`m = M(r/R)`

Enter a value for all fields

The  Mass of an Extra-solar Planet calculator computes the mass of a planet based on the mass of the star (M), the distance to the star (R) and the distance to the planet (r).

INSTRUCTIONS: Choose the preferred units and enter the following:

• (M) This is the mass of the star.
• (R) This is the orbital radius of the planet.
• (r)  This is the orbital radius of the star about the center of mass.

Planet Mass (m): The calculator returns the mass of the planet in Jupiter_Mass units (multiples of the mass of Jupiter).  However, this can be automatically converted to other mass units (e.g. Earth_Mass or kilograms) via the pull-down menu.

The Math / Science

If you know the mass of a star, and the orbital radius of the star and the planet, you can compute the mass of the planet using the fact that the center of mass obeys the relation: m•R = M•r.   The formula for the mass of a planet is:

         m = (M•r)/ R

where:

• m = mass of the planet
• M = mass of the star
• r = orbital radius radius of the star
• R = orbital radius of the planet

Example:

Consider Jupiter in our own solar system:

• (M) The mass of our star (the Sun) is 1.0 Solar_Mass
• (R) This orbital radius of Jupiter is 5.2 ua
• (r) The orbital radius of our Sun around the solar system's center of mass is 0.005 ua

If you enter the above, the calculator returns an exoplanet mass of approximately 1 Jupiter Mass which fits the model and describes our solar system. 

Astronomy Calculators

• 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
  • (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