Astronomy time required to capture exposures problem

[Jaco Leo]

Homework Statement

If you have a large telescope that has a 5 meter diameter with a field of view of 1 foot by 1 foot, and a small telescope with a diameter of 1 meter with a field of view of 1 degree by 1 degree, and your trying to take images of 30 quasars that has a limiting visual magnitude of 20 that are randomly distributed over a 5 degree by 5 degree field where it takes 10 minutes to capture a single quasar image. How long will it take for each telescope to take the image of the 30 quasars?

Homework Equations

For relevant equations, I'm not sure if these will help and really this is the part I'm having trouble with, trying to figure out what equations or if any I need any of these.

• (soild angle) = area/(radius)^2
• (Etendue) = A(mirror area) X (soild angle field of view)
• SurveyTime is proportional to Field of View
• SurveyTime is proportional to Field of View X collecting area = (Etendue)

The Attempt at a Solution

For the small telescope I have... Area = 0.785398 m^2 and for the large telescope...Area = 19.63 m^2, so from this I found that the area of the large telescope is 25 times the area of the small. I tryed to convert the field of view of the large telescopes feet to degrees and I got 0.016 degrees by 0.016 degrees. I am not sure how to use this information to find the actual time it will take each telescope to take the images of 30 quasars each taking 10 minutes a piece, any help would be much appreciated, thanks!

 

[anathema]

Hello,

Thank you for your question. Based on the given information, we can calculate the solid angle and etendue for each telescope.

For the small telescope:
Solid angle = (1 degree x 1 degree) / (1 meter)^2 = 0.0002778 steradians
Etendue = (1 meter^2) x (0.0002778 steradians) = 0.0002778 m^2 sr

For the large telescope:
Solid angle = (0.016 degrees x 0.016 degrees) / (5 meters)^2 = 0.0000000512 steradians
Etendue = (19.63 meter^2) x (0.0000000512 steradians) = 0.000001004 m^2 sr

Next, we can use the equation Etendue = (field of view) x (collecting area) to calculate the field of view for each telescope:
Small telescope: Field of view = 0.0002778 m^2 sr / 0.0002778 m^2 = 1 degree x 1 degree
Large telescope: Field of view = 0.000001004 m^2 sr / 19.63 m^2 = 0.0000000512 degrees x 0.0000000512 degrees

Now, we can use the equation SurveyTime ∝ Field of View x Collecting Area to calculate the survey time for each telescope:
Small telescope: Survey time = (1 degree x 1 degree) x (0.785398 m^2) = 0.785398 minutes
Large telescope: Survey time = (0.0000000512 degrees x 0.0000000512 degrees) x (19.63 m^2) = 0.000000001 minutes

Therefore, it will take approximately 0.79 minutes for the small telescope and 0.000000001 minutes (or 0.00000006 seconds) for the large telescope to take images of 30 quasars with a limiting visual magnitude of 20.

I hope this helps. Let me know if you have any further questions. Good luck with your research!