Eq. 10 was solved for the GSM and the GDM scheme. Fig. 4 shows the evolution of the global temperature under increasing insolation
(Eq. 2). Up to 1 Ga into the future, the temperature varies only within an interval of 
C to 
C. This
stabilization of the surface temperature is a result of the carbonate-silicate self-regulation within the Earth system. In contrast to the GSM approach, the GDM scheme shows a
temperature stabilization at a higher level in the past and a
lower one in the future.
Figure 4: Surface temperature for the GSM and GDM scheme.
The terrestrial life corridor TLC can be defined in the following way:
Then we get the following picture of the Earth system evolution (see Fig. 5).
Figure 5: Terrestrial life corridor for GSM and GDM.
Besides calculating the TLC, i.e., the evolution of atmospheric carbon regimes supporting photosynthetis-based life in time, we calculated the behaviour of our virtual Earth system at various distances from the Sun, using different insolations.
If R denotes the distance from the Sun insolation S is rescaled to
The habitable zone (HZ) can be defined by the interval , where the biologic productivity is greater than zero, i.e., the planet is within the TLC. Fig. 6 shows the HZ for the GDM and the GSM model.
Figure 6: Habitable zones for GSM and GDM.
For the geostatic case (GSM) the width of the HZ slightly
increases and shifts outward over time. In about 1 Ga the
inner boundary reaches the Earth distance from the Sun (R =
1 AU) and the biosphere ceases to exist. The GDM shows
both a shift and a narrowing of the HZ: the inner boundary
reaches the Earth distance in about 600 Ma from now, while
the outer boundary decreases in a strong nonlinear way. An
optimum distance from the Sun can be identified ( 
AU), where the life span would be extended to 
Ga.
