"Obliquity of the ecliptic for 20,000 years, calculated by Laskar (1986) reflects change from 24.2° to 22.5°.
Until 1983 the obliquity for any date was calculated from work of Newcomb, who analyzed positions of the planets until about 1895:
ε = 23° 27′ 08″.26 − 46″.845 T − 0″.0059 T2 + 0″.00181 T3
where ε is the obliquity and T is tropical centuries from B1900.0 to the date in question.
From 1984, the Jet Propulsion Laboratory's DE series of computer-generated ephemerides took over as the fundamental ephemeris of the Astronomical Almanac. Obliquity based on DE200, which analyzed observations from 1911 to 1979, was calculated:
ε = 23° 26′ 21″.45 − 46″.815 T − 0″.0006 T2 + 0″.00181 T3
where hereafter T is Julian centuries from J2000.0.
JPL's fundamental ephemerides have been continually updated. The Astronomical Almanac for 2010 specifies:
ε = 23° 26′ 21″.406 − 46″.836769 T − 0″.0001831 T2 + 0″.00200340 T3 − 0″.576×10−6 T4 − 4″.34×10−8 T5
These expressions for the obliquity are intended for high precision over a relatively short time span, perhaps ± several centuries. J. Laskar computed an expression to order T10 good to 0″.04/1000 years over 10,000 years.
All of these expressions are for the mean obliquity, that is, without the nutation of the equator included. The true or instantaneous obliquity includes the nutation."
Source: Wikipedia - Obliquity of the ecliptic
From historical Total Solar Irradiance records there is evident, that the great changes of TSI doesn't correspond to the Axial Tilt.
I could not found how much local solar radiation can be affected by Obliquity. But I have found that local solar radiation is called insolation. "Factors affect insolation (without the effect of the atmosphere):
Angle of the sun
Distance between the sun and the earth
Duration of daylight
The longer the duration of daylight, the more the insolation received per day."