- vCalc Catalog Home
- barycenter distance (r1)

# barycenter distance (r1)

vCalc.barycenter distance (r1)

The **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**) This is the distance between the two bodies - (
**m**) This is the mass of the primary body_{1} - (
**m**) This is the mass of the secondary body_{2}

**Barycenter (r _{1}):** The calculator returns the distance in kilometers. However this can be automatically converted to compatible units via the pull-down menu.

#### 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, 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:

- r
_{1}is the distance from the center of the primary body to the barycenter *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