Question

Show that the period of orbit for two masses, m1 and m2, in circular orbits of radii r1 and r2, respectively, about their common center-of-mass, is given by T=2π√r3G(m1+m2)wherer=r1+r2. (Hint: The masses orbit at radii r1 and r2, respectively where r=r1+r2.

Answer 1

Kepler's third law states that the period of orbit for two masses in circular orbits is related to the radius of the orbit.

Step-by-step explanation:

Kepler's third law states that the period of orbit for two masses in circular orbits is related to the radius of the orbit.

The period is given by the equation T = 2π√((r₁+r₂)³G(m₁+m₂)), where r₁ and r₂ are the radii of the orbits, G is the gravitational constant, and m₁ and m₂ are the masses of the objects.

The equation shows that the period of orbit is directly proportional to the square root of the cube of the sum of the radii, and inversely proportional to the square root of the sum of the masses.

For example, if the masses of the objects increase, the period of orbit will decrease.