Reduced Mass Calculator

Try the reduced mass calculator to easily calculate the reduced mass in a two-body problem.

Reduced mass9.10443e-28 galways smaller than either mass — 99.95% of the lighter one

Total mass1.67353e-24 g

Centre of mass0.00147 mmeasured on the same scale as the positions you gave

Distance from the first mass0.00147 m0.05% of the way to the second

Distance from the second mass2.69853 m

Mass split99.95% / 0.05%the centre of mass sits closer to the heavier one, in inverse proportion to the distances

Load at the first position1.64e-26 Ntreating the separation as a wheelbase and the centre of mass as the load point

Load at the second position8.933e-30 N

Front to rear distribution99.95% / 0.05%

Reduced mass if the masses were equal4.18383e-25 ga quarter of the total, which is the maximum a reduced mass can ever reach

Reduced mass with an infinitely heavy partner9.10938e-28 git tends to the lighter mass — which is why a planet orbiting a star can be treated as if the star were fixed

The formula

reduced mass = m₁m₂ ÷ (m₁+m₂); centre of mass = Σmx ÷ Σm

Two bodies become one

Reduced mass is the trick that turns a two-body problem into a one-body problem. Two masses orbiting each other behave exactly like a single body of reduced mass m₁m₂/(m₁+m₂) orbiting a fixed point, which is why the same formula appears in orbital mechanics, collision physics and molecular vibration.

It is always smaller than either mass, and it has two useful limits. When the masses are equal it is a quarter of the total, which is the largest it can ever be. When one mass hugely exceeds the other it tends to the lighter mass alone — which is the justification for treating the Sun as stationary while a planet orbits it.

Centre of mass is the weighted average of position, and it sits closer to the heavier body in inverse proportion to the distances. In vehicle terms that is weight distribution: the axle nearer the centre of mass carries more load, and the split between them is what the figures above compute.