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.
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.
2 points
Two distinct (different) points are needed to determine a line.
Two
2
A line contains an infinite number of points but it takes only two points to determine a line.
If 2 points determine a line, then a line contains infinitely many planes.
You need two points to determine a line. A single point can have an infinite number of lines passing through it.
2
It takes exactly 2 distinct points to uniquely define a line, i.e. for any two distinct points, there is a unique line containing them.
A plane can be determined by three points, as long as the three points do not lie along a single line.
If you were to have 3 points on the same line, then you would actually not be determining a plane, because there are infinitely many planes that can intersect a given line. But if you have 3 points in the form of the points (or vertices) of a triangle, then you determine a plane in the sense that there is only one possible plane upon which that triangle can be drawn (not including a degenerate triangle, which is equivalent to a line).