astronomy 105 laboratory lab 11 - sfa physics, engineering ...celestial equator ecliptic sun’s...

LAB 11

Astronomy 105 Laboratory

AST 105Review for Lab Exam

Ast 105 Lab ExamWeek of April 16, at normal lab time.

Don’t be late!!

Items to bring…- One scantron (882-E)

- two pencils

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

CONSTELLATIONS – SKY

FAMILIARIZATION

North

South

Celestial Equator

Ecliptic Sun’s Path

Eas

t

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)

SCIENTIFIC

MEASUREMENTS

Scientific Experiments / Observations

Physical quantities can never be

measured with absolute precision

How Many Significant Figures

0.089 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

Units

Provides numerical context for a measurement

Unit conversion

Ex. Convert 500 kilometers into centimeters

1000 m = 1 km 1 m = 100 cm

500 𝑘𝑚 ×1000 𝑚

1 𝑘𝑚×100 𝑐𝑚

1 𝑚= 5 × 107cm

1000 𝑚

1 𝑘𝑚= 1 and

100 𝑐𝑚

1 𝑚= 1

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 km

6

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 km

6

SUN

0.70.60.50.40.30.20.10.0AU

0.8

110 120

Verifying Kepler’s 2nd

Equal area in equal time.

Mm

a

G

4πP

322

2

324

P

a

GMm sunm

sunsunm MMm

Kepler’s 3rd

)(

4 2

MmGk

2

324

P

a

GM sun

Finding the Sun’s mass.

P2=ka3

EMISSION SPECTRA

Formation of Emission and Dark Line Spectra

THE EARTH’S ORBITAL VELOCITY

1

2

3

4

5

Velocity = 0

Increasing

Velocity

Increasing

Velocity

The Doppler Effect

o

r

cv

Arcturus

VA

VB

? ?

0A

λ

Δλcv

o

From measured

Doppler Shift

1.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 Sun

M=+5 G2

O B A F G K M

-10

-5

0

+5

+10

+15Ab

so

lute

Mag

nit

ud

e

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

Spectral

Type

Luminosity

Class

Aldebaran +0.9 -0.2 K5 III

Alpha Centauri A 0.0 +4.4 G2 V

Antares +0.9 -4.5 M1 I

Canopus -0.7 -3.1 F0 II

Fomalhaut +1.2 +2.0 A3 V

Regulus +1.4 -0.6 B7 V

Sirius -1.4 +1.4 A1 V

Spica +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

STELLAR PARALLAX

1 AU

Sun

Earth

Star 1 Star 2 Star 3

1 arcsec

1/2 arcsec

arcsec

1/3 arcsec arcsec

1 pc 2 pc 3 pc

1 parsec 2 parsec 3 parsec

A star with a parallax of 1 arcsecond is at a distance of 1 parsec (1 pc = 3.26 ly)

5 light-years 10 light-years

More distant stars have smaller parallaxes.

=1

A star’s distance in parsecs is given by

where d is in parsecs and p is in arcseconds

Stellar Parallax

• Motion of Earth cause parallax shifts

• Used to find distance to stars out to a few hundred light-years

• Parallax is ½ of measured shift

• More distant stars have a smaller parallax… a star with ½ the parallax

of another star is 2x farther away

• d = 1 / p “p” is in arc seconds and “d” is in parsecs

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-Magnitude

Diagram

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 2800210014007007001400

km/sec

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

V = 02800 2100 14007007001400

km/sec

10 Mpc 20 Mpc30 Mpc40 Mpc

Milky 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

x

x

rise

runslope = 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

Earth Distant Star

Laboratory - No Radial motion

Radial Velocity = 0

Radial Velocity -

Radial Velocity +

Laboratory Spectrum

Blueshift

Redshift

Spectral Lines Match

o

o

rλ

cΔλv

Radial Velocity -

Radial Velocity +

The Doppler Effect: Measuring the Radial Velocity of a Star

Important: Do not write or mark on theSaturn 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

BSaturn

c

VλΔλ 0B 2

o A

B

sec

km

04λ

ΔλcV

V

V

0λ

ΔλcV Doppler

c

VλΔλ 0A 2

o

sec

km

04λ

ΔλcV

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

V

R2P

Period (P) – Rotation Period

THE END