E3 - Stellar Distances

As we move, objects appear to change their relative distances. Objects closer to us appear to move more than those further away that might appear stationary. This apparent movement is called parallax and this effect can be used to measure stellar distances as the closer the star is to the earth the greater the parallax shift will be.

Angles: 3600 arc seconds (3600") = 1° = 2π/360 radians

Using distant stars as a reference the angle that the moving star makes with the earth is observed over a six month period (why? it gives the maximum angle) as shown:

Here we can see that:

tanq = 1 Au/ d

using small angle approximation we can see that this means:

q = 1 Au/ d

If q was 1 second ( (2π/360 * 60 * 60) radians ) then the distance d would be given by 1 parsec. 

  p = 1/d

where p = angle in arcsecs 

               d = distance in parsecs

This method can be used for stars up to a few 100 parsecs away after which the angle becomes so small that the uncertainties become significant.

Apparent magnitude: This is a scale to measure the apparent brightness of a celestial body where each level is equivalent to a rise of 2.51 times the brightness of the previous one and the brightness increases with the negativity of the numbers. This means that the brightest star ( sun) will have the largest negative value of all the stars.

The ratio of the apparent brightnesses of two stars bA and bB is related to their apparent magnitudes MB adn MA by:

Absolute magnitude: This is the apparent magnitude of the celestial bodies at a distance of 10 parsecs from earth.