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# barycenter distance (r1)

vCalc.barycenter distance (r1)

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.

# Description

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, `r_1` the distance from the center of the primary to the barycenter is given by:

r_{1}= (a * m_{1})/(m_{1} + m_{2})

where:

*a*is the distance between the centers of the two bodies;*m*_{1}and*m*_{2}are the masses of the two bodies.

If *a* is the semi-major axis of the system, *r*_{1} is the semi-major axis of the primary's orbit around the barycenter, and *r*_{2} = *a* − *r*_{1} 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