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== Age ==
{| class="wikitable" style="color:black; background-color:#ddd; margin-left: auto; float:right"
| [[Astronomy]], [[Math]]:
| Parallax, Triangulation
|-
| Grade Range:
| [[Middle School]], [[High School]]
|-
| Format:
| [[Hands-on]], [[Stage]]
|}


Middle School, High School
In order for students to benefit much from this demonstration, they will need some basic trigonometry skills prior to the presentation. This demonstration is very informative and a great basis for lessons in Astronomy, but students might struggle with the calculations.
 
== Format ==
 
Stage Show,Hands-on


== Materials ==
== Materials ==


    Star background board
* Large Rectangular White Board
    Star stand (a star mounted on a post)
* White Board Markers
    Laser pointer
* Laser Pointers
    2 velcro stars (these stick to the star background)
* Test Tube Stand with Holder
    Model sun on post
* Small Plastic Star
* Masking Tape or Painters Tape
* Paper and Pencil


== Safety Precautions ==
== 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.
Please read the General Safety Precautions section of the [[Demonstration Safety]] page before performing this demonstration.
 
== 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 ==
== 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.
# Set up the white board, either propped up or against a wall, and use the tape to mark a spot 10 feet in front of the board. Put the stand on the marked spot, and then mark another spot 10 feet further along the same line and mark it. This will be where the volunteers stand.
 
# Have two volunteers come up. Have one stand on the left side of the marked spot and use the laser pointer to point at the star. Mark the spot where the laser lands on the white board, and then have the second volunteer do the same, but stand on the right side of the marked spot. Mark their spot on the white board.
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.
# For a hands-on event, give everyone at the table a pencil and paper and ask them to draw the scenario as you draw it, and provide the explanation. Otherwise, for a stage show, go straight into the explanation.
 
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 This Works ==


Astronomers are often interested in the distance between us and stars, planets, and the astronomical distances in our galaxy. They calculate the distances in outer space by measuring the parallax of a stellar object in the sky. ''Parallax'' is the apparent shift of stars and planets in the night sky over the course of the year. By looking at how many degrees the object moves in those six months, we can calculate the approximate distance from here to the stellar objects by using a little trigonometry.


== Why It Is ==
When we make our two points, we can use the distance between the dots on the board to calculate the degrees of movement for the stellar object. (''For this explanation, we will use a sample value of 30 cm''). We can draw the scenario as a triangle on the board, with a straight line down the center to make two right triangles. In this case, the long line down the center is the adjacent side, and the short side would be our opposite side. The opposite side is equal to half of the measured movement, while the adjacent is our starting distance. For our starting distance, instead of using the 10 feet we were from the stand, we will use the radius of earth's orbit, at 150,000,000 km! This is because an astronomer will measure the position of the star in the sky six months apart, when the earth is on opposite sides of the sun. We replicated this by having two volunteers point at our star on opposite sides of our standing point. We can use the apparent change in distance to calculate the ''Parallax Angle'' of our observed object:
*''Note: you can opt to use the original 10 feet distance for the measurement instead of the earth's radius. By using the 10 feet (be sure to convert to cm!) you will get an end result that is likely within the solar system. By using the earth's orbit, you will likely get an object millions of light years away.''
{| class="wikitable" style="color:black; background-color:#ddd; margin-right: auto"
| Tan '''α''' = (Opposite/Adjacent)
|}


See [[#What to Say]].
This calculated value tells us how much the object moves across the night sky over the course of a year, and we can then use this value to find out how far away it is. Why is that? It is because the closer the stellar object is to us, the more it will appear to move across the night sky. This same concept is apparent to us here on earth, and it is a part of how our vision works. If you move side-to-side, you will notice that objects closer to you in the room will appear to "move" more than objects that are far away from you. Even if the object is already moving or sitting still, it will have an apparent shift based on how far away it is.


== Real Life Examples ==
Now that we have our Parallax Angle, we can try calculating how far away the stellar object is from us! To do this, we will switch around our equation a bit:
{| class="wikitable" style="color:black; background-color:#ddd; margin-right: auto"
| Adjacent = (Opposite/(Tan '''α'''))
|}
This time, the adjacent side of the triangle is the distance from earth to the object, and the opposite side is the radius of earth's orbit around the sun, approximately 150,000,000 km. This time, however, we can call the radius "1 AU", or ''Astronomical Unit'', and use it as a unit. This way, when we calculate the adjacent side, we don't get a number that is too big to look at. Based on how far away the object is, as well as any other information we have on it, we can determine what kind of stellar object it is.
* ''Note: the sample value used with earth's orbit gives you 500,000,000,000 AU, which is equal to approximately 2.4 million parsecs, or 7.8 million light years away! This means you could be looking at a star in the'' [https://www.spacetelescope.org/images/opo0919d/ dwarf galaxy IC 4662]. If you use it with the 10 ft distance, you will get approximately 12 AU, which means it is an object between Saturn and Uranus!
== Additional Information ==


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.
* Since this demonstration is more lecture-based than other demonstrations, you should only present it after thoroughly reading it over and getting some additional background knowledge on the subject.
* This demonstration is a part of the [[Astronomy Show]].

Latest revision as of 20:32, 19 July 2016

Astronomy, Math: Parallax, Triangulation
Grade Range: Middle School, High School
Format: Hands-on, Stage

In order for students to benefit much from this demonstration, they will need some basic trigonometry skills prior to the presentation. This demonstration is very informative and a great basis for lessons in Astronomy, but students might struggle with the calculations.

Materials

  • Large Rectangular White Board
  • White Board Markers
  • Laser Pointers
  • Test Tube Stand with Holder
  • Small Plastic Star
  • Masking Tape or Painters Tape
  • Paper and Pencil

Safety Precautions

Please read the General Safety Precautions section of the Demonstration Safety page before performing this demonstration.

Demonstration

  1. Set up the white board, either propped up or against a wall, and use the tape to mark a spot 10 feet in front of the board. Put the stand on the marked spot, and then mark another spot 10 feet further along the same line and mark it. This will be where the volunteers stand.
  2. Have two volunteers come up. Have one stand on the left side of the marked spot and use the laser pointer to point at the star. Mark the spot where the laser lands on the white board, and then have the second volunteer do the same, but stand on the right side of the marked spot. Mark their spot on the white board.
  3. For a hands-on event, give everyone at the table a pencil and paper and ask them to draw the scenario as you draw it, and provide the explanation. Otherwise, for a stage show, go straight into the explanation.

Why This Works

Astronomers are often interested in the distance between us and stars, planets, and the astronomical distances in our galaxy. They calculate the distances in outer space by measuring the parallax of a stellar object in the sky. Parallax is the apparent shift of stars and planets in the night sky over the course of the year. By looking at how many degrees the object moves in those six months, we can calculate the approximate distance from here to the stellar objects by using a little trigonometry.

When we make our two points, we can use the distance between the dots on the board to calculate the degrees of movement for the stellar object. (For this explanation, we will use a sample value of 30 cm). We can draw the scenario as a triangle on the board, with a straight line down the center to make two right triangles. In this case, the long line down the center is the adjacent side, and the short side would be our opposite side. The opposite side is equal to half of the measured movement, while the adjacent is our starting distance. For our starting distance, instead of using the 10 feet we were from the stand, we will use the radius of earth's orbit, at 150,000,000 km! This is because an astronomer will measure the position of the star in the sky six months apart, when the earth is on opposite sides of the sun. We replicated this by having two volunteers point at our star on opposite sides of our standing point. We can use the apparent change in distance to calculate the Parallax Angle of our observed object:

  • Note: you can opt to use the original 10 feet distance for the measurement instead of the earth's radius. By using the 10 feet (be sure to convert to cm!) you will get an end result that is likely within the solar system. By using the earth's orbit, you will likely get an object millions of light years away.
Tan α = (Opposite/Adjacent)

This calculated value tells us how much the object moves across the night sky over the course of a year, and we can then use this value to find out how far away it is. Why is that? It is because the closer the stellar object is to us, the more it will appear to move across the night sky. This same concept is apparent to us here on earth, and it is a part of how our vision works. If you move side-to-side, you will notice that objects closer to you in the room will appear to "move" more than objects that are far away from you. Even if the object is already moving or sitting still, it will have an apparent shift based on how far away it is.

Now that we have our Parallax Angle, we can try calculating how far away the stellar object is from us! To do this, we will switch around our equation a bit:

Adjacent = (Opposite/(Tan α))

This time, the adjacent side of the triangle is the distance from earth to the object, and the opposite side is the radius of earth's orbit around the sun, approximately 150,000,000 km. This time, however, we can call the radius "1 AU", or Astronomical Unit, and use it as a unit. This way, when we calculate the adjacent side, we don't get a number that is too big to look at. Based on how far away the object is, as well as any other information we have on it, we can determine what kind of stellar object it is.

  • Note: the sample value used with earth's orbit gives you 500,000,000,000 AU, which is equal to approximately 2.4 million parsecs, or 7.8 million light years away! This means you could be looking at a star in the dwarf galaxy IC 4662. If you use it with the 10 ft distance, you will get approximately 12 AU, which means it is an object between Saturn and Uranus!

Additional Information

  • Since this demonstration is more lecture-based than other demonstrations, you should only present it after thoroughly reading it over and getting some additional background knowledge on the subject.
  • This demonstration is a part of the Astronomy Show.
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