`M = {v^2 * R}/G`

375.332

The Mass from Speed and Separation calculator computes the mass of the object (e.g., star or planet) based on the orbital speed of its satellite, and the separation (R) and the universal gravity constant (G).

INSTRUCTIONS: Choose units and enter the following:

• (V) Orbital Velocity.
• (R)  Separation Distance

Mass (M):  The calculator returns the mass of the object in Earth Masses (multiples of the mass of the Earth).    However, this can be automatically converted to other mass units (e.g. kilograms) via the pull-down menu.

The Math / Science

The formula for computing the mass of an astronomical object based on the orbital velocity and distance from the greater mass (e.g. stellar object) is:

M = (v² ⋅ R) / G

where:

• M = mass of object
• v = orbital velocity
• R = distance between objects or orbital radius
• G = universal gravity constant (6.67384E-11 N·m²/kg²)

Example:

The orbital velocity of the Earth as it goes about the Sun is approximately: 29784.7357 m/s.  Use this velocity and one astronomical unit for R, and you will get a mass equal to 332968.774 Earth Masses.  If you click on the pull-down menu and select solar_mass, you will see that the mass is equal to 1 solar mass.

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