Reduced Mass Calculator

Your details

Choose the unit system for both masses. Atomic mass units are standard in molecular spectroscopy; kilograms suit orbital mechanics.
Mass of the first body in your chosen units.
kg
Mass of the second body in your chosen units.
kg
Optional: center-to-center distance between the two bodies. Used only to calculate the moment of inertia I = μr². Set to 0 to skip.
m
Reduced mass (μ)Moderately asymmetric system
72,528,333,846,118,230,000,000kg

The effective single-body mass that captures the relative motion of both bodies

Total mass (M)6,045,420,000,000,000,000,000,000kg
Mass ratio (m₁ / m₂)81.3402
Reduced / Total (μ / M)0.011997
Moment of inertia (I)10,717,030,304,304,153,000,000,000,000,000,000,000,000kg·m²
Reduced mass (μ)72,528,333,846,118,230,000,000
Total mass (M)6,045,420,000,000,000,000,000,000

Reduced mass is 7.2528e+22 kg - the effective one-body mass for this system.

  • The reduced mass (7.2528e+22 kg) is 98.8% of the lighter body - it can never exceed the lighter mass.
  • The reduced mass is 1.20% of the total system mass (6.0454e+24 kg).
  • With a mass ratio of 81.340, both bodies contribute meaningfully to the relative motion. Neither the light-body nor the equal-mass approximation is appropriate here.
  • At the given separation, the moment of inertia about the center of mass is 1.0717e+40 kg·m². This governs rotational energy levels in the rigid rotor model.

Next stepUse this reduced mass in the orbital energy equation E = -G(m₁+m₂)μ / (2a), where G is the gravitational constant and a is the semi-major axis.

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