1. Determining Stellar Distances: The Principle

2. ‘Real Life’Distance Determinations
We use various ways; you can think of several! For instance, you notice that a car down the road ‘looks small’, so must be far away: it’s safe to cross the road. This works because we know how big cars actually are! But this won’t work for stars. Here’s an important one, used for nearby objects: binocular vision  depth perception

3. It Depends on Parallax
Two different points of view: each eye sees a slightly different image. (We have ‘binocular’ [two-eyed] vision.) The brain merges these and interprets the three-dimensional nature of the situation: depth perception.

4. As Here [compare the foreground lamppost to the distant building]

5. Simulated (and Exaggerated!) in 3-D Movies (like Avatar)

6. Accomplishing the Trick - two images, one per eye

7. There is a Fundamental Limitation
More remote objects display less parallax. Our ‘depth perception’ fails us beyond a few tens of metres, and we have to use other methods. It would help if we could spread our eyes farther apart!

8. How High is the Plane? Two problems:
1. The plane is far away, so the parallax effects are small
2. It is seen against a featureless background, making any differences very hard to detect.

9. It Helps to Have a Distant Background Frame of Reference

10. Now Think About the Stars
Some stars are nearby, others much farther away (in the background). If we can spread our ‘eyes’ far enough apart, we will see any nearby star in two slightly different positions against the remote background pattern (in practice, by taking two photographs).

11. We Can Do That for the Moon: ‘Geocentric’ Parallax
Imagine two ‘eyes’ separated by hundreds of kilometers, looking at something relatively close.

12. Limitations of Geocentric Parallax If the target is too far away, the parallax effect becomes immeasurably small, even from widely-separated locations on Earth.

13. How About the Stars?
Even the very nearest stars are so far away that we don’t notice any geocentric parallax. These two people are looking in essentially parallel directions, because the star is so remote!

14. The Solution: Heliocentric Parallax
Remember that the Earth moves around the sun once a year! We can take one picture now, then a second one six months later, from a much different location (300,000,000 km away).
This ‘spreads our eyes’to yield the effect known as heliocentric parallax.

15. Can a One-Eyed Person Have Depth Perception?
Yes and no!

16. That Sounds Easy - and here it is, in principle

17. It’s Not Exactly Equivalent to Human‘Depth Perception’
Our human ‘binocular’ vision works because we compare two different views (one with each eye) at the same time. In heliocentric parallax, we are comparing two images taken at different times. But the principle is fundamentally the same.

18. You Don’t Have to Wait
The shift will, of course, be the largest after 6 months (since we are then on opposite sides of the Sun in our orbit). But you can observe at various intermediate times, and watch the star appear to move back and forth across the background. Try the Animations/Other Animations on this site: This shows the parallax effects we would see if the Earth orbited the Sun in a really huge orbit (1.5 light years across!).

19. Indeed, This Must Happen!
If the sun is truly at the centre of the Solar System, nearby stars must show this kind of parallax (because the Earth moves!) We should see any really nearby star shifting back and forth across the distant background once a year. Astronomers since Copernicus knew this, and tried to observe the effect (using the telescope, first introduced by Galileo). Their failure to do so readily was clear evidence that the stars were very far away indeed!

20. But It Seems Trivially Easy! [look back 4 panels]
If the red star is nearby, then:
in Jan, we should see this in July, we would see this
- a conspicuous change in its position!

21. So What’s the Problem?
Why did it take ~240 years, following Galileo’s first use of the telescope, to detect this behaviour?

22. Before Answering: Let’s Choose Convenient Units
We now know that stellar distances are vast: many tens of trillions of kilometers at least.
It’s more convenient to use light years.
One light year = the distance that light travels in a year ( ~ 10 trillion km). The nearest star is about 4 l.y. away.

23. But Look at our Original Drawing:
The red star is drawn as if it is less than 1.5 times as far away from the Sun as we are -- that’s closer than Mars!!

24. Sobering Reality
The very nearest star is ~ 300,000x as far away as the Sun. Try drawing our ‘heliocentric parallax’ sketch again, correctly scaled. The ‘parallax angle’ is very small. The position of the closest star changes almost imperceptibly against the background, even after 6 months!

25. How Big Will the Shift in Position Be? Let’s Define Some Angles

26. Successive Subdivisions
Look horizontally, then straight up. That shift of viewpoint is through 90 degrees (a ‘right angle’) Take just one of those degrees and split it into 60 smaller angles: ‘minutes of arc’ Take one of those minutes and split it into 60 yet smaller angles: ‘seconds of arc’ So a second of arc is a truly tiny angle.

27. The‘Angular Size’ of a Dime
One degree if it is about 1 metre away One minute of arc if it is 62 metres away a dime is 18mm in diameter One second of arc if it is 3.7 km away

28. In Other Words:
Stand on your front porch. Have a friend hold up a dime 3.7 km away Now shift your gaze from the top edge of the dime to the bottom. That’s 1 arcsec -- a truly tiny angle!

29. A New Unit of Distance If the parallax angle, p, is one second of arc
then the star is, by
definition, exactly one
parsec away.
(if there are any stars even closer
than that, they will show greater
parallax. Remote stars show less.)
1 parsec = 3.26 light years

30. Now a Sobering Dose of Reality
Other than the Sun, no star is even as close as one parsec.
In other words, as we orbit the Sun, no star will seem to shift back and forth against the distant background pattern by even as much as as one second of arc.
Little wonder this behaviour was so hard to detect and measure!

31. Meet Proxima Centauri (marked at lower right) Ask yourself how this picture will look six months from now. Proxima will indeed seem to have moved, but by less than the size of the little dot of light in the photograph. And remember that this is the closest star of all, with the most conspicuous parallax.

32. Nowadays, We Have it Easy!
We can take pictures of the sky, months apart, and intercompare them later, at leisure. Until the late 1800’s, no such technology existed. Astronomers had to measure the angles between stars to map out the detailed pattern. Repeat the exercise six months later to see if things had changed perceptibly. Repeat, year after year!

33. An Additional Complication
Individual stars move through space!Consequently, the annual parallactic shift (the tiny back-and-forth motion) is superimposed on a general accumulating change in position of any individual star.
Consider Barnard’s Star: it travels across the sky (because of its own motion), and also appears to shift back and forth (thanks to our changing vantage point as the Earth orbits the Sun).

34. Cosmic Units of Distance
Astronomers quote distances in
parsecs (for the nearby stars)
kiloparsecs (for distances within the Milky Way)
megaparsecs (for distances to other galaxies)
gigaparsecs (for the most remote observable parts of the universe)
One megaparsec is just over 3 million light years; a gigaparsec is more than 3 billion. And remember the associated ‘look-back times!’

35. There’s Yet Another Problem...
Astronomers couldn’t study all the stars in the sky, to find the few that are close enough to show barely detectable parallax. But which stars should they start with? Clearly, those that you think might be nearby for other reasons.

36. That’s Why, Historically…
…stellar parallax was so
devilishly hard to discover!
So what led to the critical breakthrough and success?