reduced_mass

Find the reduced mass between two particles.

The reduced mass is given by:

\[μ ≡ \frac{m_1 m_2}{m_1 + m_2}\]

for two objects of mass \(m_1\) and \(m_2\). The reduced mass is used to describe the effective mass in the two-body problem.

Parameters:

test_particle (particle-like) – The test particle as represented by a string, an integer representing atomic number, a Particle object, or a Quantity or Constant with units of mass.
target_particle (particle-like) – The test particle as represented by a string, an integer representing atomic number, a Particle object, or a Quantity or Constant with units of mass.

Returns:

The reduced mass between the test particle and target particle.

Return type:

Quantity

Raises:

InvalidParticleError – If either particle is invalid.
UnitConversionError – If an argument is a Quantity or Constant but does not have units of mass.
MissingParticleDataError – If the mass of either particle is not known.

Notes

The reduced mass is always less than or equal to the mass of each body (i.e., \(μ ≤ m_1\) and \(μ ≤ m_2\)).

When \(m_1 = m_2 ≡ m\), the reduced mass becomes \(μ = \frac{m}{2}\).

When \(m_1 ≫ m_2\), the reduced mass becomes \(μ ≈ m_2\).

Examples

>>> import astropy.units as u
>>> reduced_mass("p+", "e-")
<Quantity 9.10442...e-31 kg>
>>> reduced_mass(5.4e-27 * u.kg, 8.6e-27 * u.kg)
<Quantity 3.31714...e-27 kg>