We show here that the relative motion of the solar system with respect to the ambient interstellar plasma enforces a clearly pronounced upwind/downwind momentum flow asymmetry in the shocked solar wind. With the help of an analytic description of this subsonic flow regime taken from Parker (1963, Interplanetary Dynamical Processes. Interscience, New York) we were able to quantitatively determine the expected momentum flow asymmetries and the forces exerted on closed surfaces from which such a flow is originating. Assuming that the up/down asymmetry can be forwarded from the subsonic to the supersonic solar wind through the heliospheric shock by that wind component behaving subsonically everywhere, i.e. electrons, we arrive at corresponding asymmetric outer boundary conditions which the adapted supersonic solar wind solutions have to match. We shall prove in this paper that via the subsonic solar wind electrons, the solar wind expansion actually realized can be strongly influenced by the asymmetric outside LISM momentum flow conditions. Though this situation cannot be consistently treated with existing solar wind models, we nevertheless want to give an idea of its consequences. With the help of a conventional two fluid solar wind model we produce such solutions here that in a quantitative form show longitudinal solar wind asymmetries even in the region between the coronal basis and the Earth's orbit. In order to confirm the existence of such asymmetries we propose to monitor the solar wind momentum flow along the orbit of the Earth. We also calculate the braking rate of the solar system connected with such a momentum flow.