We extend a previously presented magnetotail model [Grzedzielski and Macek, 1988> to great distances in the antisolar direction. For typical solar wind parameters at ~1 AU and the most probable set of parameters of the model as determined for the ISEE 3 region of ~200 Earth radii (RE), the open geotail extends to at least (3--4)¿103 RE downstream from Earth where it forms a cavity filled with a dense (~1 cm-3), hot (≲106 K) plasma and low magnetic field strengths (1.2--0.4 nT). The cross section of this cavity in the plane perpendicular to the Earth-Sun line has dimensions of 300--400 RE parallel to the ecliptic plane, but only ~5 RE in the direction normal to the ecliptic. It seems likely that the magnetotail would become filamentary at such distances. Our results indicate that the Phobos spacecraft could have observed tail associated phenomena at distances of ~3900 RE downstream from Earth during a September 1988 transit. We compare model predictions for the characteristics of planetary magnetotails (including Neptune) in our solar system. ¿ American Geophysical Union 1989