Gravitational energy, solar radius and solar cycle

A self-consistent approach is used. From the change (1.2 W/m(2)) in the solar constant (1367 W/m(2)) during a solar cycle we deduced a relation between the change in solar radius DeltaR and the depth d = (1 - alpha) R in the convection zone where the expansion starts. A second relation is obtained by equating the gravitational energy required for the expansion and the decrease in luminosity during half a solar cycle. This yields values for DeltaR approximate to 8 km d approximate to 0.96R (super-granular region) and for the change in gravitational energy DeltaE approximate to 10(32) J. Similar considerations are made for the Maunder Minimum yielding DeltaR approximate to 60 km, d approximate to 0.94R and DeltaE approximate to 10(33) J. There is some change, say 40 per cent, if we use a quadratic expansion instead of a linear one. Moreover this theory suits a qualitative explanation why the Sun expands during a minimum of the magnetic activity.