How big is the Hubble Ultra Deep Field image? (Intermediate)

I think the Hubble Ultra Deep Field photo is amazing ... the implied numbers of galaxies and stars are mind-boggling, and hence my question.

The field of the HUDF is said to be about 1/10 the diameter of a full moon. To put the possibilities in perspective of a number that might be a little more comprehensible, how many photos that size (1/10 the Moon's diameter) would it take to cover the entire sphere of the sky?

The answer to this question relies on something called angular size, which shows up all over in astronomy. In astronomy, it often happens that you are looking at a picture of something and you don't know how far away it is, so you can't say accurately how big it really is. However, you know how big it looks. If you measure the angle between two lines that stretch from your eye out to both edges of the thing you're looking at, that is the object's angular size.

Angular size is given in units of degrees, arcminutes and arcseconds. Most of us are used to measuring angles in degrees: there are 360 degrees in a circle, the angles of a triangle add up to 180 degrees, etc. Minutes and seconds are just smaller units of angle. There are 60 arcminutes in a degree, and 60 arcseconds in one arcminute.

To measure the area of something on the sky, we use square degrees, square arcminutes, etc. These are more complicated than normal "square" units that we're used to (such as square inches or square miles). Square arcminutes have to account for the fact that when we deal with angular size, it is as if everything has been projected onto the surface of a sphere, so there is some curvature. It turns out that the sphere of the sky is 41,253 square degrees. This corresponds to 148,510,800 square arcminutes.

According to the Space Telescope Science Institute, the Hubble Ultra Deep Field has an angular size of 11.5 square arcminutes. That means that it would take 12,913,983 Deep Field images to cover the entire sphere of the sky!

Just for fun, let's calculate roughly how many stars that implies in the observable universe: The ultra deep field image has about 10,000 galaxies in it. If we assume that each galaxy has 100,000,000,000 (100 billion) stars, then the approximate number of stars in the visible universe is absolutely staggering: 123,000,000,000,000,000,000

123 quintillion stars! That's 123 billion billion. 123 million million million.

It is easy to get lost in these mind-boggling numbers. They are so overwhelmingly huge that the human mind cannot rationalize them. But at the very least, we can get a sense of things. The Ultra Deep Field shows us just how big the universe is and how small and fragile we all are.