In space the light intensity from distant stars can be used to approximate the distances between the stars and us. This idea can be mimicked in the laboratory with a light box, a lux meter and a measuring rule. Taking measurements and plotting them reveals a linear relationship between light intensity and the reciprocal of the distance squared. It turns out that they are in fact proportional to one another.
There are some obvious problems with this technique:
* Don’t know how bright the stars really are.
* We must assume that the intensity is not affected by different mediums (including the atmosphere).
Measuring Distance using Parallax
Parallax is a technique that uses trigonometry and the difference between the apparent positions (referring to the “fixed” background stars) of a distant object from two different points along a base line. The longer the base line the further you can see. On earth the best we can do is looking at the object twice with 6 months between each viewing. This gives a baseline of 2Au = 300 Million km. The angle subtended by the distant star and the two viewing points in two lots of the parallax angle. So using the diagram parallax angle = . This method is only really usable over relatively short distances.
A parsec, or 1 pc, is a unit of distance. It is defined as the distance between the Sun and an object when the parallax angle is equal to one second of arc ( of a degree).
The 1 Au on the diagram is the distance between the Earth and the Sun. Using this definition it is found that 1pc = 3.08 x 1016 m = 3.26 light yrs. If a star is further from Earth then the parallax angle is reduced. Roughly speaking:
Distance (in pc) = (when the angle is measured in seconds of arc)
Velocity of an Asteroid
By sending two pulses at an asteroid and timing the difference between the lengths of time each pulse takes to reach the asteroid and return, the velocity (relative to you) can be found. When doing such calculations it is very important to remember the factor of two involved. Generally it can be shown that:
where: v is relative velocity of asteroid, c = 3 x 108 ms-1, and change in tback and change in tout are time between getting two pulses back and time between sending two pulses respectively.
The Doppler Shift
?out and ?back are fairly self explanatory, and obviously ?back > ?out if the object is moving away, and the opposite if it is not. This differs from the method used with the asteroid as continuous waves rather than pulses are used. The formula that is used is not very different to the previous one though:
and if v << c (much less) then . The speciality of being able to use continuous waves rather than pulses is important when a one-way measuring method is used. In this the object is too far away to send a pulse to, however the object is emitting EM radiation. The change in wavelength of this radiation as it moves through space can be used to determine the relative velocity of the object. As this is one-way measuring the formula is modified (no need to account for both ways) to: . To determine the black lines in the emission spectrum that are absorbed by abundant elements in space (H and He) are tracked, and the movement of the pattern of lines, from what we know to be the true values from experiments on Earth, is used to determine how much the wavelength of the radiation has changed.
The Hubble Constant
Hubble measured the distances to galaxies using Cepheid Variables (pulsating stars, slower the pulsation the brighter the star) and the speed of recession by looking at the red-shift of the black lines in the emission spectrum. He found a remarkably strong correlation. Suggesting that so: where H0 is known as the Hubble Constant. It automatically follows that: and this time is known as Hubble Time. This time is the reciprocal of the Hubble constant elapsed since all galaxies in one place. This gives a way to find the age of the universe. However there are some problems.
* This assumes that the speed is constant for a galaxy. Due to gravity it isn’t which gives an over-estimate on the age of the universe.
* H0 is not precisely known.
Using different ways of measuring distances (eg. Type II Supernovae vs. Rotation of galaxies etc. ) different values for H0 are found. If H0 is low (which is about 50 kms-1Mpc-1) then this implies an old universe (about 20 Gyr). But this data is not what most sources currently obtain. It is increasingly popular to think that H0 is high (say 85) giving a 14 Gyr old universe. However some parts of the universe are known to be more than 15 Gyrs old. Which is an utter nonsense. It is thought that dark matter could be the missing piece that would solve this conflict. Obviously its` presence would change the rate of recession of galaxies due to gravity.
As light travels from one galaxy to another, the universe expands, which stretches the wavelength of the light (or other radiation). This causes a red-shift of the radiation, which should not be confused with the red-shift caused by the relative motion of two objects (which is known as the Doppler effect). The mathematics behind it works like this:
This result makes sense as if ?? = 0 then the ratio of the distances is 1, implying that they are the same. And also if ?? > 0 then the answer will always be greater than 1 suggesting a greater observed than emitted distance. Once again the ?? is determined from the movement of the black lines in the spectrum. The fact that everything measured shows a ?? > 0 indicates that the distances between every pair of objects is increasing (except locally where gravity can cause the reverse effect) and that the universe is expanding. This points to everything (once upon a time) being at the same place. Making this evidence for the Big Bang theory.
Cosmic Microwave Background Radiation
As time has passed since the Big Bang the background radiation from the Big Bang has been cosmologically red-shifted by the expansion of the universe. Initially high energy photons were exchanged between particles but by 300 000 yrs after the bang, the ? was stretched to 1?m and the temperature had been reduced to 3000 K. This temperature fall is observed because as ? gets longer, f gets lower, so by E = hf, E gets lower, and E ? T giving a temperature fall. Today (14 Gyr later) the ? is 1mm (microwaves) and T = 2.7 K. This is also considered to be evidence for the Big Bang.
This is a thought-experiment that suggests that if the Universe is infinite then everywhere you looked in the sky your line of sight would (eventually) end with a star, giving a white sky. Ulber found that the sky was black rather than white. He claimed that there were not enough stars for an infinite Universe, so it must be finite.