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Tog
2010-Jan-13, 07:34 AM
Because of the nightly calls from the owner of the place where I work, I have to repeatedly go over the same topics time and time again. One of the current ones is about the number of galaxies in the universe.

The Hubble Deep Field image was an area of 2.5 arcminutes, according to Wiki. I'm wondering what percentage fo the sky that really covers.

The way I've worked it out is to multiply the 360 horizontal axis by the 360 degree vertical axis, then convert to square arcminutes. This gives me 466,560,000 square arcmin.
Then I take the 2.5 arcmin of the image, and square it to get the area (6.25) and divide.

That gives me 74,649,600 images the size of the HDF to cover the entire sky at that resolution. Is this correct?

ngc3314
2010-Jan-13, 07:53 AM
If you include the fact that the geometry is spherical rather than planar, there are about 42,000 square degrees on the surface of a sphere. Folding that in, it would take only about 24.2 million 2.5-arcminute-square fields to cover it all.

hhEb09'1
2010-Jan-13, 11:40 AM
Because of the nightly calls from the owner of the place where I work, I have to repeatedly go over the same topics time and time again. One of the current ones is about the number of galaxies in the universe.They keep calling about how many galaxies are in the universe? What odd behavior. :)


That gives me 74,649,600 images the size of the HDF to cover the entire sky at that resolution. Is this correct?As ngc3314 says, you have to take into account the spherical nature of the beast, so your answer is too high by pi: 74,649,600 / pi = 23761706, so about 24 million

Veeger
2010-Jan-13, 12:04 PM
The planar area would be 360 x 180 = 64800 sq. degrees or 23238000 square arcminutes. In spherical geometry this is 20626.48 degrees or 7425533 arcminutes.

Tog
2010-Jan-13, 01:46 PM
Ah, okay. That makes sense. Thanks.

This is one topic of many, and not even some of the odd ones.

hhEb09'1
2010-Jan-13, 04:27 PM
In spherical geometry this is 20626.48 degrees or 7425533 arcminutes.Twice that, actually (Solid angle wiki (http://en.wikipedia.org/wiki/Solid_angle)). Close to ngc3314's 42,000. Not sure where you lost the two. :)

Veeger
2010-Jan-13, 06:24 PM
Probably because I was thinking of what an earth bound observer sees rather than a space telescope with no horizon.

Centaur
2010-Jan-13, 09:01 PM
Because of the nightly calls from the owner of the place where I work, I have to repeatedly go over the same topics time and time again. One of the current ones is about the number of galaxies in the universe.

The Hubble Deep Field image was an area of 2.5 arcminutes, according to Wiki. I'm wondering what percentage fo the sky that really covers.

The way I've worked it out is to multiply the 360 horizontal axis by the 360 degree vertical axis, then convert to square arcminutes. This gives me 466,560,000 square arcmin.
Then I take the 2.5 arcmin of the image, and square it to get the area (6.25) and divide.

That gives me 74,649,600 images the size of the HDF to cover the entire sky at that resolution. Is this correct?

As others have noted we’re dealing with the celestial sphere, which is not a plane. The area of a sphere is 4πrē. Therefore in square radians (steradians) its area is simply 4π. In square degrees this becomes 41,253 or in square arcminutes 148,510,660. An area of 2.5 square arcminutes would be 1 / 59,404,264 of the celestial sphere. If 2.5 arcminutes is actually the linear dimension, then as you note the area would be 6.25 square arcminutes, which is 1 / 23,761,706 of the celestial sphere. That's in agreement with hheb09’1’s calculation.

joema
2010-Jan-14, 03:37 PM
Note that Google can do these conversions directly from the query window. E.g,:

Query: 41253 square degrees IN square arc minutes
Returns: 41 253 (square degrees) = 148 510 800 square arc minutes

For some reason it won't convert between square degrees and steradians, which is:

1 sq. degree = (pi/180)^2 = 0.00030461742 steradian,

however you can directly enter those notations and Google will do the math, e.g,

Query: (pi/180)^2
Returns: (pi / 180)^2 = 0.00030461742