## Estimating Double Star Magnitudes

It is useful to provide estimates of the magnitudes of the components as well as the position angle and separation when measuring double stars. The magnitudes should be estimated to a tenth of a magnitude. A method for estimating the magnitudes is described in the Webb Society Deep-Sky Observer's Handbook, Volume 1, Double Stars (second edition), page 24.

The method is as follows: estimate the difference in magnitude between the two components, then with a low-power eyepiece, so that the double star appears as a single star, estimate the magnitude of the apparently single star. This will give the combined magnitude of the pair. The combined magnitude can be estimated by comparing the star with two other stars of known magnitudes in the field of view, in very much the same way that variable star observers make visual estimates of star magnitudes. (Such a method is described in The Webb Society Deep-Sky Observer's Handbook, Volume 8, Variable Stars, Chapter 3)

From the combined magnitude and the difference in magnitude the individual magnitudes can be determined. Let A and B be the magnitudes of the brighter and fainter components respectively. Let C be the combined magnitude and d be the difference in magnitude, i.e. C = A + B and d = B - A. The magnitudes for the individual components can be found from

A table for the different values of x for different values of d is given in the Webb Society Handbook. The values for x come from the formula x = 2.5 log10(10-04d + 1)

where d is the magnitude difference B - A, not A - B, i.e. d > 0.

The equatorial double 70 Ophiuchi appears as a single star of magnitude 3.8. When resolved through a telescope the components are found to have a magnitude difference of 1.8. The individual magnitudes are then found to be: for the primary, magnitude 4.0 and for the companion, magnitude 5.8

Providing magnitude estimates enables the stars to be monitored for any variation in brightness. Eta Geminorum and Alpha Herculis, for example, are visual binaries which each has a variable component.

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