Download Measuring the Height of the Flagpole: A Parallax Model

Measuring the Height of the Flagpole: A Parallax Model
In this lab we will measure the height of the school flagpole as a means of understanding how the distance
to nearby stars is determined. Finding the absolute distance to a star was one of the greatest achievements
of 19th century astronomy, an important test of the Copernican model of the Solar System, and a goal
sought by astronomers for over 2000 years. Astronomers use the parallax method to measure this
distance. It is based on the simple geometry of right triangles (triangles with a 90° angle) and was known
to the ancient Greeks. The general ideal of parallax method is to measure the angle to a star from the
opposite end of a known baseline that makes a 90° angle to the star. Look at the picture below.
Imagine the star lies at A. If you know the distance of line CB and
measure the angle CBA you can draw a scaled model of the triangle
on paper and figure the distance to the star, line AC. Astronomers
use the distance of the Earth to the Sun as their baseline to make the
biggest angle possible at angle ACB since the stars are so far away
(imagine a very long skinny triangle pointing to a star!).
We will measure the height of the flagpole in just this way. Here’s
what to do:
1. Cut out a protractor or get one from the basket.
2. Go outside to the flagpole with your protractor,
a meter stick, and a pencil or pen.
3. With a partner measure 10 meters from the base of the flagpole
4. Standing at the end of your measured 10 meter line, find the
angle from the ground to the top of the flagpole. Put your
protractor level on the ground and place your pencil or pen with one end in the middle of the protractor and
the other end pointed at the top of the flagpole. Your partner can help you aim the tip of your pencil or pen
at the top by looking at the pen or pencil while standing away from you.
5. Write down the angle your pen or pencil measures here: __________ degrees.
Now go back inside and make a scale of the flagpole height on paper.
6. Turn this paper over and draw a line 10 cm. at the bottom of the page. This is your baseline from
outside with 1 cm. = 1 meter. Use your protractor to measure a 90° angle at one end of the line straight up
to the edge of the paper. This is the flagpole whose height is not yet determined. Now place your
protractor at the other end of your baseline and mark the angle you measured outside and draw a line at that
angle up to the flagpole line. Where that line crosses the flagpole line represents the height of the flagpole.
Measure the height of the flagpole in cm and write it here: _______. How high is the flagpole in meters?
________
Now answer these questions.
a. Explain how you could use the scale method to find the distance to a star? What would your baseline be
(think of the longest possible baseline that could be measured from Earth)?
b. The parallax angle that astronomers measure to a star from a baseline of the Sun to Earth is so small that
it is tiny fraction of a degree (360 degrees in a circle). Degrees can be divided into 60 minutes (‘) and each
minute into 60 seconds (“). Star angles are measured in fractions of a second (“). Rather than scale a
triangle they use the formula:
parsecs =
1
where 1 parsec = 3.26 light years.
parallaxan gle
Find the distance to a star in parsecs and light years for a star with a parallax angle of 0.2”.