Measurement and uncertainties are enormous issues for astronomers.I was surprised when I knew how do astronomers measured the distancs of heavenly bodies.How about our wondertful neighbour galaxy Andromeda galaxy?How far away the star when we see the most distant star with our naked eye?How large is the Universe?
These are some of the questions.But you will be astonished by the measurement process ,measuring tools and techniques and the story behind it.In such case uncertainties play a major role.Until the end of the nineteenth century,astronomers used to measure something that is called “Parallax”.
You know about the phenomena of parallax even without realizing it.Suppose you are outside of some features of landscape e.g. a tree.You stretch your hand in front of you and raise your finger along the tree.Now close your right eye first and observe the finger with your left eye.Next open your right eye and close your left eye.You will observe that your finger will jump from right to left.Now take your fingers close to your eyes and repeat the above process.The finger will jump more i.e. effect is huge.This is parallax.This happens because we observe along different lines of sights.Our eyes are about 6.5 cm apart.
This basic idea was applied for measuring the distances of stars.6.5 cm was taken as baseline in measurement of parallax.Similarly, the diameter of the earth’s orbit around the Sun was taken as baseline.It is about 300million kilometers.As the earth revolve around the Sun in one year,so a nearest star will move in the sky relative to the more distant stars.Astronomers measured the angle, called parallax angle between the position of a nearby star 6 months apart.Astronomers measured or detected the position of the star in the sky in every month and measured the angle between the position of the star six months apart.Hence,we will get a set of measured parallax angles.The value of these parallax angles are different from each other.The parallax angle found between the position of 3 and 9 in the diagram is different from that of the angle between the position of 1 and 7.The parallax angle 4A10 is zero.So, the greatest parallax angle among such set of angles is 1A7,called alpha.Now we can easily calculate the distance of star A from earth by simple high school math(finding the value of sine of half the angle alpha,and knowing SE=radius of earth orbit, we can calculate EA).
Astronomers talk about the parallax of a star which is half the greatest parallax angle. Smaller the parallax of a star, greater the distance is.The parallax of the nearest star of the Sun, Proxima Centauri,is 0.76 arc second. It’s distance is 4.3 lightyears.
To understand how astronomers measured the distances of stars by measuring parallax and the importance of uncertainties related to it,we have to understand how small the unit arc second is. We know that a circle makes an angle 360 degrees in its center. Now divide each degree equally into 60 minutes and divide each minute into 60 seconds. Hence, there are 1296000 arc seconds in a full circle.Here is a another way to realize how small an arc second is We know the angular size of the Moon is half a degree or 30 arc minutes. If we could cut the Moon in equally 1800 equally thin slices, each slice will represent one arc second.
The parallax measured in arc second, is used to determine the distances of heavenly bodies. The technology involved in such fields developed with time and the estimates that were made by the astronomers changed.Sometimes the change is surprising. In the early nineteenth century, Thomas Henderson measured the parallax of the brightest star ,Sirius to be 0.23 arc seconds with an uncertainty of about 0.25 arc seconds and he determined the distance from the above parallax was 6.5 light years. In those time this was a great achievement. But after almost 50 years later David Gill measured the same 0.37 arc second with an uncertainty of about 0.010 arc seconds. Gills measurement was superior over Henderson because of less uncertainty. According to Gill,the distance was 8.81+/- 0.23 light years, which is much greater than 6.5 light years. In 1990s Hipparcos, a high precision parallax collecting satellite,measured the parallaxes of hundred thousand stars with an uncertainty of about a thousandth of an arc second. It measured the parallax of Sirius was 0.37921+/-0.00158 arc seconds. i.e. ,the distance is 8.601+/-0.036 light years. I think you will be very eager to know how we have to cover a distance to decrease the uncertainty in parallax by one arc second?You have to cover 2200 miles for an arc second.
The uncertainties in such measurement are due to a consequence of limited accuracy of our equipment.The challenges to overcome such uncertainty was checked by famous female astronomers but mostly ignored, Henrietta Swan Leavitt, a low level staff at Harvard Observatory in 1908. She noticed the photographic plates of Small Magellanic Clouds (SMC) that with a certain class of pulsating stars (known as Cepheid variables).She found the relationship between the brightness of star and the time period of stars. Larger the time period larger is the brightness. But the luminosity and brightness are different. Brightness is the energy received per second per square meter in the earth with an optical instrument. On the other hand, luminosity is the energy radiated by an astronomical object, e.g. luminosity of Venus in the sky is greater than that of Sirius but it’s luminosity is not intrinsic and it is very close to the earth than Sirius. Astronomers found the relationship of luminosity, brightness and distance. Later using statistical parallax techniques, Ejnar Hertzsprung in 1913 and Harlow Shapley, in 1918,were able to convert Levitt’s brightness value into luminosity. By finding it’s value they were able to calculate the distance. This process is technical too. This was a great leap in the history of astronomy. e.g. a Cepheid of period of three days having luminosity thousand times greater than Sun’s, again a Cepheid of period thirty days having luminosity greater than thirteen thousand times than Sun’s luminosity. In 2004,using Cepheid variable method, the distance of Andromeda galaxy was 2.51+/-0.13 million light years. In the next year another group measured it by using eclipsing binary stars method was 2.52+/-0.14 million light years. These were good in agreement but uncertainty was about 140000 light years, that is the distances of so many other galaxies!!!
One of the most shocking discovery in the history of astronomy also in the history of all other area of science in past century was that Universe expands itself or the galaxies in the universe are moving away from each other. This was discovered by Edwin Hubble in 1925. He observed the light emitted by galaxies shifted towards the red end,i.e. redshift. We are familiar with such effect of sound, Doppler effect. He found that farther away the galaxies were, faster they were moving away. He wrote that v=HD where, v is the velocity of a given galaxy, D is the distance of the galaxy and H=Hubble’s constant. According to him it is 500 km per second per megaparsec(1megaparsec=3.26 million light years). e.g. if a galaxy is at a distance of 10 mega parsecs or 32.6 million light years away,the velocity of the galaxy is 16300 km per second. That is the galaxies are moving away with a great speed or Universe is expanding very fast. It is clear that if we know the value of Hubble constant we can calculate the age of universe (from bigbang).Hubble himself calculated it is 2 billion years old. But the geologist measured the age of the earth to be 3 billion years. Which is in conflict with the estimated value of Hubble. Hubble himself made some systematic errors and also he was unaware of some Cepheid variables. Astronomers were struggling in finding the value of Hubble’s constant. Now it is found that it’s value is 70.4+/-1.4 kilometers per second per mega parsecs. By using this value the estimated age of the universe is nearly 14 billion years actually 13.75+/-0.11 billion years. The uncertainty of about 2% incredible!(This is measured by fabulous orbiting Hubble’s telescope).
We have developed in both mathematically and technically in measuring the distances of heavenly bodies or by knowing how they far away from us or by knowing how large is our universe. But still we don’t have any idea what the dark matter and dark energy are. They constitute the large part of our known universe. But they remain a mystery for us. We don’t know about the existing life other than our Earth. So,we have to go a long way to explore.