`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) Separation between Orbiting Bodies
• (T) Period of 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.

The Math / Science

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

Astronomy Calculators

• Hubble's Law
• Kepler's 3^rd Law formula T² = (4π • R³)/(G • M)
  • (M) - mass of the system. 
  • (T) - period of the orbit.
  • (R) - separation distance between the two objects.
  • (G) - universal gravity constant
• Small Angle Formula        Small Angle Formula    α = S / D
  • (α) - angle
  • (D) - distance to astronomical object
  • (S) - size or diameter of astronomical object
• Flux and Magnitude formulas
  • Change in Magnitude from Flux Ratio
  • Flux Ratio from Magnitudes
• Telescope formulas
  • Resolving Power of a Telescope
  • Magnification of a Telescope
• Mass formulas
  • Mass from Luminosity
  • Mass from Acceleration and Radius
  • Mass from Speed and Separation
  • Mass of extra-solar planet from mass of star, radius of star orbit and radius of exoplanet orbit
  • Mass of extra-solar planet from mass and velocity of star and velocity of planet
• Relative Size Formulas
  • Relative Size from Relative Temperature and Luminosity
  • Relative Temperature from Relative Size and Luminosity
  • Relative Luminosity from Relative Temperature and Size
• Wavelength Formulas
  • Velocity from shift in Wavelength and Unshifted Wavelength
  • Wavelength Shift from Wavelength and Speed
  • Blackbody Wavelength from Temperature
  • Blackbody Temperature from Peak Wavelength
  • Photon Energy from Wavelength
  • Photon Wavelength from Energy
• Luminosity and other Formulas
  • Distance from absolute and apparent magnitude
  • Radius from Speed and Period
  • Speed of Circular Motion
  • Hubble Time
  • Luminosity from Mass

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