Optical Powers
Size in the Sky

Teacher Page
Activity 3a - Size in the Sky

Standards (see Appendix A):

Unifying Concepts:    Evidence, Models, and Explanation: Size and Scale.

Objective:

Students will understand that just as objects on Earth appear to get smaller the further they are away from the observer; the same is true of the sky. In addition students learn that although increasing magnification increases the apparent size of an object in an image, it does not affect the object’s size relative to other objects. Students are introduced to the concept of angular size to measure distances in the sky.

Overview:

To ensure that an intended target will actually fit in the space available on a CCD chip, the astronomer must understand the apparent size of the target as measured by its angular size in arcminutes or degrees and the field of view available from the telescope/CCD system. Before students are able to understand angular size they may need to review the concept of apparent size.  This activity reinforces what students already know about distance and apparent size. Later, once students have developed an understanding of measuring angular size and the telescope/CCD system, they will learn how to calculate the field of view available from any combination of system components.

This activity is a short investigation that introduces the first step in the process by guiding students through an exploration of apparent size.  Students combine an image of the moon with an image of Jupiter to discover that a crater on the moon seems to be the same size as Jupiter.  Students repeat this procedure with another pair of images taken at greater magnification. They find that in spite of the increased magnification, the moon crater and Jupiter again have the same apparent size relative to one another.   Knowing from other resource material that Jupiter is much larger than the entire moon, they must rule out possible causes for the results.  In the end they are led to the conclusion that even though the two objects are actually different sizes, they appear to be the same size because of their distances from Earth.  At the close of this activity students are introduced to the concept of angular size as a different way of measuring distances in the night sky.

Background:

Even though students are familiar with the idea that objects appear much smaller as the distance between the observer and the object increases, many have difficulty applying what they know to the night sky.  Angular size is the angle created by lines extending from either side of the object to the observer.  Angular size changes when the distance between the object and the observer changes.   (In terms of the night sky, most objects are so far away that changes in distance are inconsequential.  However, the apparent size of solar system objects changes measurably depending on the relative positions of the Earth and the solar system object.)

The apparent size of objects in the sky can be easily measured in terms of the angular size of the object.  This gives astronomers an easy way to compare apparent sizes of objects in the sky though it tells them nothing about their actual size.  Because it is easy to imagine all the celestial objects to be on the vast dome of the night sky, it is convenient to measure their sizes using angle measurements.  We are most familiar with degrees of angles but smaller measurements are much more useful.              

                        1 degree = 60 arcminutes

                        1 arcminute = 60 arcseconds

                        1 arcsecond = 1/3600 of a degree         

In astronomy angular size is the measure in degrees, arcminutes and/or arcseconds that an object occupies in the sky.  It is a measure of the apparent size of objects

Preparation:

  1. Be sure students have access to the seven images needed for this investigation.  Images are: 3a1-jupiter.fts, 3a1-moon.fts, 3a2-combo.fts, 3a2-copernicus.fts, 3a2-jupiter.fts, 3a2-ringnebula.fts.
  2. Gather additional resources so students can look up basic information about the moon and Jupiter.

Time:  45 minutes should be sufficient for introduction, investigation and discussion.

Homework:

 If your students have access to basic resource materials at home, consider assigning the first question of the Student Page as homework.  Although this saves only a small amount of time, it does provide students with additional time to consider what they already know about the apparent size of objects and the actual sizes of the moon and Jupiter. Depending upon the time available, the worksheet conclusions can be completed as homework and discussed the following day.

Directions:

1.      As a quick introduction to angular size, have students go outside.  Standing close to a tree, instruct them to identify the angular size of the tree by holding their hands/arms out in front of them so that one hand points to the base of the tree and one hand points to the top.  Have them repeat this procedure at increasing distances from the tree.  Explain that they have just made an angular size measurement of the tree.  What happens to the angular size of the tree as you move away from the tree? Remind students that the actual size of the tree has not changed.

2.      You may want the students to estimate the angular measure to reinforce the fact that angular size is measured in degrees.  A protractor can be used to measure this angle. 

3.      Review with students how to access the images for this investigation.  If your students are less familiar with HOU-IP software, take time to go over the instructions and familiarize them with the tools used.

4.      Give students time to work through the activity instructions. Remind students describe what they see first before drawing conclusions.

Discussion of Results:

5.      First, take time to be sure everyone understands what they did and what it demonstrates.  It is equally important that students are aware of what this investigation does NOT prove.  Just because something appears larger on an image does not mean that it is larger.

6.   Regarding, question 6, students should be able to identify the fact that if the images had been taken with different telescopes that they might be different magnifications.

7.      Once you have established that good evidence exists that Jupiter is actually bigger than the moon you can introduce the term apparent size.  You may provide students with the definition or allow them to generate one on their own. 

9.      Next ask: Why might astronomers want to know the apparent size of an object in the sky?  For the purposes of this unit, the primary reason is that if you want to image a particular object then you need to be able to match the size of the object with the field of view of your telescope/CCD system.

10.  Ask students to suggest ways that astronomers could communicate the sizes of different objects before introducing them to angular size.  Explain that because we describe the night sky as a large dome, it is convenient to measure the size of an object by the amount of space it occupies on the dome.  Angles are convenient ways to measure this dimension..


The Bigger Challenge - This extension is provided as a challenge for students that move quickly through the main part of this investigation.  The image is an addition of three separate images: Saturn, Jupiter and the Ring Nebula.  All three were taken with the same telescope/CCD and are another demonstration of apparent size.  In this case, the Ring Nebula is the most distant object (2,300 light years away).  The Ring Nebula appears to be larger than Saturn and Jupiter. So, the Ring Nebula must be huge since Jupiter and Saturn are always less than two light hours from Earth.   The challenge to students will be to see if they can uncover the three components of the combined image.  If students are not familiar with the Ring Nebula, refer them to the Hubble Space Telescope web site listed below.  Once they have determined the identity of each object, encourage them to find the estimated actual size of each.

Web site resources –


Evaluation/Assessment: Given any two celestial objects, their distances and actual sizes, students should be able to predict which will have the larger angular size.

Show students an image of an eclipse.  Ask them to write a sentence describing why a total eclipse of the sun is possible.   They should be able to apply the vocabulary of angular and apparent size.

 Total Eclipse - see website www.holeinthesky.com/ 99contest.htm

You can find nice solar eclipse images at www.holeinthesky.com/ 99contest.htm

View a beginners guide to solar eclipses.  This site includes a photo gallery link under “Solar Eclipse Observing and Photography.” http://www.mreclipse.com/Special/SEprimer.html