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Relativistic Doppler Shift Using Wavelength and Observer Speed

The relativistic Doppler effect is the change in the wavelength of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect) when taking into account effects described by the special theory of relativity.

The ratio of the wavelength at the source and the wavelength observed equals the square root of the product of the speed of light minus the speed of the source away from the observer and the speed of light plus the speed of the observer toward the source divided by the product of the speed of light plus the speed of the source away from the observer and the speed of light minus the speed of the observer toward the source.

Formula

QuantityVariable[Subscript["λ", "s"], "Wavelength"]/QuantityVariable[Subscript["λ", "o"], "Wavelength"] == Sqrt[((Quantity[None, "SpeedOfLight"] + QuantityVariable[Subscript["v", "o"], "Speed"])*(Quantity[None, "SpeedOfLight"] - QuantityVariable[Subscript["v", "s"], "Speed"]))/((Quantity[None, "SpeedOfLight"] - QuantityVariable[Subscript["v", "o"], "Speed"])*(Quantity[None, "SpeedOfLight"] + QuantityVariable[Subscript["v", "s"], "Speed"]))]

symbol description physical quantity
λo wavelength observed "Wavelength"
λs wavelength at the source "Wavelength"
vo speed of the observer toward the source "Speed"
vs speed of the source away from the observer "Speed"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Relativistic Doppler Shift Using Wavelength and \ Observer Speed"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject[ "Relativistic Doppler Shift Using Wavelength and Observer Speed"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Relativistic Doppler Shift Using Wavelength and Observer Speed"], \ {QuantityVariable[ \!\(\*SubscriptBox[\("\[Lambda]"\), \("o"\)]\),"Wavelength"] -> Quantity[687.5`, "Nanometers"], QuantityVariable[ \!\(\*SubscriptBox[\("v"\), \("s"\)]\),"Speed"] -> Quantity[0.22`, "SpeedOfLight"]}]
Out[3]=

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