# Observing galaxies: area of sky would I need to survey

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1. Mar 15, 2019 at 10:51 PM

### Cedric Chia

1. The problem statement, all variables and given/known data
Given that there are 10-2 Ellipticals per Mpc3 and my garden telescope can reach to 14 mag. How large an area of sky would I need to survey to find 100 Elliptical galaxies ? (assume the typical absolute magnitude for an Elliptical galaxy is -21 mag).

2. Relevant equations
d=100.2(m-M-25)
n=N/V

3. The attempt at a solution
by substituting m=14 and M=-21 into the first equation I found d=100Mpc,

which indicates the volume of sky I could possibly observed is 4/3⋅π⋅d3 = 4188790 Mpc3,

using the second equation n=N/V , where n=number density, I have 10-2 = 100/V,

thus V=10000Mpc3, which is the volume I need to observed to find 100 galaxies.

with these values, how can I find how large the area of sky I need to survey?

2. Mar 16, 2019 at 9:47 PM

### hutchphd

You have almost finished.... What units are you going to use to report your answer (solid angle, fraction of the hemisphere sphere......)?

3. Mar 17, 2019 at 12:29 AM

### Cedric Chia

How can I find solid angle relative to the 10000MPc3?

4. Mar 17, 2019 at 12:38 AM

### hutchphd

The solid angle for a whole sphere is 4pi....for half sphere 2pi....how much of the sphere do you need to view?

5. Mar 17, 2019 at 12:46 AM

### Cedric Chia

Thank you for the quick reply,

the total volume of the sphere is 4188790 Mpc3
("which indicates the volume of sky I could possibly observed is 4/3⋅π⋅d3 = 4188790 Mpc3")

and the volume I need to view is 10000Mpc3
("thus V=10000Mpc3, which is the volume I need to observed to find 100 galaxies")

with these values how can I find solid angle?

6. Mar 17, 2019 at 6:44 AM

### hutchphd

What fraction of the total sphere volume do you need to observe?

7. Mar 17, 2019 at 7:06 AM

### Cedric Chia

I think that would be (volume I need to observe) / (total sphere volume) = (10000) / (4188790) = 2.39⋅10-3

8. Mar 17, 2019 at 7:18 AM

### hutchphd

9. Mar 17, 2019 at 7:42 AM