““The Distance to the Stars: The Distance to the Stars: How Do Scientists Know?”How Do Scientists Know?”

Teacher Training Courses in Teacher Training Courses in Ohio and Michigan,Ohio and Michigan,

June 2006June 2006

Pre-TestPre-Test

Q. 1Q. 1

Which of the following best represents your Which of the following best represents your understanding of the distances to the stars that understanding of the distances to the stars that are visible (w/o telescope) in our night sky?are visible (w/o telescope) in our night sky?

a.a. Within a small range, all of the stars are at about the Within a small range, all of the stars are at about the same distance.same distance.

b.b. All the stars we see vary greatly in distance from the All the stars we see vary greatly in distance from the Earth.Earth.

c.c. Most of the stars vary greatly in distance, however the Most of the stars vary greatly in distance, however the stars in a constellation like Orion are all at the same stars in a constellation like Orion are all at the same distance.distance.

Pre-test (con.)Pre-test (con.)

Q. 2Q. 2

Explain how you believe astronomers can Explain how you believe astronomers can measure the distance to a star.measure the distance to a star.

Q. 3Q. 3

Distinguish between the Distinguish between the BrightnessBrightness of a of a star and the star and the LuminosityLuminosity of a star. of a star.

Pre-test (con.)Pre-test (con.)

Q. 4Q. 4 Imagine a square meter in a field near Imagine a square meter in a field near

your house at high noon on a bright, your house at high noon on a bright, sunny day. Approximately how many sunny day. Approximately how many watts of light would you estimate is falling watts of light would you estimate is falling on that area?on that area?

a. 10 watts, b. 100 watts, c. 1,000 watts,a. 10 watts, b. 100 watts, c. 1,000 watts, d. 10,000 watts, e. greater than 10 KWd. 10,000 watts, e. greater than 10 KW

Pre-test (con.)Pre-test (con.)

Q. 5Q. 5 If the sun were twice as far away from the If the sun were twice as far away from the

Earth, how would you answer Q. 4?Earth, how would you answer Q. 4?

Q. 6Q. 6 Estimate how many toothpicks, laid end-Estimate how many toothpicks, laid end-

to-end, it would take to reach the planet to-end, it would take to reach the planet Mars. Assume Mars is at its closest point Mars. Assume Mars is at its closest point to the Earth.to the Earth.

Answers??Answers??

Let’s answer them together……Let’s answer them together……

““The Distance to the Stars”The Distance to the Stars”

Workshop inspired by article in Workshop inspired by article in February 2005 issue of February 2005 issue of The Science The Science TeacherTeacher, (NSTA, National Science , (NSTA, National Science Teachers Assoc.)Teachers Assoc.)

Title: “How Far Are the Stars?”Title: “How Far Are the Stars?”

Concept: Distance LadderConcept: Distance Ladder

HOU Curriculum BooksHOU Curriculum Books

Measuring DistanceMeasuring Distance: Distance Ladder : Distance Ladder introduction, Inverse Square Law, introduction, Inverse Square Law, Standard Candle introduction, using Standard Candle introduction, using Cepheid Variables to determine distance.Cepheid Variables to determine distance.

Measuring BrightnessMeasuring Brightness: SN Light Curves.: SN Light Curves.

Searching for SNeSearching for SNe: How to locate a SN.: How to locate a SN.

What to add?What to add?

ParallaxParallax

Using a Supernova Ia as a standard Using a Supernova Ia as a standard candle to calculate distance.candle to calculate distance.

Performing a “Distance Ladder” calculationPerforming a “Distance Ladder” calculation

Simple Distance Ladder ActivitySimple Distance Ladder Activity

GOAL: Determine the length of this room in GOAL: Determine the length of this room in #’s of paperclips.#’s of paperclips.

Begin with one paperclip as the smallest Begin with one paperclip as the smallest unit.unit.

Create a larger unit with X paperclips.Create a larger unit with X paperclips.

Create one unit even larger.Create one unit even larger.

Estimate the # of paperclips for this room.Estimate the # of paperclips for this room.

ParallaxParallax

Concept: thumb in front of your eyes. One Concept: thumb in front of your eyes. One eye open, one eye closed.eye open, one eye closed.

Switch open and closed eyes. What does Switch open and closed eyes. What does your thumb appear to do?your thumb appear to do?

Thumb close…….more parallax.Thumb close…….more parallax.

Thumb far…….less parallax.Thumb far…….less parallax.

An INVERSE relationship.An INVERSE relationship.

Outdoor ParallaxOutdoor Parallax

Baseline (b)

A

B

C

D

DistantBackground

“Pole”

d

p

p’

p = parallax angle

p

A

B

d

Basic Geometry

The small angle formula gives us: p = (AB/d), with p in RADIANS (pR). A little algebra manipulation gives:

d = (AB/pR)

Outdoor approximationOutdoor approximation

It’s impossible to measure p directly. It’s impossible to measure p directly. However, if the distance to the background However, if the distance to the background is >>> d, then angle p’ is approximately is >>> d, then angle p’ is approximately equal to p. Justification with long stringequal to p. Justification with long string

We can measure p’ directly by measuring We can measure p’ directly by measuring the “Angular Size” of segment CD.the “Angular Size” of segment CD.

Measuring Angular SizeMeasuring Angular Size

EYEA

B

C

D

DistantBackground

p’

x

Y

Hold ruler in front of your eye. Match up “x” with C and D. Measure x. Partner measures y.

Angular size of CD = p’ = (X/Y) radians

ExampleExample

Measure AB = 8.4 metersMeasure AB = 8.4 meters

Measure angle p’ (angular size of CD) Measure angle p’ (angular size of CD) using ruler and meter stick. x = 5 cm, y using ruler and meter stick. x = 5 cm, y = 60 cm.= 60 cm.

Calculate p’ = x/y = 0.083 radiansCalculate p’ = x/y = 0.083 radians

Calculate d = AB/pCalculate d = AB/pRR = 8.4/0.083 ~ 100 = 8.4/0.083 ~ 100 m.m.

Alternate: d = AB * (Y/X) Alternate: d = AB * (Y/X)

Setting up a baselineSetting up a baseline

Measuring the angleMeasuring the angle

Do it INSIDE with Do it INSIDE with Eye-Eye as baselineEye-Eye as baseline

Baseline = Eye to EyeBaseline = Eye to Eye

““Pole” = your thumb held at arm’s lengthPole” = your thumb held at arm’s length

Switch eyes to locate C and D on the wallSwitch eyes to locate C and D on the wall

Measure p’ using X and Y (approx.)Measure p’ using X and Y (approx.)

Measure Eye-Eye distance (approx.)Measure Eye-Eye distance (approx.)

Calculate d (to your thumb) = AB/p’Calculate d (to your thumb) = AB/p’

= (Eye to Eye distance) x (Y/X)= (Eye to Eye distance) x (Y/X)

Parallax of an AsteroidParallax of an Asteroid

Use HOU-IP: Display two images taken of Use HOU-IP: Display two images taken of an asteroid from two different telescopes an asteroid from two different telescopes OR at two different times from the same OR at two different times from the same telescope. (difficult to determine baseline)telescope. (difficult to determine baseline)Can view and measure the parallax angle Can view and measure the parallax angle directly from subtracted images. Shift in directly from subtracted images. Shift in pixels x plate scale = p” (in arcsecs)pixels x plate scale = p” (in arcsecs)Calculate distance:Calculate distance:

d = (AB/p”)*206,265d = (AB/p”)*206,265

Next steps on Distance LadderNext steps on Distance Ladder

Investigate Inverse Square Law with Light Investigate Inverse Square Law with Light probes.probes.

Clarify distinction between Brightness (B) Clarify distinction between Brightness (B) and Luminosity (L) for stars in the formula and Luminosity (L) for stars in the formula B = L/4B = L/4dd22..

Use HOU Unit on Cepheid Variables to get Use HOU Unit on Cepheid Variables to get distance measurement in our galaxy.distance measurement in our galaxy.

Use SN Ia to get d for distant galaxies.Use SN Ia to get d for distant galaxies.

Supernova Light Curve UnitSupernova Light Curve Unit

Light CurveLight CurveSupernova Light Curve

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 10 20 30 40

Night number

Brig

htne

ss r

atio

Ser ies1

Data taken from SN1994i in M51

Results from Measurements and Results from Measurements and Calculations in activityCalculations in activity

Light Curve peaks at 1.46 x Reference Star Light Curve peaks at 1.46 x Reference Star on ~day 11 and drops quicklyon ~day 11 and drops quicklyMost likely a SN type I (assume Ia although Most likely a SN type I (assume Ia although probably a Ic from spectroscopic data)probably a Ic from spectroscopic data)SN at max ~ same as galaxy coreSN at max ~ same as galaxy coreCore ~ one billion “Suns” in luminosityCore ~ one billion “Suns” in luminositySN ~ 200 million “Suns” using Aperture toolSN ~ 200 million “Suns” using Aperture tool

New Activity: Distance to M51New Activity: Distance to M51

GOALGOAL: Determine the distance to M51, : Determine the distance to M51, using a simple distance ladder.using a simple distance ladder.

Already knownAlready known: :

Max B of SN compared to Ref StarMax B of SN compared to Ref Star

L of SN in terms of “Suns”L of SN in terms of “Suns”

Relationship between L, B and dRelationship between L, B and d

Distance to M51 (con.)Distance to M51 (con.)

To measure or find on internetTo measure or find on internet::

B of the Sun on the Earth (“Solar constant” B of the Sun on the Earth (“Solar constant” from internet shows ~1370 w/mfrom internet shows ~1370 w/m22. Light . Light probe in Michigan measured ~1000 w/mprobe in Michigan measured ~1000 w/m22))

Distance from the Sun to the Earth (1 AU Distance from the Sun to the Earth (1 AU = 150 million km) **originally w/ parallax!= 150 million km) **originally w/ parallax!

B of the Ref Star (8 E-14 w/mB of the Ref Star (8 E-14 w/m22 from from http://simbad.u-strasbg.fr/sim-fid/plhttp://simbad.u-strasbg.fr/sim-fid/pl ) )

Measuring the “solar constant”Measuring the “solar constant”

Calculations:Calculations:

L (Sun): ~1000 w/m = L/4L (Sun): ~1000 w/m = L/4dd22. Inserting d . Inserting d = 1.5 E11 m. gives L ~ 2.8 E26 watts.= 1.5 E11 m. gives L ~ 2.8 E26 watts.

L (SN) ~ 200 million Suns = 2 E8 x 2.8 L (SN) ~ 200 million Suns = 2 E8 x 2.8 E26 = 5.6 E34 watts.E26 = 5.6 E34 watts.

B (SN) = 1.46 x Ref Star = 1.46 x 8 E-14 ~ B (SN) = 1.46 x Ref Star = 1.46 x 8 E-14 ~ 1.2 E-13 w/m1.2 E-13 w/m22..

Finally: d (SN) = sqrt(L/4Finally: d (SN) = sqrt(L/4B) ~ 1.9 E23 m B) ~ 1.9 E23 m ~ 20 Mly ~ 6.2 Mpc~ 20 Mly ~ 6.2 Mpc

Using Standard Candle valueUsing Standard Candle value

L of SN Ia thought to be a “standard L of SN Ia thought to be a “standard candle” at ~ 9 E34 watts.candle” at ~ 9 E34 watts.

The B of the SN in 1994i is still ~ 1.46 x The B of the SN in 1994i is still ~ 1.46 x Ref Star = 1.2 E-13 w/mRef Star = 1.2 E-13 w/m22..

Applying the inverse square law givesApplying the inverse square law gives

d ~ 8 Mpc. The published value of the d ~ 8 Mpc. The published value of the distance to M51 is ~10 Mpc!distance to M51 is ~10 Mpc!

d = ?

1 AU

L (sun) = ?

Sun

Earth

M 51

B (sun) = ?B (M 51) = ?

L (M 51) = ?