Estimating the distance to a galaxy

How can we calculate the distance to the galaxy from the images we got from SSS? You need the scale of your image; remember, the size of the box will be the number of arc minutes you specified earlier for the image extraction, so if your image is 5 centimetres across, and this is a 1 arc minute image, then a galaxy that is 2.5 centimetres long on your image will be 0.5 arc minutes long. If you measure the size of the galaxy (use a ruler!) and work out how many arc minutes this corresponds to, you know the angular size of the galaxy. You can use this to estimate the distance to the galaxy; the larger the galaxy appears to be on the sky, the closer it is. When you are measuring the size of the galaxy, remember to measure the largest extent, since the galaxy may be inclined towards or away from us. Remember, one arc minute is one 60th of a degree, so to convert from arc minutes to degrees, divide by 60.

Now use the "size-to-distance ratio" (The Cosmic Perspective p30, Mathematical Insight 2.1) to work out the distances to your five galaxies.

The distance is approximately given by (we use here that 360/2 π ≈ 60):

distance ≈ ( size / angular size ) × 60

where the angular size is measured in degrees.

We have to assume a size for the spiral galaxies; use 50,000 light years as a reasonable average size.

As an example: suppose you measure a galaxy angular size as 1.5 arcminutes; that is

1.5 / 60 = 0.025 degrees

Then the distance to the galaxy is

Distance = ( 50000 / 0.025 ) × 60

= 120,000,000 light years

= 120 million light years

(For a discussion of galaxy sizes, see The Cosmic Perspective p608, section 20.1.)

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