Kepler’s third law is written T²=Kr³ for a planet of mass m orbiting a Sun of mass M. Newton’s gravitational force is F=GMm/r². What relation connects K and G?
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Kepler’s third law is written T²=Kr³ for a planet of mass m orbiting a Sun of mass M. Newton’s gravitational force is F=GMm/r². What relation connects K and G?

G1 Physics · Accepted Answer

Step 1: For a nearly circular orbit, GMm/r²=m(4π²r/T²). Step 2: Rearranging T²=(4π²/GM)r³, so K=4π²/(GM), or GMK=4π². Final answer: B — GMK=4π².