You can think of a lens focused at inifinity as simply a pinhole for the purpose of figuring out what gets projected where.  Consider this simplified diagram of a camera:



The box is the camera, the fat line on the left the image plane (where the sensor or film is), and the small hole at right represents the effective point thru which the lens projects the outside view onto the image plane.  In this drawing, F is the focal length and S is the size of some projection onto the image plane.  From basic high school geometry, the tangent of the view angle is S/F:

&nbsp;&nbsp;tan(Ang) = S/F

Therefore obviously

&nbsp;&nbsp;Ang = arctan(S/F)

Yes, it really is that simple.  You didn't say how big the sensor is in your camera, so I'll use a 35mm frame, which is 36x24mm.  The largest circle it can fit is therefore 24mm in diameter or 12mm in radius.  You say your final effective focal length is 1300mm.  Arctan(12mm/1300mm) = 0.529&deg;.  That was the angle from the center to the edge, so double that to make the total view angle of the largest circle on your sensor, which is 1.06&deg;.

To put this in perspective, the view angle of the moon is about 0.5&deg; (it varies, but this is within its variation).  That means for a 1300mm lens and a "35mm" sensor, the moon will fill about half the height of the image.

For a cropped sensor, it would appear bigger.  Actually, the projection of the moon onto the sensor is the same regardless of how big the sensor is, but for a smaller sensor it takes up a proportionately bigger portion of the frame.  This would be reflected in the equations above in that the 12mm value would be smaller, since this was the radius of the largest circle that could fit into the sensor frame.

Also note that the simplified geometry of a camera diagrammed above works for the effective focal length.  This will be the actual focal length when the lens is focused at infinity, but can be different when the lens is focused close, depending on the lens design.  However, you are asking about astrophotography, so the focus will always be at infinity and I won't go into that further.

How to calculate the size of the image circle at infinity focus?
We've found that our users have almost universally benefited from actually going through our walkthrough. Obviously, we have some more ux work to do on our service. But, based on this information, we decided to force users through the short walkthrough in the interim. Somewhat unsurprisingly, people have protested a bit :) So, what do you think, is it ok to force users through a brief walkthrough when you know it will benefit them in the end?

Edit
We are going to add some mixpanel hooks to find out if users are leaving when presented with a walkthrough they can't exit out of.
