12. The Hubble space telescope has been used to determine the existence of plane
ID: 3308840 • Letter: 1
Question
12. 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 planet's 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 having a nominal wavelength of 600 nm emitted by the Sun that is Doppler-shifted by the motion of the Sun due to the planet Jupiter. (hint: you will need to look up the masses of the Sun and Jupiter, and the radius of Jupiter's orbit).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 ) / 600 * 10^-9
wavelength shift = 2.6 * 10^-14 m
max wavelenth = wavelength + (wavelength shift )
= 600 + 2.6 * 10^-14 = 600.00002 nm
min wavelength = wavelength - (wavelength shift )
= 600 - 2.6 * 10^-14 = 599.99998 nm
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