Recently I found myself wanting to find the chart that gives the number of stars that can be seen brighter than a given magnitude. After some minutes of unsuccessful searching on the web, I decided to reinvent the wheel using data from HIPPARCOS. For those who may be interested, here are my results (where V is the limiting magnitude, and N is the number of stars brighter than V):
| Magnitude (V) |
Number of Stars (N) |
Comments |
| -1 |
1 |
Sirus (-1.44) |
| 0 |
4 |
Sirius, Canopus, Alpha Centauri, Arcturus |
| 1 |
15 |
Sirius,
Canopus, Alpha Centauri, Arcturus, Vega, Capella, Rigel, Procyon, Achernar, Hadar, Altair, Betelgeuse, Aldebaran, Acrux, Spica |
| 2 |
49 |
|
| 3 |
172 |
|
| 4 |
507 |
1/100 as bright as Sirius |
| 5 |
1597 |
|
| 6 |
4977 |
Limit of human eye |
| 7 |
15373 |
|
| 8 |
45492 |
|
| 9 |
130400 |
Visible in regular binoculars |
| 10 |
360272 |
Visible in 2 inch telescope |
| 11 |
882935 |
Visible in 3 inch telescope |
Beyond 11th magnitude, the Hipparcos data is incomplete. So to estimate the number of stars at fainter magnitudes, I plotted log10N vs. V and did a second-order polynomial fit to come up with the following empirical relationship between N and V:
N = 10(-0.0064V^2 + 0.5589V + 0.5928)
or, if you prefer:
log10N = -0.0064V2 + 0.5589V + 0.5928
so to continue the table above by extrapolation:
| Magnitude (V) |
Number of Stars (N) |
Comments |
| 12 |
2387811 |
Requires 1.2m telescope |
| 13 |
5982738 |
Requires 1.8m telescope |
| 14 |
14554591 |
Requires 3m telescope |
| 15 |
34379535 |
Requires 4.5m telescope |
| 16 |
78849692 |
Requires 7.5m telescope |
In other words, there are about 79 million stars brighter than 16th magnitude.
Note that each magnitude step is 2.512 times fainter than the previous.
By comparison, the brightest planet Venus varies in brightness and is about -4.4 magnitude at maximum brightness, and Jupiter is about -2.2. The Moon is -12.7 magnitude at maximum brightness and the Sun is -26.75.
Adapted from a Dome-L message posted by Chris Anderson of the Faulkner Planetarium and Herrett Centennial Observatory, January 2004