how did the keplers third law help Newton to arrive at the inverse square law of gravity?
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For a uniform circular orbit of radius r, the acceleration is
a = ω2r, ω = 2π/T________(A)
where T is the orbital period. Comparing eq. (A) with Kepler's third law
T2 ∝ r3______________(B)
we conclude that the gravitational acceleration
a ∝ r−2________________(C)
is proportional to the inverse square distance r
a = ω2r, ω = 2π/T________(A)
where T is the orbital period. Comparing eq. (A) with Kepler's third law
T2 ∝ r3______________(B)
we conclude that the gravitational acceleration
a ∝ r−2________________(C)
is proportional to the inverse square distance r
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