Measuring Distances. Taking the Measure of the Universe

Transcription

1 Measuring Distances Taking the Measure of the Universe

2 The Importance of Distance We talked about how the brightness of a star can be due to 2 effects: distance or luminosity. Without a direct measurement of a star s distance, we can t determine the star s luminosity or where it is in space! This is not only true of individual stars, but of star clusters and galaxies themselves.

3 The Importance of Distance Ultimately, knowing distances across the Universe also allow us to determine the Universe s age. While distance is so critical in astronomy, it is also one of the most difficult things to measure. Fortunately, Greek astronomers imagined a method 2000 years ago that is still in use today.

4 Measuring Distances Hold your finger out in front of your face at arm s length. Look at your finger through each eye separately. What do you notice? This change in perspective is known as parallax. Ancient Greek astronomers expected to see a similar change in the positions of nearby stars if Earth actually moved around the Sun.

5 Measuring Distances This apparent shift in position is called parallax. Because we are riding on Earth as it orbits the Sun we see the same effect for faraway objects like planets or stars. To the ancient astronomers of Greece, their failure to see stellar parallax meant that Earth must not be moving!

6 Parallax The problem was ancient astronomers could not conceive of the vast distances between stars. In reality, even the stars closest to the Sun have very small parallaxes that require powerful telescopes to measure. The first stellar parallax was not measured until 1838 by Friedrich Bessel at the Berlin Observatory.

7 Parallax How small a parallax are we talking about? Imagine someone standing at the top of the MCC football stadium holding a dime. Now imagine standing on the roof of the Physical Science Building (about 1 kilometer away) looking at the face of the dime. The largest parallaxes (of the nearest stars) are equivalent to the apparent size of that dime!

8 Parallax Astronomers use a set of special units for angles: There are 60 arcseconds in 1 arcminute, and 60 arcminutes in 1 degree. (Just like units of time: hours, minutes, seconds.) An object that shows a parallax of 1 arcsecond lies at a distance of 1 parsec (parallax arcsecond). The parsec is abbreviated pc.

9 Parallax More distant objects have smaller parallax; closer objects have larger parallax. We can relate this through an equation: distance in parsecs = 1 parallax in arcseconds or d = 1 p Bessel found that the star 61 Cygni shifted by a tiny angle of 0.3 arcsecond. 1 = 3.33 parsecs So the star 61 Cygni: 0.3 arcseconds

10 The Parsec It takes a little trigonometry to determine, but: one parsec is equal to 206,265 Astronomical Units one parsec is equal to 3.26 light-years Astronomers also use: the kiloparsec (1,000 parsecs = 1 kpc) the megaparsec (1 million parsecs = 1 Mpc)

11 The modern standard Modern parallax measurements come from the HIPPARCOS satellite ( ), capable of measuring parallax angles as small as 1/500 th of an arcsecond (0.002 arcsecond). What distance does this correspond to? d = 1 p A distance of 500 pc Distances derived from a parallax shift are known as trigonometric distances or trigonometric parallaxes. This is the fundamental method for measuring the distances to nearby stars.

12 Star Alpheratz has a parallax of 0.1 arcsecond. How far away is this star? A. 0.1 light-year B. 0.1 parsec C. 10 light-years D. 10 parsecs

13 Star Kappa has an apparent magnitude of +3.6 and a parallax of 0.08 arcsecond. Which of the following is closest to the absolute magnitude of Star Kappa? A B C D. -0.2

14 Which star is the most luminous? Star A has an apparent magnitude of +0.2 and a parallax of 0.1 arcsecond. Star B has an apparent magnitude of +0.2 and a parallax of arcsecond. A. Star A B. Star B C. The two stars have equal luminosities. D. Information is not sufficient.

15 Astronomers discover a previously-unseen object with a parallax of 4.5 arcseconds. What is the distance to this object? A. About 4.5 light-years B. About 4.5 parsecs C. About 0.2 light-years D. About 0.2 parsecs

16 What could we say about the object from the previous question (the one with a parallax of 4.5 arcseconds)? A. It must have a very high luminosity to be visible at all at that distance from the Sun. B. It must have a very low luminosity to have gone undiscovered that far from the Sun. C. It must be one of the most distant stars ever discovered. D. It is likely the first individual star ever detected outside of the Milky Way.