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From Karnataka Open Educational Resources
→The Law of Periods
[[Image:Gravitation%20for%20wiki_html_m290004f7.gif]] <br>
[[Image:Gravitation%20for%20wiki_html_m290004f7.gif]] <br>
<math>G m_1*M_s / r^12 = m_1*(v^12)/ r_1</math>
<math>G m_1*M_s / r^(12) = m_1*(v^(12))/ r_1</math>
<math>v_1 = 2πr_1/T_1</math>
<math>v_1 = 2πr_1/T_1</math>
Substituting and rearranging we get
Substituting and rearranging we get
<math>T_12/r_13 = 4π^2/G*M_s</math>
<math>(T_1)^2)/(r_1)^3 = 4π^2/G*M_s</math>
Deriving this for another planet, we can arrive at the third law.<br><br>
Deriving this for another planet, we can arrive at the third law.<br><br>
