000060914 001__ 60914 000060914 005__ 20201105083206.0 000060914 0247_ $$2doi$$a10.1088/0143-0807/37/2/025004 000060914 0248_ $$2sideral$$a93998 000060914 037__ $$aART-2016-93998 000060914 041__ $$aeng 000060914 100__ $$0(orcid)0000-0003-4480-6535$$aCariñena, J. F.$$uUniversidad de Zaragoza 000060914 245__ $$aA new look at the Feynman 'hodograph' approach to the Kepler first law 000060914 260__ $$c2016 000060914 5060_ $$aAccess copy available to the general public$$fUnrestricted 000060914 5203_ $$aHodographs for the Kepler problem are circles. This fact, known for almost two centuries, still provides the simplest path to derive the Kepler first law. Through Feynman's 'lost lecture', this derivation has now reached a wider audience. Here we look again at Feynman's approach to this problem, as well as the recently suggested modification by van Haandel and Heckman (vHH), with two aims in mind, both of which extend the scope of the approach. First we review the geometric constructions of the Feynman and vHH approaches (that prove the existence of elliptic orbits without making use of integral calculus or differential equations) and then extend the geometric approach to also cover the hyperbolic orbits (corresponding to E > 0). In the second part we analyse the properties of the director circles of the conics, which are used to simplify the approach, and we relate with the properties of the hodographs and Laplace–Runge–Lenz vector the constant of motion specific to the Kepler problem. Finally, we briefly discuss the generalisation of the geometric method to the Kepler problem in configuration spaces of constant curvature, i.e. in the sphere and the hyperbolic plane. 000060914 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E24-1$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2012-33575$$9info:eu-repo/grantAgreement/ES/MINECO/MTM2014-57129 000060914 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000060914 590__ $$a0.614$$b2016 000060914 591__ $$aPHYSICS, MULTIDISCIPLINARY$$b62 / 79 = 0.785$$c2016$$dQ4$$eT3 000060914 591__ $$aEDUCATION, SCIENTIFIC DISCIPLINES$$b34 / 41 = 0.829$$c2016$$dQ4$$eT3 000060914 592__ $$a0.377$$b2016 000060914 593__ $$aPhysics and Astronomy (miscellaneous)$$c2016$$dQ3 000060914 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000060914 700__ $$0(orcid)0000-0002-8402-2332$$aRañada, M. F.$$uUniversidad de Zaragoza 000060914 700__ $$aSantander, M. 000060914 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000060914 773__ $$g37, 2 (2016), 025004 [19 pp.]$$pEur. j. phys.$$tEUROPEAN JOURNAL OF PHYSICS$$x0143-0807 000060914 8564_ $$s715761$$uhttps://zaguan.unizar.es/record/60914/files/texto_completo.pdf$$yPostprint 000060914 8564_ $$s58542$$uhttps://zaguan.unizar.es/record/60914/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000060914 909CO $$ooai:zaguan.unizar.es:60914$$particulos$$pdriver 000060914 951__ $$a2020-11-05-08:18:47 000060914 980__ $$aARTICLE