A053406 Number of stars brighter than visual magnitude n-1.

1, 4, 15, 49, 172, 511, 1600, 4968, 15328, 40858, 82484, 106963, 114376, 116592, 117100, 117127, 117128, 117129

Offset

0,2

Comments

These numbers are not well-defined and the sequence is included only for completeness.

The visual magnitude (m) scale is logarithmic: for two stars of brightness i1 and i2 (as seen from the Earth), the magnitude difference m1 - m2 = - log(i1/i2)*100^(1/5). Fainter stars have a higher magnitude number. Data collected by the Hipparcos satellite and exhaustive up to about 9 mag (n=10). At fainter magnitudes (n > 10), the data are increasingly fragmentary (thus the slowing rate of increase from there).

Links

Table of n, a(n) for n=0..17.

Author?, Source [Broken link?]

Author?, Source [Broken link?]

Formula

a(n) would be proportional to 10^(0.6*n) in the simplifying hypothesis of a uniform distribution of identical stars in an infinite universe. Any empirical formula matching the actual sequence for n=0 to 10 is welcome.

Example

There is 1 star brighter than -1 mag (Sirius, -1.44 mag). There are 4968 stars brighter than 6 mag, which is about the faintest brightness visible to the naked eye.

Crossrefs

Cf. A072171.

Sequence in context: A178704 A099167 A056337 * A225265 A143215 A301973

Adjacent sequences: A053403 A053404 A053405 * A053407 A053408 A053409

Keyword

nonn,dumb

Author

Jean Fontaine (jfontain(AT)odyssee.net), Jan 08 2000

Status

approved