KEY QUESTION

If we could count all the stars we see in the sky, how many would we count?

POSSIBLE PRECONCEPTIONS

Some students may think we can millions of stars with the unaided eye.

KEY CONCEPT

Using geometry and a readily available Precision Scientific Instrument (PSI), it's possible to estimate the total number of stars visible to the unaided eye at any one time.

GENERAL INFORMATION

Target Grades: Upper elementary through high school

Participant Size: Individual learning or groups of 2

Length of Activity: 45 minutes

Where: Outside

When: Night (preferably a moonless night)

Method: Teacher-directed laboratory and problem solving

Focus: Stars; scale of the universe

Skills: Questioning, observing, using numbers, interpreting data, controlling variables

Materials List

A Precision Scientific Instrument (A toilet paper tube)

Writing paper

Small flashlight or candle

Pencil

Calculator (optional)

METHOD

Using toilet paper tubes, students count the number of stars in ten different areas of the sky, then estimate the number of stars that will be visible in the entire sky.

PROCEDURE

Preparation

Try to schedule the night viewing with your students when moonlight won’t interfere with the viewing. Also try to find a location away from lights.

Each student or group of students will need a toilet paper tube; have your students bring their own, or ask for donations from parents, custodians, and faculty.

Doing the Activity

This activity can be done by one person, but it’s more fun with two. Go outside on a dark night. The best results will be obtained when the Moon is not visible. It is also best to get away from brightly lit areas.

One person should act as the recorder, while the other person counts stars. The recorder should stand several feet away from the counter so the light the recorder uses doesn't affect the counter's night vision. Perhaps the recorder can be on the other side of a tree.

When the counter is ready, they should hold up the toilet paper tube to one eye and count the number of stars visible through it. The tube should not be moved while the stars are counted. The counter should look at 10 different parts of the sky and the recorder should write down the count for all ten sections. These counts should be averaged. Multiply the average count by 104 to get an estimate of the number of stars that can be seen from your location.

CLOSURE

Under ideal conditions, a person can see about 3,000 stars with the unaided eye. Astronomers estimate that our galaxy, the Milky Way, contains several hundred billion stars and that the universe contains some hundred billion galaxies. Thus, even the clearest sky allows us to see with our unaided eye only a tiny fraction of the total number of stars in the universe.

EXTENSIONS

Students could discover how light pollution affects the sky by taking star counts in different locations ranging from lighted towns to dark beach or jungle. Although light pollution is not a problem on most of the smaller islands, it is becoming a problem in the cities of the larger islands like Guam. In urban areas, like most of Japan, only the very brightest stars can now be seen because the city lights make the sky like day.

BACKGROUND

The number of stars estimated in this activity does not represent all the stars that exist, only the ones that are bright enough for us to see. Light pollution from human activities can drastically affect the number of stars that are visible to the unaided human eye. Light pollution also makes Earth-based astronomy difficult; research telescopes must be located away from cities so they can detect faint stellar light sources. Some telescopes, like the 5-meter (200-inch) telescope at Mt. Palomar, have lost some of their usefulness, as cities have grown up around them (in this case, San Diego). The Hubble Space Telescope, a remote-controlled orbiting observatory, was designed to give astronomers a view of the sky unimpeded by light pollution or clouds.

The number 104 that was used in the calculation in the activity (the average star count was multiplied by 104) was derived from the following calculation:

Think of the length of the toilet paper tube as the radius of a sphere. If the end of the tube swept out a full spherical surface, then the area of that surface would be expressed as A=4R²^,where R is the length of the tube, or equivalently, the radius of the sphere. A typical toilet paper tube is 11.5 cm (4.5 in) long. A sphere of that radius has a surface area of about 1660cm². As one looks through the tube, one sees an area that is equal to the area of a circle with a radius equal to the radius of the tube. This area can be expressed as a=r²(where r=radius of the tube, about 2.3 cm (0.9 in) for a typical toilet paper tube). The area of the end of a typical toilet paper tube is about 16 cm². When one looks at the sky with the tube one is looking at a portion of the sky equal to the tube-end area divided by the tube- length spherical area. This is a fraction of about 16/1660 of the total area of the sky; it would take about 1660/16 tubes to fill the entire sky (i.e. about 104 tubes).

Keep in mind that this calculation leads to an estimate of the total number of stars visible to the unaided eye from the entire Earth. To get an estimate of the stars visible to the unaided eye from any one location, divide the total by two (because only one-half the sky is visible from any one location at any given time). About 6,000 stars are visible to the unaided eye under ideal conditions from the entire planet. Given that only one-half of the sky is visible from any one location on Earth at a given time, only about 3,000 stars will be visible under ideal conditions. In heavily developed areas, that number can drop to a few hundred; in the center of a city, it can drop to only a few.