In an orbital system governed by gravity between two primary celestial bodies, how many distinct points of equilibrium (known as Lagrange points) exist?

The correct option is Five.

In an orbital system governed by gravity between two primary celestial bodies, there are exactly five distinct points of equilibrium where a smaller third body can maintain a constant relative position. These locations are known as Lagrange points (labeled L₁ through L₅).

At these equilibrium points, the combined gravitational pull of the two large masses provides precisely the centripetal force required for a small object to orbit together with them.

The five Lagrange points are categorized as follows:
1. Collinear Points (L₁, L₂, L₃): These three points lie along the imaginary line connecting the centers of the two primary bodies. They represent unstable points of equilibrium.
2. Triangular Points (L₄, L₅): These two points form the vertices of equilateral triangles whose base is the line segment connecting the two main bodies. Point L₄ leads the orbit of the smaller primary body by 60°, and L₅ trails it by 60°. These points can form stable points of equilibrium depending on the ratio of the primary masses.

Therefore, a total of Five Lagrange points exist in such an orbital system.