86.3 Kepler's laws of planetary motion 1. Kepler’ s first I The path of a planet orbiting the sun is an ellipse ith the Sun at one focus of the ellipse; the oth focus is empty. a(1-E r+sEa gcos 0 Paph 1+8 ≡ r.1 M polar coordinate e--eccentricit a--SemImajor axis 86.3 Kepler's laws of planetary motion Newton found that the elliptical paths described by Kepler are the consequence of a central inverse-square force law More generally, Newton showed that the paths of the mass under the influence of this force had to be conic sections 222 ○○11 • c c O §6.3 Kepler’s laws of planetary motion 1. Kepler’s first law The path of a planet orbiting the sun is an ellipse with the Sun at one focus of the ellipse; the other focus is empty. ε ε ε θ ε − + = − − = 1 1 1 cos (1 ) peri aph 2 r r a r s r + s = 2a a c ε ≡ r —polar coordinate ε --eccentricity a—semimajor axis peri aph Newton found that the elliptical paths described by Kepler are the consequence of a central inverse-square force law. More generally, Newton showed that the paths of the mass under the influence of this force had to be conic sections. §6.3 Kepler’s laws of planetary motion