The Hubble space telescope has been used to determine the existence of planets o

Question

The Hubble space telescope has been used to determine the existence of planets orbiting around distant stars. A planet orbiting a star will cause the star to wobble with the same period as the planets orbit. Because of this wobble, light from the star will be Doppler-shifted up and down periodically. Estimate the maximum and minimum wavelengths of light of nominal wavelength 500 nm emitted by the Sun that is Doppler-shifted by the motion of the Sun due to the planet Jupiter. (Round your answers to five decimal places.)

Explanation / Answer

As seen from a distant vantage point, the reflex motion of the Sun caused by Jupiter is 13 meters per second.

v = c * (wavelength shift ) / wavelength

13 = 3*10^8 * (wavelength shift ) / 500 * 10^-9

(wavelength shift ) = 2.1666 * 10^-14 m

max wavelenth = wavelength + (wavelength shift ) = 500.00002 nm

min wavelength = wavelength - (wavelength shift ) = 499.99998 nm

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