Reduced Mass Calculator
Calculate the reduced mass of a two-body system for simplified physics problems
Calculate Reduced Mass
Mass of the first object in the two-body system
Mass of the second object in the two-body system
Reduced Mass Results
Formula used: μ = (m₁ × m₂) / (m₁ + m₂)
Input masses: m₁ = 0 kg, m₂ = 0 kg
Properties: μ ≤ min(m₁, m₂) and μ ≤ (m₁ + m₂)/2
Example Calculations
Earth-Sun System
Earth mass (m₁): 5.972 × 10²⁴ kg
Sun mass (m₂): 1.989 × 10³⁰ kg
Calculation: μ = (5.972×10²⁴ × 1.989×10³⁰) / (5.972×10²⁴ + 1.989×10³⁰)
Result: μ ≈ 5.972 × 10²⁴ kg ≈ 1 Earth mass
Hydrogen Atom (Proton-Electron)
Proton mass: 1.673 × 10⁻²⁷ kg
Electron mass: 9.109 × 10⁻³¹ kg
Reduced mass: μ ≈ 9.105 × 10⁻³¹ kg ≈ 0.9995 mₑ
Physics Applications
Orbital Mechanics
Planetary and satellite orbits
Atomic Physics
Hydrogen atom and molecular systems
Binary Stars
Double star systems and dynamics
Quantum Mechanics
Two-particle quantum systems
Key Properties
Always smaller than both individual masses
Symmetric: μ(m₁,m₂) = μ(m₂,m₁)
Approaches smaller mass when masses differ greatly
Equals m/2 when both masses are equal
Understanding Reduced Mass
What is Reduced Mass?
Reduced mass is a physical quantity that allows us to convert a two-body problem into an equivalent one-body problem. Instead of tracking two objects affecting each other, we can analyze the relative motion using a single effective mass.
Why Use Reduced Mass?
- •Simplifies complex two-body dynamics
- •Enables analytical solutions for orbital problems
- •Essential for quantum mechanical calculations
- •Separates center-of-mass and relative motion
Mathematical Formula
μ = (m₁ × m₂) / (m₁ + m₂)
- μ (mu): Reduced mass
- m₁: Mass of first object
- m₂: Mass of second object
Alternative form: 1/μ = 1/m₁ + 1/m₂
Physical Interpretation
The reduced mass represents the effective mass that would produce the same relative motion between two objects as if one object were fixed and the other moved with mass μ.