Gravity is what makes objects orbit around other objects, and gravity is a reflection of an object's mass. So why doesn' the mass of the objects appear in Kepler's third law??

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Solution

For the same reason why all objects have the same
acceleration in the gravitational field, i.e. all
objects near the surface of the earth have an acceleration
of 9.8 m/s2. The acceleration (which is what
describes the orbit) is F/m but the force
is MmG/r2, so the acceleration
is MG/r2.

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Gravity is what makes objects orbit around other objects, and gravity is a reflection of an object's mass. So why doesn' the mass of the objects appear in Kepler's third law??

For the same reason why all objects have the same acceleration in the gravitational field, i.e. all objects near the surface of the earth have an acceleration of 9.8 m/s2. The acceleration (which is what describes the orbit) is F/m but the force is MmG/r2, so the acceleration is MG/r2.

For the same reason why all objects have the same
acceleration in the gravitational field, i.e. all
objects near the surface of the earth have an acceleration
of 9.8 m/s2. The acceleration (which is what
describes the orbit) is F/m but the force
is MmG/r2, so the acceleration
is MG/r2.