Astronomy Principles and Practice Fourth Edition.pdf

Solar disc phenomena: practical exercises 433
1 . 1
1 . 0
July 6
July 7
Log R
0 . 9
0 . 8
0 . 7
0 1 2
Sec ζ
Figure 24.21. Data of the apparent solar brightness obtained by a pinhole photometer revealing the sec ζ
dependence from which the zenith extinction is calculated.
as the instrument is adjusted in its pointing direction. When the best value from the detector is achieved,
make a note of it and the time. From data obtained in this way, say at twenty minute intervals, it is
then possible to explore Bouger’s law (section 19.7.2) and determine the local zenith extinction for
the wavelength passband associated with the sensitivity of the detector. This is done by plotting the
logarithm of the readings against the secant of the solar zenith distance calculated from equation (24.1),
namely
cos z = sin φ sin δ ⊙ + cos φ cos δ ⊙ cos H. (24.1)
An example of data obtained from such an exercise is shown in figure 24.21. Equation (19.11)
describes the behaviour of the apparent magnitude (arbitrary system), equivalent to the logarithm of
the signal, with the secant of the zenith as
m(ζ ) = m 0 + m sec ζ.
Extrapolation of the measurements corresponding to ζ = 1 provides a value for m(0) which may also
be expressed as
m(0) = m 0 + m.
Further extrapolation of the measurements to ζ = 0 provides a value for m 0 . Rearranging the previous
equation gives
m = m(0) − m 0 .
For the behaviour of the data displayed in figure 24.21, m(0) = 0·88 and m 0 = 1·02, giving a
value for m =−0·14. It may be noted that such a value for extinction is fairly low with respect to
optical measurements but it must be appreciated that the peak sensitivity of silicon diodes is in the far
red of the spectrum.