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The National Aeronautics and Space Administration (NASA), Jet Propulsion Laboratory (JPL)-deep space network (DSN) subnet of 34-m beam waveguide (BWG) antennas was recently upgraded with Ka-band (32-GHz) frequency feeds for space research and communication. For normal telemetry tracking a Ka-band monopulse system is used, which typically yields 1.6-mdeg mean radial error (MRE) pointing accuracy on the 34-m diameter antennas. However, for the monopulse to be able to acquire and lock, for special radio science applications where monopulse cannot be used, or as a back-up for the monopulse, high-precision open-loop blind pointing is required. This paper describes a new 4th order pointing model and calibration technique, which was developed and applied to the DSN 34-m BWG antennas yielding 1.8 to 3.0-mdeg MRE pointing accuracy and amplitude stability of 0.2 dB, at Ka-band, and successfully used for the CASSINI spacecraft occultation experiment at Saturn and Titan. In addition, the new 4th order pointing model was used during a telemetry experiment at Ka-band (32 GHz) utilizing the Mars Reconnaissance Orbiter (MRO) spacecraft while at a distance of 0.225 astronomical units (AU) from Earth and communicating with a DSN 34-m BWG antenna at a record high rate of 6-megabits per second (Mb/s).