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Light from a distant star has undergone a red shift. Which of these conclusions is correct about the star? Its pitch is increasing. Its parallax is increasing. It is moving towards Earth. It is moving away from Earth.

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AL2006
We've never discovered any way for wavelengths of light to
appear to get longer after they leave the source, except for
the Doppler effect ... when the observer and the source of
the light are moving apart.  

Since we don't know any other way for it to happen, whenever
we see a star or a galaxy whose light is red-shifted, we conclude
that it is moving away from Earth.

If you think about this for a few seconds, there are two things
about it that should blow your mind:

#1). "Red-shifted" means that the wavelengths of the light we see
are longer than the wavelengths of the light that left the star.
How do we know what the wavelength was when it left the star ?

#2). Our whole picture of the "expanding universe" ... which is a
big part of the foundation that supports the whole picture of the
"big bang" ... rests on the red-shift of light from distant galaxies,
and our conclusion that they are all moving away from us.
If we ever discover a DIFFERENT way that light can become
red-shifted, that may be IT for the expanding universe and the
big bang, both.  They may both be out the window. 

Answer:

It is moving away from Earth.

Explanation:

As the source comes closer to the observer then we can say that its frequency will increase.

So here we know that

[tex]\frac{\Delta \nu}{\nu} = \frac{v}{c}[/tex]

here we know that

v = speed of the star

c = speed of light

now if we know that speed of the star is towards us then the frequency will increase and hence the wavelength will decrease.

So it is known as Blue shift

While if the star is moving away from us then in that case the frequency will decrease and hence the wavelength will increase.

So here it is known as Red Shift.

So here correct answer will be

It is moving away from Earth.

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