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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.



  • 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.


  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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