K=G
K=1/G
GMK=4π²
GK=4π²
The gravitational force is providing centripetal force to the planets orbital circular motion
GMm/r² = mv²/r → v = √(GM/r)
The time period for the planet in one revolution will be
T = 2πr/v = 2πr/√(GM/r)
squaring each side
T² = 4π²r³/GM
comparing with given equation T² = Kr³
K = 4π²/GM
GMK = 4π²
hence, the correct answer is option C