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The DESI Legacy Imaging Surveys says it produces a model of “the 14,000 square degrees of extragalactic sky visible from the northern hemisphere”. But I thought the whole celestial sphere (like any other sphere) had only $(180/\pi)^2 \approx 3282.8$ square degrees. How should I understand this? Is this counting each of the 7 bands it scans in (in which case it’s an average of 62% of the whole sky)?

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The whole sphere has approximately 41,253 square degrees of solid angle. $$4\pi\left(\frac{180}{\pi}\right)^{2}\approx 41,253$$ so for a hemisphere there should be half this number or about 20,627 deg2. I think you computation is missing the $4\pi$ steradians in a sphere term.

This doesn't solve the disparity however. Perhaps the key is the term "extragalactic sky" that is used in the referenced web page. Is there a cutout in the coverage to account for the Milky Way?

For further reference see square degree at Wikipedia.

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    $\begingroup$ Extragalactic surveys will miss out a strip around the Galactic plane where extinction is high. $\endgroup$
    – ProfRob
    Commented Jan 16, 2022 at 14:08
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    $\begingroup$ Thanks for this… it’s a dumb mistake I made, but I should probably leave this up for others who do the same thing. $\endgroup$
    – Charles
    Commented Jan 16, 2022 at 16:53
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    $\begingroup$ @Charles in nice sites like this that's laudable. In less-nice sites it's sometimes necessary to delete to avoid a deluge of pile-on silent down votes. :-) $\endgroup$
    – uhoh
    Commented Jan 16, 2022 at 21:57
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    $\begingroup$ It's worth adding that the value OP has computed (3282.8) is the number of square degrees per steradian and not for an entire sphere. $\endgroup$
    – J...
    Commented Jan 17, 2022 at 16:50
  • $\begingroup$ 41 square degrees for the whole sphere doesn't sound right. It's as if there can only be about 82 non-overlapping full-Moon objects in the sky, which is too few to be true. $\endgroup$
    – Ruslan
    Commented Jan 18, 2022 at 11:16
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GrapefruitIsAwesome has already explained why the sky is significantly larger than 3300 square degrees; I'd like to explain why the sky coverage is precisely the value it is.

The wording is admittedly not ideal. The portion of the sky visible to the surveys are limited by 1) dust in the Galactic plane that prevents them from observing extragalactic sources beyond it, and 2) the finite declination range of a given telescope, arising from both its latitude and the limits on its elevation range.

Dey et al. 2019 provide basic parameters of the DESI surveys; that $\approx14,000$ deg$^2$ area is defined to be the portions of the sky with galactic latitudes above $15^{\circ}$ (the Galactic plane at work) and declinations of $\delta>-20^{\circ}$ (the limit imposed by the position of Kitt Peak, one of the observing sites). Dust in the plane actually cuts this into two separate regions, the North Galactic Cap and the South Galactic Cap, which together have the total area listed. Even this is in fact slightly modified even further, to "minimize scheduling issues" and to avoid regions with more stars - not an excellent thing to have in an extragalactic survey.

Here's what this ultimately looks like (Fig. 1, Dey et al.), with the regions surveyed outlined in red. The other shading and labels denote coverage by other spectroscopic surveys.

Image showing northern sky (and part of the southern sky) covered by DESI, which appears as two separate chunks.

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