`r_1 = ( "a" * m_2 )/( m_1 + m_2 )`

Enter a value for all fields

The Distance to Barycenter calculator computes the distance from the center of the primary body to the barycenter (+) of the two body system.

INSTRUCTIONS: Choose units and enter the following:

• (a) Distance between Two Bodies
• (m₁) Mass of Primary Body
• (m₂) Mass of Secondary Body

Distance to Barycenter (r₁): The calculator returns the distance in kilometers.  However this can be automatically converted to compatible units via the pull-down menu.  Note: the default units for the primary body is in solar masses.  The default unit for the secondary body is in Earth masses, and the default units for the distance is in astronomical units.  

The Math / Science

The distance from the center of the primary body to the barycenter equation computes the distance in a two body system based on the distance between the bodies and their two masses.

The barycenter is one of the foci of the elliptical orbit of each body. This is an important concept in the fields of astronomy, astrophysics, and the like. In a simple two-body case, r₁ the distance from the center of the primary to the barycenter is given by:

                    r₁= (a • m₁)/(m₁ + m₂)

where:

• r₁ is the distance from the center of the primary body to the barycenter
• a is the distance between the centers of the two bodies;
• m₁ and m₂ are the masses of the two bodies.

If a is the semi-major axis of the system, r₁ is the semi-major axis of the primary's orbit around the barycenter, and r₂ = a − r₁ is the semi-major axis of the secondary's orbit. When the barycenter is located within the more massive body, that body will appear to "wobble" rather than to follow a discernible orbit.

References

• Wikipedia - en.wikipedia.org/wiki/Barycentric_coordinates_%28astronomy%29

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
• Kepler's 3^rd Law Calc has Kepler's 3^rd law solved for each parameter.
• Distance to Barycenter
• 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