Astronomy 105 Laboratory
LAB 06
Lab 06
THE EARTH’S ORBITAL VELOCITY
Light Source at Rest
c=xf

Light Source
No shift observed
1
2
The Doppler
Effect
3
4
5
5
4
3
2
1
Wavelength is shorter;
frequency is higher.
Wavelength is longer;
frequency is lower.
Blueshift
Redshift
No shift observed
The Doppler Effect
Velocity = 0
1
2
3
4
5
Increasing
Velocity
Increasing
Velocity
The Doppler Effect
indicates my velocity
is 0 mph?
The Doppler Effect
indicates I’m
approaching the bus
at 20 mph.
V = 80 mph
V = 60 mph
V = 40 mph
V = 80 mph
V = 40 mph
V = 60 mph
The Doppler Effect
indicates I’m receding
from the ambulance
at 20 mph.
The Doppler Effect
indicates I’m
approaching the
sports car at 160
mph? YIKES !!
V = 80 mph
V = 80 mph
The Doppler Effect: Measuring the Radial Velocity of a Star
Laboratory Spectrum
Laboratory - No Radial motion
Earth
Spectral Lines Match
Distant Star
Δλ  c
vr 
λo
Radial Velocity = 0
Radial Velocity -
Blueshift
Radial Velocity -
Redshift
Radial Velocity +
Radial Velocity +
o 
Arcturus
North
East
South
West
About 30°
from Ecliptic
+ VEarth
VA
Relative velocity between star
and Earth from Doppler shift
?
Arcturus
VA = Vstar + VEarth
VB = Vstar - VEarth
?
Vstar
VEarth = 1/2(VA - VB)
- VEarth
VB
Vo

To
Arcturus
Ve
To
Ecliptic
Vstar = 1/2(VA + VB)
VEarth = 1/2(VA - VB)
0.86
Vstar = 1/2(VA + VB)
Important: Do not write or mark on the
Arcturus Handout
Emission Lines
(no Doppler shift)
Redder
Bluer
Absorption Lines
(Arcturus Spectra)
same wavelength
Bluer
same wavelength
426.048 nm
427.176 nm
same wavelength
same wavelength
429.413 nm
Redder
430.791 nm
VA (July 1, 1939)
redshift
Redder
Bluer
blueshift
VB (January 19, 1940)
427.176 nm
λo
λ
c = 300,000 km/s
c  Δλ
vB 
λo
Plate Scale
Redder
Bluer
P. S. =
nm
4.743 nm
430.791 nm − 426.048 nm
= 0.03840
=
mm
distance between 1 and 7 (mm) 123.5 mm
nm
= −0.0461 nm
∆λ = −1.2 mm × 0.03840
mm
c ∙ ∆λ 300,000 km/s ∙ (−0.0461 nm)
vB =
= −32.2 km/s
=
λo
429.413 nm
SPECTRUM B - January 19, 1940
Ref.
No.
nm
1
426.048
2
427.116
5
429.413
7
430.791
Shift
(mm)
λ
Shift x P.S.
-1.2
-0.0461
VB
(km/sec)
-32
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
Finding the Radius of the Earth’s Orbit
distance
Vearth =
time
Vearth
The distance the Earth travels around
sun in one year is approximately the
circumference of the Earth's Orbit (2R)
Vearth =
R
2πR
time
(Vearth)(time)
R=
2π
time = 1 year = 31,600,000 seconds
π = 3.1416
THE END