Processing...

`M = (4 \pi^2)/G R^3/T^2`

Enter a value for all fields

The **Mass from Period and Separation** calculator uses Kepler's 3^{rd} law to compute the mass of a system (**M**) based on the distance (**R**) between astronomical bodies (e.g. a star and exoplanet) and the orbital period (**T**).

**INSTRUCTIONS:** Chose the preferred units and enter the following:

- (
**R**) This is the separation between the orbiting bodies. - (
**T**) This is the period of the orbit.

**Mass of the System:** The calculator returns the mass of the orbital system (**M**) in multiples of the mass of the Sun. However, this can be automatically converted to other mass units (e.g. kilograms or masses of the Earth or Jupiter) via the pull-down menu.

In a binary system in which two objects orbit a common center of mass the mass of the system is related to the distance between the two objects (separation) and the period of their common orbit. This equation computes the mass of the entire system (both masses added together) given the two other quantities.

The formula for the Mass using Kepler's 3rd law is:

`M = (4 pi^2)/G R^3/T^2`

where:

- M is the total mass of the system
- R is the separation distance between the two objects.
- T is the period of the orbit.
- G is the universal gravity constant

- Hubble's Law
- Kepler's 3
^{rd}Law formula T² = (4π • R³)/(G • M) - Small Angle Formula
*Small Angle Formula**α = S / D* - Flux and Magnitude formulas
- Telescope formulas
- Mass formulas
- Relative Size Formulas
- Wavelength Formulas
- Luminosity and other Formulas

**Related Astro Calculators:**

- Kepler's 3
^{rd}Law Calc has Kepler's 3^{rd}law solved for each parameter. - Astronomy Calculator contains basic formulas for a college level Introduction to Astronomy
- Exoplanet Calculator contains formulas for studying planets outside of our Solar System.
- Astronomical Distance Calculator provides the distance from the Earth to numerous astronomical bodies (e.g. Sun, Moon, planets, stars, Milky Way's Center and Edge, Andromeda Galaxy)
- Astronomical Distance Travel Time Calculator computes the time to travel to distant parts of space at different velocities.
- Ellipse Calculator
- 3D Vector Calculator:
- Drake Equation Calculator
- Seager Equation Calculator
- Friedman Equation Calculator
- Exoplanet Calculator contains formulas for studying planets outside of our Solar System.
- Astronomical Distance Calculator provides the distance from the Earth to numerous astronomical bodies (e.g. Sun, Moon, planets, stars, Milky Way's Center and Edge, Andromeda Galaxy)
- Astronomical Distance Travel Time Calculator computes the time to travel to distant parts of space at different velocities.
- Radius of Perigee
- Radius of Apogee