1. Astronomy 105 Laboratory
Lab 06

2. The Earth’s Orbital velocity
Lab 06
The Earth’s Orbital velocity

3. Light Source at Rest
c =  x f 
Light Source

4. The Doppler Effect Blueshift Redshift 1 2 3 4 5
No shift observed
The Doppler Effect
Wavelength is shorter; frequency is higher.
Blueshift
Wavelength is longer; frequency is lower.
Redshift

5. The Doppler Effect 1 2 3 4 5 Increasing Velocity Increasing Velocity

6. V = 60 mph V = 40 mph V = 40 mph V = 60 mph V = 80 mph V = 80 mph
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

7. Laboratory - No Radial motion
The Doppler Effect: Measuring the Radial Velocity of a Star
Laboratory Spectrum
Spectral Lines Match
Laboratory - No Radial motion
Earth
Distant Star
Radial Velocity = 0
Blueshift
Radial Velocity -
Radial Velocity -
Redshift o 
Radial Velocity +
Radial Velocity +

8. VEarth = 1/2(VA - VB) Vstar = 1/2(VA + VB) 0.86 VA = Vstar + VEarth
Relative velocity between star and Earth from Doppler shift
VA = Vstar + VEarth
VB = Vstar - VEarth
Arcturus ?
Vstar
VEarth = 1/2(VA - VB)
Vstar = 1/2(VA + VB) VB
- VEarth
VEarth = 1/2(VA - VB)
Vstar = 1/2(VA + VB)
 0.86 Vo Ve 
To Ecliptic
To Arcturus

9. Arcturus About 30° from Ecliptic North West East South 30° Vo Ve
To Ecliptic
To Arcturus
About 30° from Ecliptic
East
West
South

10. Important: Do not write or mark on the Arcturus Handout

11. Emission Lines Absorption Lines (no Doppler shift) Redder Bluer
(Arcturus Spectra)

12. same wavelength same wavelength same wavelength same wavelength Bluer
Redder nm nm nm nm

13. λ λo c = 300,000 km/s VA (July 1, 1939) redshift blueshift
Bluer
Redder
blueshift λ
VB (January 19, 1940) nm λo
c = 300,000 km/s

14. Plate Scale P.S.= 430.791 nm−426.048 nm distance between 1 and 7 (mm)
Bluer
Redder
P.S.= nm− nm distance between 1 and 7 (mm)
= nm mm
= nm mm
SPECTRUM B - January 19, 1940
Ref. No. nm
Shift
(mm) λ
Shift x P.S. VB
(km/sec) 1 2 5 7
∆λ=−1.2 mm× nm mm
=− nm
v B = c∙∆λ λ o
= 300,000 km/s∙(− nm) nm
=−32.2 km/s
-1.2
-32

15. 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

16. Finding the Radius of the Earth’s Orbit
Vearth =
distance
time R
Vearth
The distance the Earth travels around sun in one year is approximately the circumference of the Earth's Orbit (2R)
Vearth =
2 π R
time
R =
2 π
(Vearth)(time)
time = 1 year = 31,600,000 seconds
π =

17. The End

18. Astronomy 105 Laboratory
Lab 06

19. Lab Quiz 06

20. When an electron in an atom moves from a high energy level to a lower energy level
a photon of light is emitted.
a photon of light is absorbed.
the atom becomes ionized.
the atom gains a proton. 30

21. Which one of the above is an emission spectra?
400 nm
500 nm
600 nm
700 nm A B C
Which one of the above is an emission spectra? A B C 15

22. The pattern of absorption lines in a star’s spectrum can be used to find its _____.
distance
mass
chemical composition
motion through space 30

23. In today’s lab you will determine the orbital velocity of the Earth using spectra from the star _____.
Arcturus
Betelgeuse
Canopus
Fomalhaut
Spica 30

24. We will use the _______ to find the velocity of this star.
Zeeman effect
stellar brightness
Doppler Effect
chemical composition 30