In a two-particle system where both particles have equal mass, the center of mass of the system lies exactly halfway between the two particles.
The center of mass is a point that represents the average position of the entire system, taking into account the mass and distribution of the particles. For a system with two particles of equal mass, the center of mass will be located at the midpoint between the particles along the line connecting them.
Mathematically, if the two particles are located at positions (x1, y1, z1) and (x2, y2, z2), then the coordinates of the center of mass (x_cm, y_cm, z_cm) can be calculated using the following formulas:
x_cm = (x1 + x2) / 2 y_cm = (y1 + y2) / 2 z_cm = (z1 + z2) / 2
So, the center of mass will lie exactly halfway between the two particles, regardless of the specific coordinates or orientation of the system.