A spiral arm galaxy is large group of stars which rotates about a central bulge.

Question

A spiral arm galaxy is large group of stars which rotates about a central bulge. Our own Milky Way galaxy is just one such formation. Let's assume we have another spiral arm galaxy whose center is 23.6 light-years from earth and is moving away from earth at a velocity of 33 X105 m/sec. The galaxy is rotating such that points in the extreme parts of it's spiral arms are rotating with a speed of 55 X105 m/sec relative to the center. Light with a particular frequency of 8.32 X 1014Hz is emitted from stars in both arms.

1)

What is frequency of this light detected by astronomers that are observer the glaxay arm that is moving away from the earth?

faway =

Hz  

2)

What is frequency of this light detected by astronomers that are observer the glaxay arm that is moving towards the earth?

ftowards =

Hz  

Explanation / Answer

The formula used to finding frequency in this case will be

fo = fs x sqrt [ ( c -v ) / (c + v) ]

where, fo is obserevd freq, fs freq of light source , c is the speed of light and v is relative velocity.

Part (1) Freq when the glaxay arm that is moving away from the earth

v = 33 x 105 + 55 x 105 = 88 x 105 m/s

So, fo = 8.32 x 1014 sqrt [ ( 3 x 108 - 88 x 105) / ( 3 x 108 + 88 x 105?) ]

faway = fo = 8.04 x 1014 Hz

Part (2)

In this case the rel vel v will be

v = 33 x 105 - 55 x 105 = -22 x 105 m/s

fo = 8.32 x 1014 sqrt [ ( 3 x 108 + 22 x 105) / ( 3 x 108 - 22 x 105?) ]

ftowards = fo = 9.53 x 1014 Hz

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