Measuring the Distance to Nearby Stars Using Parallax
The astronomer Friedrich Bessel used the exact method you used to measure the height of the flagpole to find the distance to a nearby star, 61 Cygni, in 1838. This was a monumental achievement that came about due to technological improvements in telescopes that gave humans their first realistic glimpse of the vast dimensions of the Universe beyond our Solar System. Bessel knew that if he could measure a star once in December and later in June when the Earth was on the opposite side of the Sun he could measure the parallax shift of that star relative to background stars. Once he knew the stars parallax shift he could apply the ancient Greek mathematics of trigonometry to find 61 Cygni’s distance from the Sun. Galileo also knew that he could find the distances to stars this way and would have had further proof of the Copernican model of the Solar System, but was stymied by the primitive telescopes of his day.
Notice from the pictures that astronomers measure the star’s position against background stars, first in Decemberand again in June when the Earth is opposite from where it was 6 months ago. Now notice that the Earth in December to the star and back to the Earth in June makes an angle. It is this angle that astronomers measure. Astronomers take the angle from the Earth in June to the star to the Earth in December and divide it by two. This angle is called the parallax angle and creates a right triangle from the Sun to the Earthand to the Star being measured, like the right triangle you made when looking up at the flagpole! On the picture above,draw a line from the star to the Sun to make a right triangle from the Earth in June to the star to the Sun. Mark the right angle. Finally, remember that the distance of the Earth to the Sun is one AU and we need to know this distance and the parallax angle to find the distance to the star. Now they simply do the trigonometry! Use the formula below to solve the following problems. Remember to divide the angle to the star by 2 to get the parallax angle!
1 AU/ tan of parallax angle = Distance to Star in AU’s
1. An angleto a star is found to be 4 degrees when measured from Earth in Juneto the star and back to Earth in December. Find the parallax angle, and the distance to the star in AU’s.
2. An angleto a star is found to be 4 degrees when measured from Earth in June to the star and back to Earth in December. Find the parallax angle, and the distance to the star in AU’s.
3. Why won’t the parallax method work for stars at great distances from Earth?