Assumptions - Binary Star System

The applet simulates the motion of two stars revolving around each other, the gravitational forces exerted by the stars on each other, the stars' momenta and velocities, and the kinetic and potential energies of the system.

  1. The two stars are assumed to be spheres of uniform mass density. With this assumption, the magnitude F of the gravitational force that either star exerts on the other is given by

    F = Gm1m2 / d2 space(1)

    where G is the universal gravitational constant, m1 and m2 are the masses of the two stars, and d is the center-to-center distance between the stars.

    The potential energy PE of the two-star system corresponding to this force is given by

    PE = -Gm1m2 / d + const. space(2)

    The additive constant in this expression can be chosen to have any value. It is customary to set it equal to zero so that PE = 0 when the two stars are infinitely far apart. This is the choice made in the applet's default state.

  2. It is assumed that no forces are acting on the stars other than the gravitational forces exerted by the stars on each other.

  3. All values displayed by the applet are in dimensionless units because no explicit values for the masses of the stars and the distances are assumed.

  4. The stars are assumed not to be rotating about an internal axis so that the kinetic energy of the system is the sum of only the translational kinetic energies of the stars, effectively treating the stars as mass points.