A major misconception with students of astronomy deals with
the student's understanding of scale. Even the ancient astronomers
considered the stars to be all at the same fixed distance in the heavens.

This lesson is designed to introduce students to both celestial
coordinates and to the first rung on the distance determination ladder,
parallax. Students will convert spherical coordinates, together with parallax,
to cartesian coordinates to construct a three dimensional model of a
constellation which can be viewed from any angle.

The following points should be made with students:

The stars are all at different distances from us.

Parallax only works on the nearest stars to us.

The stars only appear to move across the sky throughout the
night because of the Earth's motion. With small exceptions, they
appear to be fixed relative to each other.

The pattern made by different constellations is purely due to our
perspective.

Standards

The exploration meets the following National Standards: Science Content
Standards: 9-12

CONTENT STANDARD A:

Abilities necessary to do scientific inquiry

Understandings about scientific inquiry

Fundamental abilities and concepts that underlie this standard include:

Use technology and mathematics to improve investigations and communications.

Formulate and revise scientific explanations and models using logic and evidence.

Recognize and analyze alternative explanations and models.

Communicate and defend a scientific argument.

CONTENT STANDARD B:

Physical Science Standards

Structure and properties of matter

interactions of energy and matter

Earth and Space Science Standards

Origin and evolution of the universe

Origin and evolution of the earth system

History of Science Standards

Nature of scientific knowledge

Solutions

Suppose you could take the stars that make up the big dipper, and
rotate the whole thing by 90 degrees. Draw a picture of what you think
the Big Dipper might look like from this perspective.
This is a leading question meant to allow students to face
their misconceptions. Many students will think that from the
side, a constellation would look "flat".

How many arc-minutes as used for Dec are in one minute of angle as
used for RA?
Declination is expressed in hours, arc-minutes, and arc-seconds.
If 24 hours of arc is 360 degrees, then 1 hour of arc is
15 degrees, and 1 arc-minute (1/60th of an arc-hour) is 0.25 degrees.
A minute of angle measured in degrees, minutes, and seconds is
1/60th of a degree, or 0.0167 degrees. An arc-minute of angle is larger
than a minute of angle.

As you look at stars that are further and further away, what happens
to the parallax of those stars?
Parallax effects get smaller as the objects being observed are
further away.

Why can parallax only be used for nearby stars?
Since parallax effects get smaller for stars that are further away, they
become more difficult to measure.

Look up the data for the Big Dipper. Convert RA, Dec, and parallax to
X, Y, and Z coordinates for each star, and make a 3-D model. You can do this
either with materials such as paper mache or styrofoam balls and sticks,
or you can use a computer program.
Click on the big dipper model to open a window with a solution.