2.  Parallax, p, is defined as half the angle through which a star’s direction changes as the Earth moves from one extremity of its orbit to the other.  This change in angle is measured against the relatively stationary background stars.  An important concept here the distance of the AU.  The AU, or astronomical unit, is defined as the average distance from the Earth to the Sun (~1.5 x 10 11 m)

3. D = 1 AU/tan p  This equation comes from the trigonometric relationship between our 3 variables.  Even the closest stars are really far away and as you can see, p gets smaller for more distant stars.  Parallax angles as small as 1/360000 o can be measured which equates to a distance of about 100 light years

5.  The parsec is defined as the distance between a base of 1AU at an angle of 1 arcsecond.  This means that 1pc = 3.086 x 10 16 m

6.  This is NOT a definition of time.  It is the distance that light can travel through a vacuum in 1 year.  If you work it out it is – 9.461 x 10 15 m When you consider the ridiculous distance involved in astronomy, it makes sense to have large units!

7.  Olbers showed that in an infinite, uniform Universe the sky at night would be bright, but this is not so.  BUT … the Universe must be infinite or it would collapse under its own gravitational forces.  This is the paradox.

8.  Imagine a thin shell in space at radius r from Earth.  Radiation from these stars reaches Earth with small, yet definite intensity.  Another shell, at 2r, has the same density of stars, so has 4 times as many star in the shell but we receive ¼ of the light from each star due to the inverse square law.  Therefore, we receive the same intensity of light from each shell.  This means that we receive starlight from all directions at all time, so the sky should be infinitely bright.

9.  All of this stems from logical mathematics yet is clearly not true.  Therefore Olber deduced that the Universe is not infinite.  He did however make some assumptions –  that the Universe is infinite and uniform  the space extends indefinitely in all directions, independent of any matter  That the Universe is static The paradox is – ‘With an infinite number of stars in an infinite Universe, it does not matter where you look, there will always be a star in your line of sight. Therefore the night sky should be as bright as day.’