I think this would happen if L1 was a stable lagrange point, like L4 and L5. That's not the case though, L1, L2 and L3 are unstable. To put it differently, igno

I think this would happen if L1 was a stable lagrange point, like L4 and L5. That's not the case though, L1, L2 and L3 are unstable. To put it differently, ignoring the centrifugal force, at L1 the gravitational pull of Mars is equal to the gravitational pull of the Sun; when you move the sail towards Mars, the pull towards Mars increases, the one towards the Sun decreases, and the resultant points in the same direction as the pressure on the sail (i.e. towards Mars). Nothing is balanced, in the end the sail falls towards Mars.