Reduced mass

Reduced mass is the effective mass of two interacting bodies for their relative motion. It equals the product of their masses divided by their sum, reducing the two-body problem to one body in a central potential.

Center of mass: The mass-weighted average position of a system, whose motion tracks the system as a whole. Separating center-of-mass motion from relative motion produces the coordinate governed by reduced mass.
Inertial mass: A measure of how strongly an object's acceleration resists an applied force. The two inertial masses combine into the effective mass for relative acceleration.
Hydrogen atom: The simplest atom, consisting of one proton bound to one electron. Its electron–proton relative motion uses a reduced mass slightly below the electron mass.
Total mass: The sum of the masses of all bodies in a system. It governs center-of-mass motion, whereas reduced mass governs relative motion.
Relative coordinate: The vector difference between the positions of two bodies. Reduced mass multiplies the acceleration associated with this coordinate.
Newton's second law: The law stating that net force equals mass times acceleration. Applying it to each body yields the reduced-mass equation for relative motion.
Rydberg formula: A formula giving the wavelengths of spectral lines emitted or absorbed by hydrogen-like atoms. Using the electron–nucleus reduced mass accounts for the isotope-dependent spectral scale.
Rest mass: The invariant mass of a physical object or system, independent of its reference frame. Reduced mass is a dynamical combination of two masses, not the invariant mass of their combined system.
Two-body problem: The problem of predicting the motion of two bodies interacting with each other. Reduced mass converts its relative-motion part into a one-body problem.
Momentum: The product of an object's mass and velocity, a conserved quantity in isolated systems. Conservation of total momentum separates the system's overall motion from its internal motion.

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