I am using a code on EUCLID future mission. The original author of this code has set a value for the density of galaxy equal to :

ng = 354543085.80106884

I think this is expressed in inverse steradian. I think that EUCLID mission has a $30\text{ arcmin}^{-2}$ value for density of galaxies.

Is the conversion correct betweeen $30\text{ arcmin}^{-2}$ and $354543085.8010688 \text{ sr}^{-1}$ ?

and how to do this conversion ?

Indeed, I would like to calculate ng with a density of $48 \text{ arcmin}^{-2}$.



There are 60 arc minutes in a degree and $180/ \pi$ degrees in a radian.

So 1 radian is 57.2957795 degrees or 3437.746771 arc minutes.

As long as you are talking about units, you can square any of these angular units to obtain solid angle units.

So 1 steradian is 3282.80635 square degrees, or 11818102.860 square arc minutes.

Let's try your theory:

1/354543085.801 steradians is 9.259259E-06 square degrees, or 0.0333333 square arc minutes.

The answer is that it is 1/30th of a square arc minute, so YES it is 30 inverse square arc minutes!

Then 48 per square arcminute is:

$$48 \times 60^2 \times \frac{180^2}{\pi^2} \approx 567268937.282 \ \ \text{sr}^{-1}.$$

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