We investigate the effects of varying Saturns orbit on the atmospheric circulation and surface methane distribution of Titan. Using a new general circulation model of Titans atmosphere, we simulate its climate under four characteristic configurations of orbital parameters that correspond to snapshots over the past 42 kyr, capturing the amplitude range of long-period cyclic variations in eccentricity and longitude of perihelion. The model, which covers pressures from the surface to 0.5 mbar, reproduces the present-day temperature profile and tropospheric superrotation. In all four simulations, the atmosphere efficiently transports methane poleward, drying out the low- and mid-latitudes, indicating that these regions have been desert-like for at least tens of thousands of years. Though circulation patterns are not significantly different, the amount of surface methane that builds up over either pole strongly depends on the insolation distribution; in the present-day, methane builds up preferentially in the north, in agreement with observations, where summer is milder but longer. The same is true, to a lesser extent, for the configuration 14 kyr ago, while the south pole gains more methane in the case for 28 kyr ago, and the system is almost symmetric 42 kyr ago. This confirms the hypothesis that orbital forcing influences the distribution of surface liquids, and that the current observed asymmetry could have been partially or fully reversed in the past. The evolution of the orbital forcing implies that the surface reservoir is transported on timescales of $sim$30 kyr, in which case the asymmetry reverses with a period of $sim$125 kyr. Otherwise, the orbital forcing does not produce a net asymmetry over longer timescales, and is not a likely mechanism for generating the observed dichotomy.
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