Dr. Aaron Titus | Department of Physics, High Point University PHY1050      Astronomy of Stars, Galaxies, and the Cosmos home | WebAssign | textbook | course calendar

## distance to nearby stars

Distance to nearby stars is measured using trigonometric parallax.

To calculate the luminosity of a star, we must measure its brightness and its distance. Brightness is easy to measure using a telescope and an instrument called a photometer. However, how do we measure distance to a star?

The method used for nearby stars is called trigonometric parallax. While this method is very precise, this only works for nearby stars. For further stars, we'll have to use other techniques.

Parallax is the apparent shift in the position of a star as a result of looking at it from two different vantage points. It's fairly easy to understand by doing the following activity.

1. With both eyes open, hold your index finger about 6-9 inches in front of your eyes, between you and the 0 on the scale below.
3. Now, open your right eye and close your left eye and use the scale to measure the position of your finger.

When I did this experiment, I found that my finger was at the 3.0 mark with my left eye open and at the -3.0 mark with my right eye open. Your numbers will depend on how far away your finger is from your eyes. Thus, the difference in the positions as measured by each eye is 6.0.

Now, repeat this experiment with your index finger about 15-18 inches in front of your eyes. Again record the position of your finger measured with your left eye closed and the position of your finger measured with your right eye closed.

You should have noticed a difference in measurements that is less than what you measured before. In my case, with my finger about 18 inches in front of my eyes, I measure my finger at 1.0 and -1.0 for a difference of 2.

The greater the distance of my finger from my eyes, the less the apparent shift in the position of my finger as measured using the scale. The amount of apparent shift can be used to calculate the distance from my eyes to my finger. This method is called trigonometrix parallax, or just parallax for short.

For the case of stars, we measure the RA and DEC of a nearby star. Then, we wait 6 months and measure the RA and DEC of the same star. Half of the difference in these anglular positions is called the parallax (or parallax angle) p of the star and is measured as an angle in arcseconds.

The distance to a star for which the parallax is 1 arcsecond is defined to be 1 parsec (pc) which happens to be equal to 3.26 ly. The closest star is Proxima Centauri with is 1.3 pc or 4.2 ly.

Note that the distance to the star and the parallax of the star are inversely proportional. The smaller the parallax, the larger the distance to the star.

For stars at distances greater than about 300,000 light-years, the parallax is so small that it can't be measured.

parallax.mov--This video demonstrates the apparent shift in the position of star as a result of viewing the star from a different vantage point as Earth orbits Sun. One single back and forth motion of a star represents the apparent shift in the star's position during a time duration of 1 year.

The simulation from the video is shown below. By viewing the apparent motion of the nearby stars (due to Earth's orbit around Sun), can you tell which ones are closer? Click the "Show Trails" button to see the shift in the stars' apparent position due to parallax. Reload this page to see a new, randomized set of stars. Click anywhere in the scene to start and stop the animation. Double-click a star to view its distance.

The European Space Agency's Hipparcos satellite (HIgh Precision PARallax COllecting Satellite) measured the positions of about 118,000 stars from 1989-1993. It measured parallax angles with a precision of 1 arcsecond. Thus, it could be used to measure (within 10% accuracy) distances to stars as far as 300 ly.

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