Radio Telescope Resolution - Centaurus A

[Timiop2008]

Problem:
Centaurus A is 15 million light years away and a radio telescope can resolve structures of 1s of arc across. Show that the Structure is 75 light years across.
Please Help!

 

[mgb_phys]

1 sec of arc is 1 / 60 * 1/60 of a degree.
Imagine a circle 15M light years in radius with you at the centre, what length of the circumference would 1arcsec measure?

 

[thomate1]

I understand your confusion and will be happy to help you with this problem. To begin with, let's define what we mean by "resolution" in the context of radio telescopes. Resolution refers to the ability of a telescope to distinguish between two closely spaced objects. In other words, it is the smallest angular separation at which two objects can be seen as separate entities.

Now, let's apply this concept to the given information. We know that the radio telescope has a resolution of 1s of arc across, which means it can distinguish between objects that are separated by 1s of arc. This can also be written as 1/3600 of a degree (since there are 3600 seconds in a degree).

Next, we need to calculate the actual angular separation between the two objects in question, which are Centaurus A and the structure that is 15 million light years away. This can be done using the formula:

Angular separation = Distance between objects / Distance to the observer

In this case, the distance between Centaurus A and the structure is 15 million light years, and the distance to the observer (i.e. us on Earth) is essentially 0 since we are observing from within our own galaxy. Therefore, the angular separation between Centaurus A and the structure is equal to the distance between them, which is 15 million light years.

Now, let's convert this angular separation into degrees. We know that 1 degree is equal to 3600 seconds, so the angular separation of 15 million light years can be expressed as:

15 million light years * (1 degree / 3600 seconds) = 4167 degrees

Finally, to find the actual size of the structure that we can resolve, we need to multiply the angular separation by the resolution of the radio telescope (1s of arc or 1/3600 of a degree). This gives us:

4167 degrees * (1/3600 of a degree) = 1.16 degrees

Since we know that 1 degree is equal to 60 arc minutes, and 1 arc minute is equal to 60 arc seconds, we can convert the result into arc seconds:

1.16 degrees * (60 arc minutes / 1 degree) * (60 arc seconds / 1 arc minute) = 4176 arc seconds

This means that the structure that we can resolve with the radio telescope is 4176 arc seconds or