Measuring Astronomical distances Report

Team Name___________________________

Group Members Name Role

___________________________ Leader (manages people and time, makes sure all participate)

___________________________ Recorder (keeps track of results and records lab report)

___________________________ Checker (makes sure all results are correctly reported)

With this document open on your computer, fill in your group’s responses as you go. Include names of all the group members and their roles above. Your instructor will review items on this sheet with the class before the lab ends today. Quizzes later on in lab may include information from this worksheet, so be sure you understand it. The Recorder should submit the report on Blackboard. Each group member will write a short report of what they did in the lab today in accordance with their role.

Objectives of this lab exercise:

After completing this exercise you should - Understand measuring tools Learn how astronomers are able to determine distances to celestial objects Understand the vast dimensions of the universe and how to scale those dimensions to build

a modelPart I – Exploring everyday measuring tools [10 points]

From the time it takes to get ready to go to school in the morning to the temperature of your coffee, or the speed you drive when you go home, you use rough tools to estimate measurements all the time during the day. Science involves observing, asking questions, coming up with ideas about cause and effect and testing the ideas. But at some level science is all about measuring. One of the most important parts of doing astronomy is measuring distances and luminosity of stars. But we have a problem right at the start. How can you measure something so far away? A measuring tape won’t do it, and even sending out a pulse of light and figuring out how long it takes to return is useless for stars since even the closest star is much too far away and would not reflect the light anyhow. So how do we know if a star is far, but very bright, or close and relatively dim? We will explore ways of determining distance during the semester, but first think a little closer to home. How DO you measure things in everyday life, and what tools do you use?

1. List tools that you use for measuring in your everyday life. There are some common tools in the lab, but as a group think of as many as you can. (These can be used for measuring anything, including volume or weight, list as many as you can in about 3 minutes).

2. If you were going to measure the area of classroom what kind of measuring tools might you use?

Part II – Measuring distant objects [30 points]

Parallax is an interesting way of measuring the distance of an object by how much it appears to move when viewed against a much more distant background from one location, then another (the distance between the locations is called the baseline) See a demonstration of stellar parallax, using the position of the Earth in orbit for a long baseline. http://sci2.esa.int/interactive/media/flashes/2_1_1.htm

Parallax measurements1:

1. Have your partner hold a pencil at the 50 cm mark on a meterstick. While the partner holds the pencil in place, position the “0” end of the meterstick against your chin so it is horizontal. Then shut first one eye, then the other and observe how the pencil moves against objects in the background. Describe what happens.

2. Have your partner move the pencil closer, to the 25 cm mark. What happens to the motion of the pencil now? Can you quantify the difference? Is the motion apparently twice as much as it was before? Five times as much? Write your answers below.

3. Now have your partner move the pencil to the 100 cm end of the meter stick, as far as it can get from your eyes. Again quantify the motion compared to when the pencil was at the 50 cm position.

4. The pencil at 50 cm is shown below. Explain how the drawing would change for the 100 cm and 25 cm situations. In particular describe how the parallax angle, the angle between the two sight lines, changes as the distance of the pencil from the eyes changes. Does the angle double when the distance doubles?

1 This exercise adapted from the Parallax Tutorial on the University of Washington astronomy lab page at http://www.astro.washington.edu/courses/labs/clearinghouse/labs/Parallax/parallax_stars_tutorial.pdf

Pencil 50 cm from eyes.

Distant object or wall

eyes

5. Using the marks on the whiteboard, take at least 5 measurements at different distances of how far the pencil appears to move when viewed from first one eye, then the other. Plot your values on the chart below by using Insert:Shapes and choosing a small marker to plot each point.

Num

ber o

f mar

ks sh

ifted

Number of centimeters from eyes to pencil

6. Describe the shape you would get if you drew a smooth curve through the points you plotted. What kind of relationship is there between the distance the object appears to move against the background and the distance the pencil is from your eyes.

7. At some point the distance between your eyes will not be large enough for you to spot parallax. Try this out in the hall. Have your partner carry the pencil down the hall until you can no longer see the shift of the pencil with respect to the end of the hallway. About how far did your partner have to go?

8. Parallax can be accurately measured if you have the right tools. What kinds of instruments would improve on what you used in lab?

9. Parallax is the first step on the ladder to measure distance to the stars. What kind of baseline do you think astronomers use to measure distance to the nearby stars? List some possibilities below.

Part III – Stellar magnitudes [15 points]i

The apparent brightness of stars is rated on a scale based on that developed by Hipparchus about 150 years B.C.E. That system classified stars from 1 to 6. Stars classified 1 were the brightest in the sky, 6 were near the limit of what can be observed with the naked eye. In modern astronomy the scale is similar but more precise with each step increase corresponding to approximately 2.5 times the brightness. On the original scale a star with a magnitude of 6 would be 100 times dimmer than a star with a magnitude of 1. The modern scale includes both much dimmer objects and brighter objects with negative magnitudes. The Sun’s apparent magnitude is approximately -26.7.

Remember that apparent magnitude is just what we perceive. If your friend shines a flashlight at you from across the room it will appear brighter than if you see the same flashlight across the length of a football field. Astronomers use the letter “m” for apparent magnitude and the value of m in this flashlight example would change depending on where your friend is in relation to you.

Astronomers define another quantity as well, the absolute magnitude of a star (M) which is what its magnitude would be if it were at a distance from us of 10 parsecs. The absolute magnitude can be used to determine how much energy the star radiates – how luminous it is – and is an important measure of what the star is like. For stars with known distance from parallax measurements astronomers can figure out both apparent and absolute magnitude. There are other methods that you will learn later in lab for determining absolute magnitude of some stars. If both apparent and absolute magnitude are known it is possible to calculate distances. The relationship that connects distance (in parsecs, you can read about this measurement in your astronomy text, but it is about 3.26 light years) and apparent and absolute magnitude is:

D = 10(m-M+5)/5

Use this relationship in the exercises below.

1. The star -Orionis (Betelgeuse) in the image below has an apparent magnitude of m = 0.45 and an αabsolute magnitude of M = –5.14. Find the distance to Betelgeuse. Betelgeuse is the red star at the left shoulder of Orion (seen from Earth) and is a red supergiant. When viewed with the naked eye, it has a clear orange-red hue.

2. -Cygni (Deneb) is the upper left star in the Summer Triangle (see photo below) and the main star αin the Swan. Its apparent magnitude is 1.25 and the distance to Deneb is 993 parsec. Calculate the absolute magnitude for Deneb. What does this tell you about the nature of Deneb?

Part IV – How big is the universe?

Realm of the Earth and Moon [30 points]

We will begin by shrinking the Earth to a two – inch diameter circle, then scaling other objects close to earth to see how they compare.

Earth has a diameter of approximately 12756 km. We will use the metric system measurements for all astronomical objects today. Since one inch is 2.54 cm, it would be more consistent with the metric system to think of this a 5 cm universe. However, since the United States still doesn’t use the metric standard, most of us are used to thinking in terms of inches and feet and have a better idea of what an inch is (about the length of your thumb from top joint to tip) than what a cm is.

Now do the math. In this realm 2 inches = 12756 km and the Moon is 3475 km in diameter, so how many inches in diameter would it be in our two inch Earth/Moon system?

¿earth∈2−inchmodel¿earth∈kilometers

=¿Moon∈2−inchmodel¿Moon∈kilometers

or, putting in the numbers 2∈ ¿12756 km

= x3475 km

¿

so x=2( 347512756

) inches (the km units cancel).

In other words the moon’s diameter is about .54 inches, or about ¼ the diameter of the Earth.

Do the same process to calculate the distance the Moon is from Earth. In this case x is the distance of Moon from Earth in the model, but you will now need to use the fact that the Moon is about 384403 km away from Earth on average when measuring from the centers of Earth and Moon.

Now we have:

2inches12756 km

= x384403 km

Doing the math we get x = 2 (384403/12756) or 60 inches. Since 1 foot = 12 inches that is about 5 feet away.

Other sizes and distances

In this model, where the Earth is 2 inches across, the Sun is about 18 feet in diameter (imagine a round, glowing mini-van!) and is 1800 feet, or about 6 football fields away from Earth

Realm of the Sun

The next stage of this exercise is to shrink the Sun down to a 2 inch diameter. The Sun is approximate 1400000 km in diameter. Write this number in scientific notation.

1. Sun’s diameter in scientific notation:2. Estimate of Earth’s size and distance from the Sun in this model3. Earth’s estimated diameter:4. Earth’s estimated distance from the Sun:5. We use the same routine to calculate Earth’s size in this model:

2∈ ¿1400000km

= x12756km

¿

Finish finding Earth’s diameter and then distance in this model:

6. Calculated size of Earth in model:7. Calculated distance of Earth from Sun in this model:8. Comparison of your estimate and results in this model:

Other objects and distances shrunk to this scale:

Earth Size - A grain of salt, with a dust-speck Moon 1/2 inch away from it Sun-Earth Distance - 20 feet (5.5 m) away Pluto's Orbit - 2.5 soccer fields away from the 2-inch Sun Nearest Star to Sun - 900 miles away (1500 km)

Realm of the Solar System

Although Pluto is no longer considered a planet, we can still use the average distance of Pluto from the Sun as the boundary for our Solar System. In reality the solar system – the objects that are gravitationally controlled by the Sun – extends much farther, but let’s put the boundary for our purposes today at Pluto.

Now shrink the solar system diameter to the size of a 2 inch circle so that Pluto would orbit around the edge of the 2 inch circle. Do the appropriate calculations to find the distances and sizes of the objects listed below.

9. Estimate of Earth’s distance from the Sun:10. Show steps in calculation of distance of Earth from Sun in the 2 inch solar system model:11. Comparison of estimate and calculated result:

Other sizes and distances:

Nearby Star Discovered to Have Orbiting Planets - 5 soccer fields away. Two planets have been discovered around the star Epsilon Eridani, which is visible from the southern hemisphere.

Our Milky Way Galaxy - Size of North America. At this scale, our 2-inch Solar System is part of a continent-sized system of 200 billion shining speck stars. These stars, spread 30 miles (50 km) high, are generally separated from each other by more than 2 soccer fields.

Realm of the Galaxy

Finally take a look at the galaxy realm. Remember that in the 2 in solar system model the galaxy was about the size of North America (roughly speaking of course!). But when it is re-scaled to the size of a 2 inch circle we get a better perspective on the size of the universe it, and we, are embedded in.

Size of Sun and Stars - Individual stars are invisible, smaller than atoms, at this 2-inch scale. The bright specks in this galaxy image come from the added light of thousands of stars.

Location of Sun - 1/2 inch (about 1 cm) from edge of 2-inch galaxy image Distance to Andromeda Galaxy, the Nearest Spiral - 5 feet (1.5 m) at this scale - hold the two

galaxy images apart with your arms spread wide. Distance to Farthest Galaxies Observed by Hubble Telescope - 4 miles (6.5 km). In the Hubble

image of the "Ultra Deep Field" almost all the fuzzy spots of light are distant galaxies. Because light takes time to travel through space, we see the farthest of these not as they are now, but as they were 12 billion years ago.

Size of the Whole Universe? - No one knows...it could be infinite. Light Travel Time - It would take 100,000 years for a beam of light to cross our galaxy and 2.5

million years for light to travel from the Andromeda Galaxy to us.

Conclusion questions [Grade points: 15]

1. The absolute magnitude, M, is defined as the apparent magnitude a star would have if it were placed 10 parsecs from the Sun. But wouldn’t it be more correct to measure this distance from the Earth? Does it make a difference whether we measure this distance from the Sun or from the Earth?

2. Explain how this exercise has impacted your thinking about the size and importance of Earth in the universe.

i This exercise adapted from the ESO/ESA astronomy exercise series found at http://www.astroex.org/english/toolkit/astronomical_tasks.php