnitude (a measure of the total amount of light being given out by the star in all directions) can be found and so the distance. The absolute magnitude is directly related to the star’s luminosity and the apparent magnitude (brightness of a star as observed from here on Earth) can be measured here on Earth. From the Inverse Square Law , we can deduce an equation connecting the magnitudes and the star’s distance. This allows us to calculate the distance in parsecs if we can find the star’s apparent and absolute magnitudes.

Expansion of Universe

Edwin Hubble was an American astronomer who discovered that universe is expanding. Furthermore it’s not only expanding but further the object (galaxy/star) is the faster it is receding away from us. Now how can this be used to determine the distances?

For that we need to first determine how fast the object is moving. We use the Doppler Effect for this. For galaxies coming towards you, the light appears slightly blue. For galaxies going away, it appears slightly red. By looking at the spectrum of a galaxy, astronomers can work out exactly how much the light has been changed and so determine the speed of the galaxy away from the Earth.

Now that we have determined the speed, we can approximate the distance using the Hubble Graph. The slope of this graph is the Hubble’s constant.

These are some methods astronomers use to determine distances which are beyond the scales of any measuring instrument. It’s just fascinating that we can determine such huge distances with an impressive accuracy.