Calculate the Barycenter
Calculator for the barycenter of two orbiting celestial bodies. The barycenter is the point around which two stars, planets, or moons revolve in orbit. It is the center of mass of such a two-body system. While we say, for example, that the moon revolves around the Earth, which isn't entirely wrong, it is not exactly correct either. Because the Earth is much heavier than the moon, the barycenter of these two bodies is much closer to the Earth than to the moon. In fact it is so close, that it lies within the Earth's interior, but not at the Earth's center.
Please enter the masses of two orbiting celestial bodies and their distances. The masses can be given as absolute values without units or as a ratio. For example, absolute values are 597.2 for the Earth and 7.3 for the Moon. The unit in this case would be 1022 kg, which is omitted. Alternatively, the ratio can be 81 and 1, which corresponds to the mass ratio of the Earth and Moon. The unit for the distance is also arbitrary, as the results will be given in the same unit. m₁B is the distance from the barycenter to the first celestial body, m₂B is the distance to the second.
Round to decimal places.Example: With a mass of 81 for the Earth and 1 for the Moon, corresponding to their mass ratio, and a distance of 384 for thousand kilometers, we obtain the following: The distance of the barycenter to the Earth's center, m₁B, is 4.683 thousand, or 4683 kilometers, and the distance of the barycenter to the Moon's center, m₂B, is 379.317 thousand, or 379317 kilometers. Since the Earth's radius is approximately 6370 kilometers, the barycenter lies just under 1700 kilometers below the Earth's surface.
The formulas for calculating the distances between the center of a celestial body and its barycenter are:
Celestial body 1: m₁B = d * m₂/(m₁+m₂)
Celestial body 2: m₂B = d * m₁/(m₁+m₂)
with the distance d between the centers of the two celestial bodies and their masses m₁ and m₂.
This calculation applies to a two-body system. With more than two bodies, it becomes very complicated. However, if two bodies strongly dominate in a multi-body system, then a two-body system can be assumed as a simplification. In the solar system, these two dominant bodies would be the Sun and Jupiter.
Last updated on 02/21/2026. Author: Jürgen Kummer
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