Determining the Size of Objects in the Sky

By now you have learned how to interpret the x-ray photons that are collected by the Chandra telescope.  You can determine the approximate position of different objects in relation to the Earth.  But how do scientists determine how large objects in the universe are when they are so far away?  Let's find out, but this time you will be determining the size of an object not those scientists at NASA.

First, let's review some geometry.

Above are common shapes.  You probably learned in elementary school that the lines of different shapes intersect to form angles of different magnitudes.  The total degrees that make up a geometric object help to characterize the shape.  For example, a rectangle has 360^o and a triangle has 180^o. 

How many degrees make up a circle?

Many times in science and math, we use radians instead of degrees to measure the angles in a circle. 

There are 2 radians in a circle.  Therefore, 2 = 360^o. 

How many degrees are in 1 radian?

If you need help, click here.

You learned in the lesson on coordinate systems that there is 1 degree in 60 minutes of arc and 60 seconds of arc in one minute of arc. 

From this, can you determine how many arc seconds are in one radian?

If you need help, click here.

Now, how many radians are in one arc second?

Click here to learn more about scales and angular measurement.

When we see an object in the sky, it is much smaller than in reality.  If we know the diameter across the object from our point of view and the distance the object is from our point of view, then we can approximately determine how wide the object is in reality.  Look at the picture below.  We can determine how wide an object is by using the relationship,
s = r , where r is the distance from the Earth to the object and is in radians.

For example, the moon is approximately 0.51 degrees across and about 384,000 kilometers from Earth.  Therefore, the moon is approximately, 3418 kilometers.

Now that we know how to determine the size of an object in the sky, let's determine the size of Cas-A based on its X-ray image.  In order to do this, we will have to load the Cas-A image. 

1.)  Determine the number of pixels across the Cas-A
      image (physical).

2.) Each pixel is 0.5 arc seconds.

3.)  Determine the arc seconds across Cas-A.

4.)  Use the approximation that Cas-A is about 9.25 X 10¹⁶
      kilometers from the Earth.  

5.)  Use the relationship above to determine the actual
      length across Cas-A.

What is the length of Cas-A?

How does this length compare to the moon?

Is your answer approximately equal to the answer I obtained?  Click here to see.

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