
The Method of Parallax
Parallax is the apparent shift of a nearby star against the fixed
background that can be seen as the Earth goes around the Sun. A star's
parallax angle is given by the formula:
If you know any two of these variables (the parallax angle and the
radius of the Earth's orbit, for example), you can solve for the third
(the distance to the star).
Finding the Distance to HT Cas Using Parallax
You know that parallax is the most accurate method for finding the distance
to nearby stars, and you hope that you can use this method for HT Cas.
First you need to find the right images. Shown below are idealized images
of the sky around HT Cas taken six months apart with an optical telescope.
(In order to achieve the resolution or fine detail in these idealized
images, you would have to have a telescope a kilometer across!).
Image of HT Cas taken 06/96 
Image of HT Cas taken 12/96 
In the image below, the two images have been combined. HT Cas is
highlighted in red. You can measure the apparent shift during this six
month period if you know the scale of the picture. From a stellar
astrometric catalog, you find that the two stars closest to HT Cas are a
distance of 0.01" (" stands for units of arcseconds) apart. Measure the
apparent shift of HT Cas over this six month period. Half this angular
value is the star's parallax, which you can now use to calculate the
distance to HT Cas.
Composite image of measurements of HT Cas taken six months
apart
