Teilo wrote:
Could anyone tell me how to calculate the position of the sunrise at
the winter sostice for a particular latitude. Thanks

Assuming this isn't homework, use this formula:

azimuth = 90° +/- arcsin(sin(23.4°)/cos(latitude))

where +/- 23.4 degrees is the declination of the Sun at the solstices.
(It isn't that, exactly, but close enough for our purposes.) I use the
north = 0, east = 90 convention.

Thus, for instance, for your latitude of 52 degrees (north, I assume),
the formula yields

azimuth = 90° +/- arcsin(0.397/0.616)
= 90° +/- arcsin(0.645)
= 90° +/- 40°

If you're in the northern hemisphere, azimuth of the sunrise is thus 50
degrees at the summer solstice and 130 degrees at the winter solstice;
if you're in the southern hemisphere, it's vice versa. Note that at
latitudes above 66.6 degrees in either hemisphere (in the Arctic and
Antarctic circles, in other words), the argument of the arcsin function
is above 1, and the formula correctly indicates that the Sun does not
rise at all at the winter solstice.

Some calculators/computers use radians instead of degrees; if so, be
sure to take care with your units. Pi radians equal 180 degrees; or to
put it another way, one radian equals about 57.3 degrees.

This formula neglects two effects of some importance: refraction, and
the fact that in many places, sunrise is defined as the moment at which
the Sun's disc first peeks over the ideal horizon, not when its center
does. At temperate latitudes, the combined impact is to decrease the
azimuth of sunrise by a bit less than a degree in the northern
hemisphere, and to increase it by the same amount in the southern
hemisphere.

--
Brian Tung
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