I'm developing a C++ computer library with the formulas in the book "Practical Astronomy with your Calculator or Spreadsheet 4th Edition" but I have a problem with the formula 49, "Sunrise and sunset". I have a problem with something called "vertical shift". In the book says:
We shall take the Sun’s angular diameter to be 0.533 degrees, its horizontal parallax to be 8.79 arcseconds, and the refraction due to the atmosphere as 34 arcminutes and, having added on half of the Sun’s angular diameter and a small correction for parallax, we arrive at a total vertical shift at the horizon of the upper limb of 0.833333 degrees.
To compute the vertical shift I do the following (this is C++ code but it is easy to understand):
// SunAngularDiameter value is in degrees. // SunHorizontalParallax value is in arcseconds. double angularDim = SunAngularDiameter * 60.0; // arcminutes. double parallax = SunHorizontalParallax / 60.0; // arcminutes. // atmosphereRefraction value is in arcminutes. double verticalShift = ((angularDim / 2) + parallax + atmosphereRefraction) / 60.0; // degrees
Using the values given in the book I get that the value of vertical shift (
verticalShift variable) is
0.83560833333333329 but the book said that is must be
I've been wondering how to obtain the value
0.833333 and, if I don't add the
parallax I get it. In other words, to get the vavlue
0.833333 I have to this:
double verticalShift = ((angularDim / 2) + atmosphereRefraction) / 60.0; // degrees
Is this an errata in the book of the correct way to compute the vertical shift is without the parallax?