Suppose a small M type star (mass less than 0.1 solar masses) is orbiting an invisible object in space. The radius of the orbit is 2.0 A.U., the period is 2.0 years. How massive is the invisible object? Could it be a burned out white dwarf star?
What will be an ideal response?
Using Kepler's third law, P2 = a3/(M + m), and using solar system units of years, A.U.s, and solar masses, the sum of the masses must be M + m = 2.0 solar masses. If the smaller mass is less than 0.1 solar mass then the larger mass must be greater than 1.9 solar masses. This would be appropriate for a neutron star.
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