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
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
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