Binary Star Motions

Half of all stars in the sky are members of binary systems!

Kepler's Laws apply to binary stars also!

The stars orbit in ellipses around a common center of mass. Notice that at any time, the line that connects the two stars must pass through the center of mass.

Each star follows the second law on its own, sweeping out equal areas in equal times within its own orbit.

In the example shown here, notice that because the orbits are quite elliptical, the stars must travel at quite different speeds as they orbit.

The third law also applies, but somewhat more formally than when we are dealing with the planets.

Here, the period and separation are related as in the solar system case, but Kepler's third law also includes the masses of both objects.

Remember that in the Solar System, the mass of the Sun is much bigger than the mass of any of the planets. Therefore, we can ignore the mass of the planet and use the mass of the Sun in place of the sum of the masses.

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