Reduced Mass Calculator
Table of contents
Reduced mass equation and definitionThe importance of the reduced massHow to use the reduced mass calculatorThe reduced mass calculator allows you to obtain the reduced mass of a twobody system. This very useful physical value helps simplify the twobody problem, making it much easier to find the equations of motion for such a system.
If you are studying mass and wish for further information, be sure to check our center of mass calculator.
Reduced mass equation and definition
Reduced mass is a physical quantity used when solving the twobody problem to turn it into an equivalent onebody problem that can be solved faster and easier. The complexity of the twobody problem arises from the fact that the movement of one body affects the other, which in turn affects the first one... in an endless loop of additive effects from one body to the other. A typical example of a twobody problem is that of two objects of comparable mass orbiting each other.
The formula for the reduced mass of a twoobject system is the inverse of the sum of the inverses of each mass, and it is denoted by the Greek letter $\mu$. The reduced mass calculator computes the value of the reduced mass of a twobody system by using the defining reduced mass equation:
Mred = m₁ × m₂ / (m₁ + m₂)
The importance of the reduced mass
Using the reduced mass, you can decompose the twobody problem into 2 onebody problems that are much easier to solve. One of these onebody problems would describe the movement of the center of mass, while the other would describe the relative motion of the two bodies with respect to the center of mass as described on distance calculator, position, and other physical quantities of each system using, the gravity equation calculator.
. Once the problem is solved, we can calculate the distance using theThe usefulness of the reduced mass calculator is not limited to gravitational problems since any two objects orbiting each other (due to any kind of force) constitute a twobody problem that can be simplified and decomposed by means of the reduced mass. Such other problems include some of the most known problems in physics, such as the (semi)classical solution for the hydrogen atom and other planetarylike systems.
How to use the reduced mass calculator
The reduced mass calculator is a very simple calculator and is composed of three different parameters, as we have seen in the reduced mass equation above. Let's see what they mean and use the example of the Earth and the Sun to illustrate possible values.

m₁ is the mass of the first of the two objects that appear in the twobody problem. For the Earth, that is 5.972 × 10^{24} kg (or 1 Earth).

m₂ is the mass of the second of the two objects that appear in the twobody problem. For the Sun, that is 1.989 × 10^{30} kg.

Mred, also called μ, is the reduced mass of the system. In the twobody problem of the Earth and the Sun, it turns out to be approximately the mass of the Earth due to the big difference in mass between the two bodies.
Due to the properties of the formula to calculate the reduced mass, m_{1}, and m_{2} are interchangeable, and the Mred is always smaller than or equal to m_{1} and m_{2}.