A paper describes algorithms for guidance and control (G&C) of a spacecraft maneuvering near a planet, moon, asteroid, comet, or other small astronomical body. The algorithms were developed following a model- predictive-control approach along with a convexification of the governing dynamical equations, control constraints, and trajectory and state constraints. The open-loop guidance problem is solved in advance or in real time by use of the pseudo-waypoint generation (PWG) method, which is a blend of classical waypoint and state-of-theart, real-time trajectory-generation methods. The PWG method includes satisfaction of required thruster silent times during maneuvers. Feedback control is implemented to track PWG trajectories in a manner that guarantees the resolvability of the open-loop-control problem, enabling updating of G&C in a provably robust, model-predictive manner. Thruster firing times and models of the gravitational field of the body are incorporated into discretized versions of the dynamical equations that are solved as part of an optimal-control problem to minimize consumption of fuel or energy. The optimal- control problem is cast as a linear matrix inequality (specifically a secondorder cone program), then solved through semi-definite-programming techniques in a computationally efficient manner that guarantees convergence and satisfaction of constraints.