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
- Kepler's 3rd Law formula T² = (4π • R³)/(G • M)
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