## 1. Find the Distance to HT Cas Using Parallax

### 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).

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illustrating a star's parallax motion on the sky |

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### 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 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