The Measurement of The Measurement of Distance 1.7Distance 1.7

Astronomers track and record Astronomers track and record the positions of the stars.the positions of the stars.

They must know They must know directiondirection and and distancedistance..

Determining the distance to a star Determining the distance to a star is difficult because we cannot is difficult because we cannot actually travel to the star and actually travel to the star and measure the distance.measure the distance.

Instead, astronomers must be very clever Instead, astronomers must be very clever and measure the distance indirectly. and measure the distance indirectly.

One distance measurement One distance measurement method is called method is called triangulation.triangulation.

Based on the principles of geometry.Based on the principles of geometry. Surveyors use this to measure the Surveyors use this to measure the

distance to faraway objects.distance to faraway objects. TriangulationTriangulation makes up the makes up the cosmic cosmic

distance scaledistance scale..

ParallaxParallax Parallax measurements take advantage of Parallax measurements take advantage of

the fact that, as the Earth orbits around the the fact that, as the Earth orbits around the Sun, relatively near-by stars appear to Sun, relatively near-by stars appear to move with respect to the fixed, very distant move with respect to the fixed, very distant stars.stars.

This is the same thing that This is the same thing that happens when you look at a happens when you look at a close object with first one close object with first one eye and then the other. eye and then the other.

For example, hold your thumb at the tip of For example, hold your thumb at the tip of your nose. Look at your thumb with first your nose. Look at your thumb with first your right eye and then your left. Your your right eye and then your left. Your thumb appears to move because your thumb appears to move because your eyes are not at exactly the same place, so eyes are not at exactly the same place, so each eye views the thumb from a different each eye views the thumb from a different angle.angle.

Now hold your thumb at arm's Now hold your thumb at arm's length and repeat the experiment. length and repeat the experiment. Your thumb will still appear to Your thumb will still appear to shift, but will not appear to move shift, but will not appear to move as much as it did when it was as much as it did when it was closer. closer.

The same thing happens to stars. The same thing happens to stars.

The closer stars appear to shift more than The closer stars appear to shift more than the farther stars. The "fixed" background the farther stars. The "fixed" background stars are not really fixed; they are just so stars are not really fixed; they are just so far away that we cannot distinguish their far away that we cannot distinguish their apparent shift. The apparent shift of the apparent shift. The apparent shift of the stars is called their parallax. stars is called their parallax.

Parallax is simply the apparent change in Parallax is simply the apparent change in the position of an object due to a change the position of an object due to a change in the location of the observer. In order to in the location of the observer. In order to measure the parallax of stars which are measure the parallax of stars which are very far away, we must use the largest very far away, we must use the largest baselinebaseline possible. possible.

((The baseline is the distance between the The baseline is the distance between the two points where we take the two points where we take the measurements. For the experiment above measurements. For the experiment above with your thumb, the baseline is the with your thumb, the baseline is the distance between your eyes.) A larger distance between your eyes.) A larger baseline results in a larger shift, which baseline results in a larger shift, which means that we can measure the parallax means that we can measure the parallax of stars which are farther away. of stars which are farther away.

The largest baseline we can use for The largest baseline we can use for ground based observations is the diameter ground based observations is the diameter of the Earth's orbit. Using the Earth's orbit, of the Earth's orbit. Using the Earth's orbit, we make one measurement of the position we make one measurement of the position of a star in, say, June, and the second of a star in, say, June, and the second measurement in December (6 months measurement in December (6 months later). later).