Open up the Simulator

Things to notice:

• The earth is going around the sun
• There are two fiducial reference stars labeled A and B
• Every six months a measurement is made
• The transparent circle represents the actual movement of the position of the object star (in this case the red star) relative to A and B
• The parallax angle is indicated by the triangle and the graph that says "Error Histogram". Every time a measurement is made, a new piont is added to that graph - in the time its taken you to read this, there should be 20 or so measurements by now.
• In this example, there is no error associated with a measurement, all measurements are perfect, therefore the same valuye of 0.1 arc seconds is obtained.
• The distance to this star would then be 1/.1 arc seconds or 10 parsecs.
• Don't concern yourself with the lower panel labeled HR Diagram at this time.

Now let's observe the same star but with errors

• In this case, the error per measurement is about 5 times smaller than the actual parallax

• Every time a measurement is made, an offset between the observed position and the position that would be measured without error flashes.

• The error histogram is now filling out

• After about 50 measurements you should see a reasonably well defined error histogram with an average value of about 0.1 (actually you should just leave this running for an hour or so because its also a good demonstration of the way that random errors work).

Because of the positional errors imposed by our atmosphere, our ability to measure the stellar parallax is limited (which is why the HIPPARCOS mission was very important).

Example of observing a distant star

• In this case, the star really is too far away to measure, given the error/limitation of the earth's atmosphere.

• This is because the error is of the same amplitude as the actual parallax so each individual measurement has a very large percentage error (not that "negative" measurement are not recorded so the error histogram will appear somewhat skewed)

Example of observing a fairly nearby star

• Here you can see that the measurement error per measurement is relatively small (the white open circle usually falls close to a white dot) and so the distance can be accurately determined after just a few measurements.

• Unfortunately, there are very few (< 10) of such nearby stars!

the angle is very small because the stars are very distant (first parallax measurement was done in 1839).

individual position measurements of stars are "blurred" out by our atmosphere. Therefore it takes years of measurement to beat down this error.

There is a limiting distance from the earth for which parallax measurements can not be made from the ground. This is why the Hipparcos Satellite mission occurred.