Talk:Polaris

The figure for the semimajor axis of the companion, given as 5 AU, is obviously in error. Here's why: a = cuberoot of the total mass times the period squared (say, 30 years). For any reasonable value of M (which can hardly be less than 10 times our sun's, given the luminosity of Polaris A), the size of the orbit comes out at about the distance of Pluto from the sun--not Jupiter!--for having extra mass in the system, causes them to revolve FASTER.

Addendum. When i wrote the foregoing, i didn't have precise figures for Polaris's mass. By the Cepheid relation M = .58 + .24 log P (in days) the mass of the primary should be about 5.29 times the Sun (not 8 to 10, which is more typical of a F-type supergiant of this luminosity). Assuming for the moment that the unseen companion is about 300 times dimmer than the visible primary, this comes out to a mass ratio of about Ma/Ma+Mb of 0.75; & the semimajor axis is 18.35 Astronomical Units (or 18.7, if you use Burnham's period of 30.5 years)...more like the distance of Neptune. (Its eccentricity takes the two stars from 7 to 29 AU separation.) The displacement of the primary amounts to about 4.58 AU, or 426 million miles, presumably the source of the quoted figures (with 290 million miles, given by Burnham, the mass of the companion becomes very small indeed). But this is a small portion of the entire orbit.

This is a good subject for calculating derived figures on, for the values derived from Cepheid equations can be tallied with the observed type F3 main sequence third star; thus the range of distances possible is fairly narrow, in comparison with many other supergiant stars, e.g. Canopus or Rigel.