barycenter distance (r1)

vCalc Reviewed
Equation / Last modified by KurtHeckman on 2019/07/30 00:13
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vCalc.barycenter distance (r1)
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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
  • (m1) This is the mass of the primary body
  • (m2) This is the mass of the secondary body

Barycenter (r1): 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.

Orbit3.gif

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 = ar1 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