GNSS positioning relies on orbit and clock information, which is predicted on ground and transmitted by the individual satellites as part of their broadcast navigation message. The predictions are typically refreshed at least once per day and partitioned into short-arc ephemeris data sets covering a representative validity period of 0.5-4 h. For an increased autonomy of either the space or user segment, the capability to predict a GNSS satellite orbit over extended periods of up to two weeks is studied. A tailored force model for numerical orbit propagation is proposed that offers high accuracy but can still be used in real-time environments. Aside from Earth-orientation parameters, six state vector components and three empirical solar radiation pressure parameters are employed for each satellite and adjusted to past orbits. Using the Galileo constellation with its high-grade hydrogen maser clocks as an example, global average signal-in-space range errors of less than 25 m RMS and 3D position errors of less than about 50 m are demonstrated after two week predictions in 95% of all test cases over a half-year period. The autonomous orbit prediction model thus enables adequate quality for a rapid first fix or contingency navigation in case of lacking ground segment updates.