Question

If the Earth and distant stars were stationary (motionless) in space, what would we observe about the wavelength from these stars?
A.Wavelengths measured would match the actual wavelengths emitted.
B.Wavelengths measured would be shorter than the actual wavelengths emitted.
C.Wavelengths measured would be longer than the actual wavelengths emitted.

If a star is moving toward us in space, what would we observe about the wavelength from these stars?

A.Wavelengths measured would be shorter than the actual wavelengths emitted.

B.Wavelengths measured would match the actual wavelengths emitted.

C.Wavelengths measured would be longer than the actual wavelengths emitted.

Answer 1

1) In the first case, the correct answer is
A.Wavelengths measured would match the actual wavelengths emitted.
In fact, the stars are not moving relative to Earth, so there is no shift in the measured wavelength.

2) In this second case, the correct answer is
A.Wavelengths measured would be shorter than the actual wavelengths emitted.
in fact, since the stars in this case are moving towards the Earth, then apparent frequency of their emitted light will be larger than the actual frequency, because of the Doppler effect, according to the formula:
$f'= \frac{c}{c+v_s} f_0$
where f0 is the actual frequency, f' the apparent frequency, c the speed of light and vs the velocity of the source (the stars) relative to the obsever (Earth). Vs is negative when the source is moving towards the observer, so the apparent frequency f' is larger than the actual frequency f0. But the wavelength is inversely proportional to the frequency, so the apparent wavelength will be shorter than the actual wavelength.