LAB 11Astronomy 105 Laboratory

LAB QUIZ 11

Hubble discovered that galaxies are moving away from the Milky Way with velocities that are proportional to their

1. size.2. color.3. distance.4. mass.

Consider two galaxies which are different distances from the Milky Way. One galaxy is 10 Mly distance and the other 30 Mly. How much larger or smaller is the recessional velocity of the more distant galaxy? 1. 3 times larger

2. 6 times larger3. 9 times larger4. 3 times smaller5. 6 times smaller6. 9 times smaller

Consider two galaxies that are the same size but one is twice as far away as the other. The more distant galaxy will have ____ compared to the closer galaxy. 1. ½ the angular size

2. ¼ the angular size3. 2 times the angular size4. 4 times the angular size

In today’s lab you will determine the rotation rate of the planet Saturn by using

1. Hubble’s Law.2. Newton’s Law of Gravity.3. the Doppler Effect.4. the luminosity-distance formula.5. the distance modulus.

AST 105 Review for Lab Exam

Exam Next Week!

Study!

About 3-5 questions from each lab exercise Review

Main concepts covered Procedures and measurements Questions and calculations Bring a scantron: 882-E Review material – Power point slides online

EXPERIMENTAL MEASUREMENTS

Scientific Experiments / Observations

Physical quantities can never be measured with absolute precision

How Many Significant Figures0.089 2

1.089 4

12000 2

12001 5

Scientific Notation

3.502 x 106

decimal number (1-9)10 raised to an integer power

Number Significant Figures Scientific Notation

9004 4 9.004 x 103

0.000007 1 7 x 10-6

43 2 4.3 x 101

7,805,000,000 4 7.805 x 109

0.0408 3 4.08 x 10-2

8.4 2 8.4 x 100

To multiply two numbers in scientific notation multiply the decimal parts of the numbers and add the exponents algebraically.

(4.0 x 104)(2.0 x 103) =(4.0 x 2.0)(104 x 103) =(8.0) x (104+3) =8.0 x 107

(6.0 x 102)(2.0 x 105) = 12.0 x 107 = 1.2 x 108

CONSTELLATIONS – SKY FAMILIARIZATION

North

South

Celestial Equator

Ecliptic Sun’s Path

East

Summer Solstice

Vernal Equinox

Autumnal Equinox

North

South

East

March 7 @ 8:00 p.m

Meridian

Zenith

32° X

West Horizon

March 7 @ 8:00 p.m

Meridian

not visible

WestEast

East HorizonWest Horizon

Sky Familiarization

A Few More Things to Remember Any vertical line on your SC-1 (north-south) is a

meridian. Approximately one half of the stars on the SC-1

are visible at any given time (12 hours of RA). Meridian moves eastward 4 minutes each day

(Earth’s revolution) Meridian moves eastward 1 hour of RA for every

hour of time (Earth’s rotation)

THE MOON

N.P.N.P. N.P.

N.P.

N.P.

Synchronous Rotation

Does the Moon rotate on it’s axis?

What is the Moon’s hidden side?

N.P. Noon

Sunset

Midnight

Sunrise

N.P. Noon

Sunset

Midnight

Sunrise

N.P. Phase: 1st quarter

Rise Time:

Set Time:

Transit:

Noon

Midnight

Sunset

MERCURY’S ORBIT

10 20 30 40 50 60 70 80 90 100010 km6

SUN

Name (print):__________________________________ Section: _____

0.70.60.50.40.30.20.10.0AU

0.8

110 120

Mercury’s Orbit

Major Axis

Equal Time Intervals

F F

Verifying Kepler’s 1st

Mercury’s Orbit

Major Axis

10 20 30 40 50 60 70 80 90 100010 km6

SUN

0.70.60.50.40.30.20.10.0AU

0.8

110 120

Verifying Kepler’s 2nd

Equal area in equal time.

Mma

G4πP

322

2

324Pa

GMm sunm

sunsunm MMm

Kepler’s 3rd

)(4 2

MmGk

2

324Pa

GM sun

Finding the Sun’s mass.

P2=ka3

EMISSION SPECTRA

Formation of Emission and Dark Line Spectra

THE EARTH’S ORBITAL VELOCITY

12

345

Velocity = 0

Increasing Velocity

Increasing Velocity

The Doppler Effect

or

cv

Arcturus

VA

VB

? ?

0A λ

Δλcv

o

From measured Doppler Shift1.Orbital velocity of Earth

2.Radial velocity of Arcturus

3.Radius of the Earth’s Orbit

THE HR DIAGRAM

Apparent Brightness of Stars

Stellar Luminosity -- Total amount of light energy emitted each second Surface Area Temperature

Distance from the Earth

Magnitude

Stellar Brightness Apparent Magnitude (mv) - Brightness from Earth Absolute Magnitude (Mv) - Brightness from 10 pc

Absolute magnitude depends only on a star’s luminosity (the star’s wattage)Magnitude Difference

Brightness Ratio (Brightness Difference)

1 (2.512)1 2.5 2 (2.512)2 6.3 3 (2.512)3 15.9 4 (2.512)4 40 5 (2.512)5 100 6 (2.512)6 251

Spectral Classification

B

The SunM=+5 G2

O B A F G K M

-10-5 0+5+10+15A

bsol

ute

Mag

nitu

de

Temperature

HR Diagram

Luminosity Class

Size

Ia & Ib Supergiant

II Bright Giant

III Giant

IV Sub-giant

V Dwarf

The Sun’s Spectral and Luminosity Class: G2 V

Star mv Mv

SpectralType

LuminosityClass

Aldebaran +0.9 -0.2 K5 IIIAlpha Centauri A 0.0 +4.4 G2 V

Antares +0.9 -4.5 M1 ICanopus -0.7 -3.1 F0 II

Fomalhaut +1.2 +2.0 A3 VRegulus +1.4 -0.6 B7 V

Sirius -1.4 +1.4 A1 VSpica +0.9 -3.6 B1 V

Which star appears faintest in our sky? Regulus

Which star has the greatest luminosity? Which star has the highest surface temperature? Which star is a red giant?

Which main-sequence star has the longest lifetime?

Antares

Spica

Aldebaran

Alpha Centauri

THE DISTANCE TO THE PLEIADES

Stars in a Cluster• Common Properties

• Distance• Age

• Different Properties• Spectral Types (temperature)• Luminosity Class (size)

d >10 pc

10 pc

d <10 pc

10 pc

Star Cluster

d >10 pc

d <10 pc

O B A F G K M-0.4 color index 1.3

Main-sequence

HR Diagram

-0.4 color index 1.3

Color-MagnitudeDiagram

Distance Modulus = m - M The difference between the absolute magnitude and the apparent magnitude can be used to find the distance to a star cluster.  If m-M > 0 then the distance to the cluster is > 10 pc.If m-M = 0 then the distance to the cluster is = 10 pc.If m-M < 0 then the distance to the cluster is < 10 pc.  

 

DM{

Cluster A: Distance 50 ly

Cluster B: Distance ?

The apparent brightness of the stars in Cluster B are 4 times fainter than the stars in Cluster A.

What is the distance to Cluster B?

Inverse-Square Law: √4 = 2

Cluster B is 2 times farther or 100 ly.

AGES AND DISTANCES TO CLUSTERS

Interstellar Dust Reddens Light (makes stars appear cooler) Dims Light (makes stars appear further away)

age of cluster = lifetime of stars at main-sequence turnoff point

B6 stars -- 60 million yrs. MS lifetime

Pleiades - Open Cluster

Distance - 380 ly Age - 60 million years

HUBBLE’S LAB

V = 0 2800210014007007001400km/sec

10 Mpc 20 Mpc 30 Mpc 40 MpcMilky Way A B C

V = 02800 2100 14007007001400km/sec

10 Mpc 20 Mpc30 Mpc40 MpcMilky Way A B C

10 Mpc20 Mpc Alien’s Galaxy

Recessional Velocity is Proportional to Distance

The Universe is Expanding!!

v = Ho dHubble Diagram

Finding a Galaxy’s Distance Hubble’s

Law

d = v / Ho

To Find Distance: Measure recessional velocity (red shift)

132 Mpc

Sample Galaxies

Distance images

Recessional Velocity spectra

v = Ho x dHubble Diagram

Hubble Diagram

Procedure- plot data- draw best fit line- find slope (Ho)x

x

x

xx

rise

run slope = rise/run

ROTATION OF SATURN

Earth Distant Star

Laboratory - No Radial motion

Radial Velocity = 0

Radial Velocity -

Radial Velocity +

Laboratory Spectrum

Blueshift

Redshift

Spectral Lines Match

o

Important: Do not write or mark on the

Saturn Handout

Spectroscope Slit

No Doppler Shift from this Light

Light from here shows the largest Blue Shift

Light from here shows the largest Red Shift

A

BSaturncV

λΔλ 0B 2

o A

B

seckm

04λΔλcV

V

V

0λΔλcV Doppler

cV

λΔλ 0A 2

o

seckm

04λΔλcV

Top

Bottom

(mm) = Top Distance – Bottom Distance

Reference Line

c = 300,000 km/s

o = 6200 Å

Finding the Rotation Period of Saturn

Saturn

V Period = Distance / Velocity

Distance = Equatorial Circumference = 2RR

P = 2 R / V

VR2P

Period (P) – Rotation Period

THE END

5 pc 10 pc 15 pc-26.5

1.3

3.3

2.0

4.2

Sun

A

B

C

D

5.06.0

0.0

2.0

Apparent Magnitude

Absolute Magnitude

1 parsec (pc) = 3.26 ly

Verifying Kepler’s 2nd

Equal area in equal time.

A2

A1

base

periluna

Center

Verifying Kepler’s 1st

P1L1

L2

P2

L3

L4

The AST105 Lab Exam is the week of November 29 (Week after Thanksgiving).1. True2. False

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