Gravity and Orbits

In the 1500's and 1600's scientists found how the planets orbit the Sun. Then in 1687 Isaac Newton published his Principia, which put forward laws of motion and of gravity that explain how gravity bends the paths of the planets into orbits around the Sun.

This applies to two stars also. They can be held in orbit by their mutual gravitational attraction. This is common. Roughly half of stars are found to be such binary star systems.

Each star orbits in an elliptical orbit about a point in space between the two stars. This point is called the center of mass. The center of mass is nearer to the heavier star:

M₁/M₂ = r₂/r₁

Each star moves in an elliptical orbit about the center of mass. (That is, one focus of the ellipse is at the center of mass.)

As the two stars move, the center of mass stays stationary. (That is, stationary relative to a suitable observer. Relative to us, the whole system might be moving.)

Newton's laws relate the sum of the masses of the two stars to the period P and the semimajor axis a of the orbit:

Here we measure the masses in units of M_sun, the semimajor axis in AU and the period in years.

Davison E. Soper, Institute of Theoretical Science, University of Oregon, Eugene OR 97403 USA soper@bovine.uoregon.edu