Parallax

Age

Middle School, High School

Format

Stage Show,Hands-on

Materials

   Star background board
   Star stand (a star mounted on a post)
   Laser pointer
   2 velcro stars (these stick to the star background)
   Model sun on post 

Safety Precautions

Science Theatre demonstrators must keep the safety of themselves and their audience in mind at all times. All Science Theatre demonstrators must have read through the Safety Training page. The ST Safety Box with first aid kit, fire extinguisher, etc. should always be available to demonstrators. Always wear safety gloves, glasses, and a labcoat if handling chemicals; always perform potentially dangerous demonstrations at a safe distance from the audience; and always keep a very close eye on any volunteers you call from the audience. Whenever volunteers from the audience are given materials, they should be supervised carefully. In particular, make sure the volunteers do not aim the laser points at anyone's face.

Preparation

Prepare the background board. It is a felt board with a night sky design and a few stars and a printed scale in arcminutes (1/60 degrees) that is calibrated for the distance at which it will be placed from the sun. If the background-sun distance is 20ft, then the scale is 1 inch ~ 14 arcminutes. For 15 ft, it's 19 arcmin/inch. For 10ft, it's 29 arcmin/inch. The trigonometry to calculate the scale is simple (see diagram below), but the unit conversions are tricky!

Arrange the sun, star stand, and background board in a straight line and at the same height (about shoulder-level to the height of the kids). See diagram.

It is most important that the audience be able to see the background board.

Demonstration

1. Arrange the materials as described in the Preparation section. Call for three volunteers: a Summer-time observer, a Winter-time observer, and a star mapper. Assign the summertime and wintertime volunteers to spots on opposite sides of the sun and give the former the laser pointers. Assign the star mapper to the star background board and give him/her the two velcro stars.

2. Have the Summer observer describe where he/she sees the nearby star (the star on the stand) in relation to the background. Have the star mapper place the velcro star on the background board where the observer has described. Now have the Summer observer use the laser pointer to point at the nearby star (the star on the stand). Move the star stand out of the way for a moment so that the laser falls on the background board - it should fall very near to where the velcro star was placed. Move the velcro star to where the laser pointed, to make things perfect.

3. Repeat step 2 for the Winter observer. It is important that the Winter observer be standing the same distance from the sun as the Summer observer and that they hold out the laser pointer at the same length.

4. Have the star mapper use the scale on the background board to measure the distance that the star has moved in arcminutes.

What to Say

You can motivate the demonstration with a discussion like this: "Have you ever thought about how you know how far away things are? In some cases, you just rely on the known size of an object. For instance, if a pencil looks very large, that must be because it is very close. If it looks very small, that's because it's very far away. We can estimate the distance of familiar objects based on their apparent size. But what about objects that are not familiar? If you have no idea how big an object is, how do you know how far away it is? If it looks large, it could be very close, or it could be far away and just be a very large object. Well, thanks to our binocular vision, the fact that we have two eyes, humans have a special ability called depth perception. Depth perception allows us to figure out how far away an object is even if we have no idea of its actual size. Now think about a star in the sky - how do you know how far away it is? Astronomers use a concept called "parallax" to figure this out, which works just like the depth perception in your everyday vision."

You may wish to let the audience try the effect out themselves, first. Ask everyone to hold up one finger very near to their face. Ask them to focus on an object in the background. Now have them close one eye, then open that eye and close the other. They should see the finger's position move a great distance relative to the background as they switch eyes (switch viewing angle). Now have them hold the finger further away and do the same. The object movement relative to the background will be much smaller.

Following the Demonstration section, above:

1. Now ask for volunteers to perform the demonstration. Place the summer-time observer on one side of the sun, facing the stars. Tell the audience that he represents an astronomer on Earth in the summer. Ask the audience where the winter-time observer should go - make sure they know it's on the opposite side of the sun from the summer-time one. Place the winter-time observer at the same distance from the sun as the summer observer. Explain that the nearby star is one fairly near to our sun. The background stars are much further away - maybe on the other side of our galaxy. They could even be very bright things that are even further away, like distant galaxies! Things very far away never seem to move much do to parallax, so they form a static background.

2. Make sure the audience understands that the observer does not see the star at the very center of the background board because he is viewing it at an angle. Make sure they understand that the laser dot is falling on the background board at the exact same position as the observer is seeing it.

3. Explain that we have waited six months and that the Earth has moved to the other side of the sun. Now we have a Winter observer looking at the same star, but they will see it in a different spot on the background!

4. Now we want to know how far the star has appeared to move. Remember - the star hasn't actually moved by very much at all within the Milky Way galaxy during these six months. However, the Earth has moved to the opposite side of the sun, so now we are looking at the star from a slightly different perspective. The fact that the star has appeared to move relative to things even farther away is called "parallax shift." We can use this parallax shift to figure out how far away the star is!

All we need to know now is the angle that the star has moved - its apparent motion in the sky. Astronomers use a variety of complicated tools to perform this astrometric calibration. The simplest tool you can use is something like a sextant, which helps you to point at two objects at once and measure the angle between them using a protractor. This is the type of tool that land surveyors use. Let's skip that part - we have drawn a scale on our background map of stars which will tell us the angle.

Now take the angle and use it to calculate the distance. You should draw this out on a chalkboard. The distance to the star equals the distance separating either observer from the sun (1AU in the solar system, a few feet in our model) divided by the tangent of the angle. Remember - when you're calculating the tangent, one degree equals 60 arcminutes!

Astronomers use parallax in this same way to measure the distances to nearby stars. But what about stars that are further away? Try moving the star stand farther away, towards the background stars. Now if you repeat the laser pointing, the apparent movement of the star is much smaller. It's harder to tell that the star has moved at all! Astronomers have built instruments to discern parallax shift for stars out to several hundred parsecs in distance - but this is only about one hundredth the distance across the galaxy! We couldn't measure the parallax shift of an object on the other side of the galaxy or outside our galaxy, but there are other distance measuring tools that astronomers can use.

Why It Is

See #What to Say.

Real Life Examples

We use parallax every day in the depth perception of our vision. The Global Positioning System (GPS) uses a technique related to parallax called triangulation to figure out where you are on the Earth's surface based on the GPS receiver's "observations" of signals from satellites in orbit.