LAB 06

Astronomy 105 Laboratory

THE EARTH’S ORBITAL VELOCITY

Lab 06

Light Source

c = x f

Light Source at Rest

5 4 3 2 1

1

2

3

4

5

Wavelength is shorter;

frequency is higher.

Blueshift

Wavelength is longer;

frequency is lower.

Redshift

The Doppler Effect

No shift observed

No shift observed

1

2

3

4

5

Velocity = 0

Increasing

Velocity

Increasing

Velocity

The Doppler Effect

The Doppler Effect

indicates my velocity

is 0 mph?

V = 80 mph V = 80 mph

The Doppler Effect

indicates I’m approaching

the bus at 20 mph.

V = 60 mph V = 40 mph

The Doppler Effect

indicates I’m receding from

the ambulance at 20 mph.

V = 40 mph V = 60 mph

The Doppler Effect

indicates I’m approaching

the sports car at 160 mph?

YIKES !!

V = 80 mph V = 80 mph

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

Vstar

Arcturus

VA

VB

? ?

VA = Vstar + VEarth

VB = Vstar - VEarth

VEarth = 1/2(VA - VB)

Vstar = 1/2(VA + VB)- VEarth

+ VEarth

VEarth = 1/2(VA - VB)

Vstar = 1/2(VA + VB)

0.86Vo

Ve

To

Ecliptic

To

Arcturus

Relative velocity between star

and Earth from Doppler shift

South

East

NorthW

est

Arcturus

About 30°

from Ecliptic

Vo

Ve30°To

Ecliptic

To

Arcturus

Important: Do not write or mark on theArcturus Handout

Bluer Redder

Absorption Lines

Emission Lines (no Doppler shift)

(Arcturus Spectra)

426.048 nm 430.791 nm

Bluer Reddersame wavelength

same wavelength

same wavelengthsame wavelength

427.176 nm 429.413 nm

Bluer Redder

redshift

VB (January 19, 1940)

blueshift

427.176 nm

VA (July 1, 1939)

o

Bλ

Δλcv

λλo

c = 300,000 km/s

Bluer Redder

Plate Scale

SPECTRUM B - January 19, 1940

Ref.

No.

nmShift

(mm)

λ

Shift x P.S.

VB

(km/sec)

1 426.048

2 427.116

5 429.413

7 430.791

-1.2 -0.0461 -32

P. S. =430.791 nm − 426.048 nm

distance between 1 and 7 (mm)=

4.743 nm

123.5 mm= 0.03840

nm

mm

∆λ = −1.2 mm× 0.03840nm

mm= −0.0461 nm

vB =c ∙ ∆λ

λo=300,000 km/s ∙ (−0.0461 nm)

429.413 nm= −32.2 km/s

Lab Objectives

By measuring the Doppler shift of

Arcturus’ absorption lines you will

Determine the Earth’s orbital velocity

Vearth = 1/2(VA - VB)/0.86

Determine the radial velocity of Arcturus

Vstar = 1/2(VA + VB)

Determine the radius of the Earth’s orbit

R = (Vearth x time)/2

R

Vearth

Finding the Radius of the Earth’s Orbit

The distance the Earth travels around

sun in one year is approximately the

circumference of the Earth's Orbit (2R)

Vearth =distance

time

Vearth =2 π R

time

R =2 π

(Vearth)(time)time = 1 year = 31,600,000 seconds

π = 3.1416

THE END