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PROM/SE Summer 2006
Science Institute
High School Earth-Space Science
“The Distance to the Stars:
How Do Scientists Know?”
Facilitator’s Guide
PROM/SE Science Institute summer 2006
HS Earth-Space Science
Rich Lohman and Carl Pennypacker
The distance to the stars: How do scientists know?
Introduction:
People young and old have always been fascinated and awed by imagining how large and
how old the Universe is and how far away the stars and the galaxies are from us. Today,
many simply accept these huge numbers they hear as fact, without wondering how they
are ascertained. In a typical introductory astronomy course one might hear the
following…..”We know that the star Vega is 3.6 times larger than the sun, shines with the
energy of 73 suns and is located at a distance of 25.3 light years from the earth.” Or that
“The nearest galaxy to our Milky Way is Andromeda, 2.7 million light years away.” Or
that “The Universe is 13.7 billion years old!” The more astute student wants to know,
“How do they know that?” This course is intended to help answer that question.
There are many “measuring sticks” that are used to measure distance in astronomy. They
are placed in order on what is called the Distance Ladder. Some of the “rungs” on this
ladder are named as follows: Parallax, Spectroscopic parallax, star clusters, Cepheid
Variable Stars, Type Ia Supernovae
The process of “measuring” the stars and the distance to them is a combination of direct
measurement, inference and indirect measurement. All direct measurements of stars, and
the only measurements that can be made, involve the detection of the energy they emit
(typically the visible light energy) to determine: position, movement in time, brightness
and color.
The initial “rung” on the distance ladder (parallax) involves measuring the position of a
star from two different locations. Then a calculation is made, using relatively simple
geometry, to determine the distance to that star. It is an indirect measurement.
The “rungs” following the first one all involve measuring the brightness (and sometimes
the color) of the light coming from a star. Based upon this initial measurement an
inference is usually required to identify the type of star being observed. Finally
astrophysicists use the well-known “inverse square law” of illumination to calculate the
distance to the star. This law is often written as follows: B = L/4d2, where B is the
brightness of the star directly measured from the earth, L is the luminosity of the star
(which is inferred by its type) and d is the distance to the star. Since d is calculated it is
an indirect measurement.
In this course we will be studying two of the “rungs” of the Distance Ladder: parallax and
Type Ia Supernovae. In both cases the participants will experience the processes that
“real-world” astronomers and astrophysicsts use in their professional work
Major Concepts addressed in the HS Earth-Space Science Course
Distance ladder
Parallax
Distance vs. Brightness
Factors determining brightness
Inverse square law
Supernova
Standard candle
Misconceptions addressed:
Stars are all at the same distance, but of different sizes/brightness.
Stars are all the same size and brightness, but at different distances.
Stars and “stars”….all the same “kind”.
All stars in the same constellation are at the same distance.
You can use a telescope, and only a telescope, to measure the distance to a star. (It’s a
direct measurement.)
Measurements of distance to planets, stars, etc. are only accessible to the professional
astronomer.
Vocabulary
Constellation, Brightness, Luminosity, Light year (ly), Parsec (pc),
Astronomical Unit (AU), Parallax, Baseline, Energy, Power, Lumens/Lux,
Watts/Watts per m2, Fusion, Supernova, Spectrum, Light Curve, Galaxy,
Reference Star
Learning Outcomes
The student should understand:
 how a telescope is used to measure distance to the stars
 the concept of a distance ladder
 several “rungs” on the distance ladder
 the general concept of parallax in everyday situations
 the factors that influence parallax
 the concept of parallax as used with stars
 the basic properties of a supernova
 the concept of a standard candle as used in astronomy
 the use of the inverse square law in astronomy
 the factors that determine a star’s brightness
The student should be able to:
 describe the idea of the distance ladder in astronomy and identify at least two
“rungs” on it
 define parallax
 demonstrate a simple example of parallax in a classroom or outdoor setting (nonastronomical) and describe the effect of changing baseline
 measure the parallax of a nearby object (tree, flagpole, etc.) using an appropriate
baseline and determine the distance to that object
 recognize the parallax of a nearby astronomical object (asteroid, planet, star) by
viewing computer images
 measure the parallax of a nearby astronomical object from a set of computer
images and, knowing the baseline for the images, determine the distance to that
object
 take a measurement of the brightness of a luminous object (light bulb or sun)
using a light probe and a computer
 describe in words the relationship between brightness and distance of a star as it is
embodied in the inverse square law
 perform the three different types of calculations involved in using the inverse
square law (with a calculator)
 create a supernova light curve by taking measurements from a computer image
 determine the distance to a galaxy knowing the brightness and “standard candle”
luminosity of a supernova in that galaxy
Unifying theme: Systems
System of stars, galaxies, the universe.
Distance ladder: rung to rung to rung in sequential steps.
Logic system: direct measurement, inference, indirect measurement.
Instrument systems: eyes + starlight, light sensor + light bulb, telescope w/CCD camera +
stars/galaxies.
Mathematical system: algebra, geometry, trigonometry, inverse square law of physics
Technical system: computer + software
Unifying Principle: Energy
Gravitational Energy pulling together the mass of a star to “ignite” the fusion reaction.
Nuclear Energy (fusion) generating the heat, light and other electromagnetic energy of a
star.
Light Energy (E/M waves) from a star converted to Electrical Energy in a photodetector,
a CCD camera or your eyes. This is the only “energy” coming from a star that we can
measure.
Flow of the 4 day course:
Day 1:
a. Introduction to the Distance Ladder; Activity: Creating a Distance Ladder
b. Investigation of common thinking about distance and brightness of stars.
c. Activity: Building a model for a well-known constellation. (Use of Hipparcos satellite
data.)
d. Group presentation of models.
Day 2:
a. Introduction to Parallax; Activity: Measurement of parallax on indoor objects.
b. Presentation: Parallax geometry/mathematics.
c. Activity: Measurement of parallax on an outdoor object (in the vicinity of the training
site).
d. Group presentation of results of measurements.
e. Activity: Outdoor measurement of the sun’s brightness. (for use later in week)
f. Presentation: Using computer software to investigate astronomical images.
g. Activity: Measurement of the parallax of an asteroid from astronomical images on a
computer.
Day 3:
a. Activity: Investigation of the relationship between brightness and distance using light
probes and light bulbs.
b. Group presentation of measurements and results.
c. Presentation/Activity: Working with mathematical aspects of the Inverse Square Law.
d. Activity: Outdoor measurement of the sun’s brightness.
e. Presentation: Introduction of the concept of a Standard Candle in astronomy: the Type
Ia Supernova (SN). Implications for determining distance to stars.
f. Activity: Measurement of Supernova Light Curve (taking data from computer images).
Day 4:
a. Presentation: Typing SN explosions using SN Light Curves and spectrographic data.
b. Final Activity: Determining the distance to the Whirlpool Galaxy (M51) which
contains a known supernova. Use of measurement data from previous days and
reasonable assumptions.
Each Day:
We will begin each day (except for Monday) discussing questions and points of
clarification from the previous day. In addition we will deal with questions which may
have come up in the previous night’s reading assignment.
We will end each day (our Earth-Space Science section) with some time for individual
reflection and writing. This will be a time for you to clarify what you have learned that
day and what remains unclear. You may want to make connections between what you
are learning and the standards you teach during the school year. Finally, you may want to
reflect on HOW you are learning. What are your “learning styles”?
Evening reading assignments:
Monday evening:
Required: “How Far are the Stars?” from The Science Teacher (NSTA)
Questions to answer: What is parallax? How does the parallax of a star relate to the
distance to that star? What are the 3 factors that determine a star’s brightness?
Recommended: “Magnitude System” (especially pp 2-4) and “Hipparcos Overview”
(European Space Agency)
Tuesday evening:
Required: “Supernova Light Curves Unit” (Hands-On Universe)
We will do this activity near the end of the day tomorrow (Wed.). Focus your reading on
the first page and on the last four.
Questions to answer: Generally, what is a supernova? What distinguishes a Type I for a
Type II supernova? Which type of SN is considered to be a Standard Candle? Where
was the iron in your body created?
Wednesday evening:
Recommended: “Supernovae, Dark Energy, and the Accelerating Universe” (Physics
Today, April 2003). This is general background material and not an easy read. We
encourage you to take in what you can and don’t go for the detail.
Detail of 4 days:
Day 1:
A. Brief personal and group introductions. Administer the Pre-Assessment.
B. Use “Introduction” (above) to begin the course and the day.
Go through (briefly) the Participant Guide, highlighting the “Flow of the 4 day course”,
the “Each Day” reflection time and the “Evening reading assignments”. Make sure
they have the materials for Monday evening: “How Far Are the Stars?”, “Magnitude
System” and “Hipparcos Overview”.
C. Activity: “Creating a Distance Ladder” (See Handout) Link to Pre-Assessment
question about toothpicks.
Assignment in small groups: Determine the approximate length of the school (or
building we are in) in units of paper clips. Condition: You must stay in the room we’re
in, although access to any windows or doors is permitted. Materials: paper clips
D. Groups report back their results including assumptions, methods, etc. Summarize
activity and relate it to the Distance Ladder in Astronomy.
E. Activity: Astronomical images: What do you see, and what do you know about
what you see? (See Handout) Intended to deal with possible misconceptions about
brightness and distance.
Show a series of images: Open cluster (Pleiades, M45), Globular cluster (M2), Orion
constellation, Crab nebula (M1), Galaxy (M101), Galaxy cluster (A2218)
Questions for pondering individually, then in small groups. (On Handout) Focus the
majority of their time on Orion.
F. Report out from small groups. Record on paper charts.
G. Introduce the Hipparcos satellite data file and use the distance values from that table
for the 7 brightest stars of Orion. Use HOU Auto-Aperture on the stars in the image to
get the x, y coordinates and brightness counts. Teachers record the data in the table.
For now, we will consider the temperature to be the same for the 7 stars.
H. Activity: “3-D Model of the constellation Orion” (See Handout)
Small groups plan and build a 3-D diorama of Orion. Group decides scale, sizes,
assumptions to use. Materials: boxes, rulers, thread, tape, pins, styrofoam balls,
aluminum foil.
I. Group presentations of their models. What assumptions were used to create them?
Where is the group unsure about the placement of the stars? What more information is
needed to make the model more accurate?
J. Present data on Temperature and Radius and handout “Life Cycle of Stars”. Have
teachers reflect on impact of this new data on their models. Generate possible questions
for future days.
K. Time for individual reflection on day’s learnings and remaining questions. Have each
participant aim for identifying at least one question or confusion that came out of the
day….for clarification on the following day. Also, what was the process of “learning”
that went on?
(** If time permits, sometime during today, go outside and measure the brightness of the
sun with the light probes. This could be done by just a few people as an initial reading.
Everyone will do it on Tuesday and Wednesday. Monday will probably be too short for
this.)
Reminder about Evening Reading Assignment.
Day 2:
(Take some time at the beginning of this session to address questions/clarifications
from previous day AND from evening reading assignment.)
A. Introduce the concept of parallax as the first rung in the Distance Ladder.
(Actually it’s the second, radar measurements being the first.) Thumb in front of
eyes…close one eye, etc. What do you notice behind the thumb? Has the thumb moved?
B. Activity: “Parallax Measurements”
Have class (in small groups) carry this investigation further. Experiment with holding
thumb closer, farther away from the eyes. Difference? The same? Any general
statement of “parallax shift” from objects closer or farther away?
Hold a large “star” at various positions in the room. Have teachers from different parts
of the room say where they “see” the star located. (Develop the concept of
baseline….larger baseline gives greater parallax shift.) Teachers take notes on
observations and continue working with Handout which contains questions to answer.
Teachers do a few measurements of Angular Size.
Report back to group.
C. Powerpoint presentation on Parallax: The geometrical/mathematical basis of parallax.
Diagrams and simple equations will be included here. Also introduce the outdoor activity
to follow. Monitor time and energy level of the teachers to determine whether to present
parallax measurement of asteroid here.
D. Outside Activity: Continue to use Handout: “Parallax Measurements”. Set up
longer baseline. Use parallax concept to measure the distance to a nearby object (a flag
pole, light pole, notable monument or house, etc.) using the distant background for
locations. End with calculation to the object. Materials: meter sticks, rulers,
protractors
E. (While still outside, weather and ambient noise permitting) Reports and discussion of
measurements and calculations.
F. (and…while still outside) Measure brightness of sun using light probes. See Handout:
“Using a Light Sensor to measure…..” All groups take a reading and record for use on
Thursday.
G. Back inside to computer lab (or, possibly, the regular room to finish instruction on
asteroid parallax measurement). Instruction on use of HOU Image Processing software
tools: opening files, min/max, (x,y) coordinates, Auto-Aperture and measuring small
angles on computer images. Possibly….subtracting images.
Activity: “The Parallax of Asteroid ‘Austria’”.
Use the two images of asteroid “Austria” to determine its parallax shift (angle in arcsecs).
Use this parallax angle and the given baseline to calculate the distance to “Austria”.
H. Describe the Hipparcos satellite data as very accurate, available data to the nearest
stars. Hipparcos used parallax for its measurement method and was able to measure
parallax angles to about 0.001” or 1 milliarcsec. (Refer to Monday night reading on
Hipparcos.) Make connection back to Distance Ladder. Indicate the maximum star
distance possible for using parallax measurement is a few thousand light years.
I. Individual reflection time
Reminder of evening reading assignment.
Day 3:
(Time for questions/clarifications from previous day and evening reading.)
A. Make connection to Distance Ladder once again. There is a need for an understanding
of distance vs. brightness. Primary question (to small groups): Is there a clear
relationship between distance and brightness? If so, what is it?
Activity: “Determining the relationship between Brightness and Distance of a light
source” (See Handout)
Explain the basic use/procedures for using the light sensor/interface setup. The charge:
How does light intensity vary as you move farther away from the source? Be as explicit
as possible. Aim for a graphical and, perhaps, mathematical relationship. Materials:
light sensor + interface, laptop computers, meter sticks, rulers, light bulbs in
sockets, lab books with graph paper.
There will probably be a need to help groups isolate themselves somewhat to avoid
ambient light and light spillover from other groups.
B. Group presentation: Groups make presentation of methods, data and
“results/conclusions” to each other. Include a discussion of accuracy in measurements.
Ultimate aim is for “discovery” or at least “verification” of the inverse square law,
however encourage all results as legitimate data towards finding the relationship between
brightness and distance.
C. Presentation of the “Inverse Square Law” as critical to the Distance Ladder.
Practice with the mathematical aspects of the inverse square law and clarification of units
used (watts, watts/m2 vs lumens, lux). Have teachers work a number of examples where
2 of the 3 variables are known and the third must be calculated. (Basic practice in the
algebra involved, use of calculators and working with the proper units.) End with
examples which have the the brightness and luminosity known (e.g. it’s a 100 W light
bulb and you measure 3 W/m2 at some unknown distance. What is the distance?) Final
question: How could you use the above info to measure an unknown distance? What
assumptions would you need to make to do this? Finish with the conversion of lux to
watts/m2.
D. Go outside briefly with light probes to measure the sun’s brightness. Record data.
E. Powerpoint presentation: “Supernovae and Standard Candles”
Make reference back to the Distance Ladder. Go up the rungs briefly to get to
supernovae. Introduce supernovae in general. What is a supernova? How does it
happen? How bright does it get? What are the different types? How are they
distinguished one from another? End with Type Ia SN as the “standard candle”. Do
some sample calculations using astronomical distances.
F. Have teachers use HOU-IP to measure a SN light curve. Taking the raw data here
should be quite quick. The data analysis can occur the next day if needed.
G. Individual reflection time.
Reminder of evening reading assignment.
Day 4: (a short day)
(Time for questions/clarifications from previous day and evening reading.)
A. Once again, make connection to Distance Ladder. Indicate that the goal of today is
to determine the distance to the supernova and, consequently, to the Whirlpool
Galaxy (M51) in yesterday’s activity (SN Light Curve). We will do this using some of
our own measurements of the sun’s brightness and making some reasonable assumptions
and inferences.
B. Brief presentation of the Supernova Taxonomy Chart…..how to determine a Type Ia
Supernova. (We may not do this….depending on earlier question/clarification time and
need to complete Final Activity.)
C. Final activity: “Determining the Distance to the Whirlpool Galaxy (M51) using a
Distance Ladder”
Goal: To determine the distance to the Whirlpool Galaxy in Light Years or Parsecs.
See Handout for all details.
D. Report out from groups.
E. Final time for individual reflection on learnings and questions. Provide a bit of time at
the end to respond to some of the questions that remain.
F. Administer the Post-Assessment.