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From earliest times man has know that the stars are farther away than the planets because on occasions a planet would cover a star, but a star would never block our view of a planet. But how far? Answering this question has called for a combination of technical brilliance and human ingenuity and we’re still working on the problem today.
The earliest and still most accurate method of determine the distance to a star is parallax. You can demonstrate parallax to yourself by stretching you’re your hand out while holding your thumb upwards. First look at your thumb through one eye and then the other. Your thumb will “jump”. This is because each of your eyes is in a slightly different position. It was realized some time ago that the same technique could be used for measuring the distance to the stars. First you measure the exact position of a star and then wait half a year while the Earth rotates around the Sun. The Earth has now moved about 300 million kilometers from its original position. Measure the position of the star again. The change of Earth’s position should cause the star’s position also to slightly change and with the help of simple geometry the star’s distance can be calculated. The less the star “jumps” the greater the star’s distance. You can experiment with your thumb at different distances from your eyes and you will discover the same affect.
The problem with parallax is that even the nearest stars are so far away that the jump made as the Earth changes its position by 300 million kilometers is very small. The nearest star will only move less than one arc second. This is about one two thousandth (0.0005) of the Moon’s diameter. This small change was measured near the end of the 19th century and we finally knew how far away are the nearest stars. But the parallax method was only able to determine distances of stars that were no more than 50 light years away from the Earth.
Except for parallax, all the other techniques for measuring distance are based on comparing the apparent and inherent brightness of a star or other distant object. Astronomers call a star’s brightness its “magnitude”. A light that is farther away will of course appear to be dimmer than the closer light provided that the inherent brightness of both is the same. In other words, if you take two car headlights, of the same make that are equally bright, but one is only half the distance away of the other, it will appear to be brighter. Apparent brightness is how bright a star or other object appears to us on Earth while its inherent birghtness is how bright the star or object really is. The apparent brightness can be measured to great accuracy. So all that is needed is a star’s inherent brightness and by comparing that with its apparent brightness, its distance is determined.
Once the astronomers were able to start accurately measure the distance of the closest stars, they were also able to determine the stars’ inherent brightness and made a remarkable discovery. Reds stars were dimmer while blue stars were brighter. The astronomers are able to determine a star’s color much more exactly than our eyes. Take a look at this chart and you will see the connection between the star’s brightness and color. The astronomers reasoned that this same connection between a star’s brightness and color that was discovered among the near stars would also exist among the stars farther away. They would measure a distant star’s color in order to find out its inherent brightness. They would then measure a star’s apparent brightness (how bright it looks to us on from the Earth) and then by comparing these two values discover how far the star was. This method worked for stars much farther away - even thousands of light years.
The astronomer Henrietta Swan Leavitt (1868-1921) while working at the Harvard College Observatory was studying the stars of the Magellanic Clouds which are two small galaxies very close to our own and can only be seen from the Southern Hemisphere. She was observing a particular type of star called the Cepheids whose brightness would vary in a predictable manner. She noticed that the brighter a Cepheid was, the longer its cycle of varying from dim to bright and back again. Since all the stars of the Magellanic Clouds are almost the same distance from the Earth, any changes of brightness were because of the inherent brightness of the stars and not their varying distance from the Earth. Assuming that all Cepheids were similar, all that was needed was a single Cepheid to calibrate the others. If we knew how exactly how inherently bright a single Cepheid is and the length of its cycle, it would be possible to know from the cycle length of other Cepheids their inherent brightness and from that (and their apparent brightness) their distance. Furthermore, Cepheids are very bright stars and can be seen from much farther away than many other stars.
It was not a simple manner of finding a Cepheid to calculate the others. No Cepheid was close enough to be accurately measure by parallax and it turned out that there were two different types of Cepheids which complicated matters further, but eventually using the Main Sequence fitting it was possible to find out a Cepheid’s inherent brightness from the length of its cycle and it was then possible to measure the distance of objects tens of thousands of light years form the Earth.
All the techniques used to measure distances to the stars have done so by carefully measuring the stars’ position, brightness and color. But there is also a way of measuring a star’s movement by using the Doppler effect. If you ever stand on the side of a highway while a car rushing by blows its horn, you’ll notice a change of pitch. As the car approaches, the horn’s blare is a high sound and, after it passes, the pitch of the sound will be much lower. This is the Doppler effect and can be used to determine if the object making the sound is approaching, distancing itself and how fast. The Doppler effect works not only for sound but also for light. If a star or group of stars is approaching the Earth at a fast speed, certain colors of light will be shifted from their usual position on the spectrum.
When astronomers started to analyze the light coming from spiral galaxies that faced us “edge” on, they discovered that the stars on one edge of the galaxy were approaching us while the those stars on the opposite edge were moving away. A spiral galaxy is similar to a huge spinning plate. If you look at a spinning plate from its edge, the left part of the plate will be moving in one direction and the right in the opposite direction. Our Milky Way galaxy which is a typical spiral galaxy rotates once every 240 million years. By comparing the movement from both edges of a spiral galaxy, an astronomer is able to determine how fast even a distant galaxy is rotating.
Thanks to the Cepheids, which are so bright that they can be seen even outside of our own galaxy, the astronomers were able to determine how inherently bright some of these galaxies are and they also discovered the “Tully-Fisher” relations which is that the faster a galaxy rotates, the more massive and brighter the galaxy is also. Although this relationship has been observed time and time again, there is no clearly accepted explanation for it, maybe because we still don’t yet fully understand how a galaxy is formed. One theory is that the faster the galaxy rotates creating a force pushing the stars away from its center, the greater the gravity that is created by more stars is needed to counteract that force.
In any case, even without fully understanding the Tuller-Fisher relationship, we can use it. There are distant galaxies that are too far away to measure through their Cepheids but whose speed of rotation CAN be measured. By measuring the rotation speed of a spiral galaxy one get a good approximation of its inherent brightness. As usual, its inherent brightness is compared to its apparent brightness (how bright it appears to be from the Earth) and we know its distance. Using the Tully-Fisher relationship it’s possible to estimate the distance of galaxies hundreds of millions of light years from the earth.
This article lists only some of the techniques that have been used how far away some of the most distant objects in the Universe. You probably notices accept for parallax, every technique is dependent on the others. Tully-Fisher is based on the Cepheids, the Cepheids on Main Sequence fitting, and Main Sequence fitting on parallax. If parallax gives results that are off by say 20%, none of the other techniques will be more than 20% accurate either. That’s why more and more accurate measuring of the stars is taking place even now so that the parallax and other techniques will also produce better results.
If someone claims that a certain star is exactly 837.12 light years away, you can be quite sure that they don’t know what they’re talking about, because we just can’t measure such enormous distances to a high accuracy. But the fact that we able to make good estimates of distances that are billions and billions of miles away from is a tribute not only to technical expertise but to the human spirit.