Infinitely many. The trajectory of a typical space mission may be adjusted several hundred times and all these changes need to be accommodated in the set of points.
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To determine a trajectory line, only two points are needed. These two points can be used to calculate the slope, which represents the direction and angle of the trajectory. Additional points can be used to further refine the trajectory line and estimate its accuracy.
The answer depends on the sort of trajectory. If it isthe trajectory of a projectile, affected only by gravity then 3 points are enough. As soon as you add other forces: such a drag or continued propulsion, the number of points required increases.
Two distinct (different) points are needed to determine a line.
2 points determine a line.
A plane can be determined by three points, as long as the three points do not lie along a single line.
3 points which do not all lie on the same line.