Velocity Space and the Geometry of Planetary Orbits
We develop a theory of orbits for the inverse-square central force law which differs considerably from the usual deductive approach. In particular, we make no explicit use of calculus. By beginning with qualitative aspects of solutions, we are led to a number of geometrically realizable physica...
| Main Authors: | , , |
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| Language: | en_US |
| Published: |
2004
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| Online Access: | http://hdl.handle.net/1721.1/5788 |
| _version_ | 1826211104853852160 |
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| author | Abelson, Harold diSessa, Andrea Rudolph, Lee |
| author_facet | Abelson, Harold diSessa, Andrea Rudolph, Lee |
| author_sort | Abelson, Harold |
| collection | MIT |
| description | We develop a theory of orbits for the inverse-square central force law which differs considerably from the usual deductive approach. In particular, we make no explicit use of calculus. By beginning with qualitative aspects of solutions, we are led to a number of geometrically realizable physical invariants of the orbits. Consequently most of our theorems rely only on simple geometrical relationships. Despite its simplicity, our planetary geometry is powerful enough to treat a wide range of perturbations with relative ease. Furthermore, without introducing any more machinery, we obtain full quantitative results. The paper concludes with sugestions for further research into the geometry of planetary orbits. |
| first_indexed | 2024-09-23T15:00:39Z |
| id | mit-1721.1/5788 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:00:39Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/57882019-04-11T04:54:29Z Velocity Space and the Geometry of Planetary Orbits Abelson, Harold diSessa, Andrea Rudolph, Lee We develop a theory of orbits for the inverse-square central force law which differs considerably from the usual deductive approach. In particular, we make no explicit use of calculus. By beginning with qualitative aspects of solutions, we are led to a number of geometrically realizable physical invariants of the orbits. Consequently most of our theorems rely only on simple geometrical relationships. Despite its simplicity, our planetary geometry is powerful enough to treat a wide range of perturbations with relative ease. Furthermore, without introducing any more machinery, we obtain full quantitative results. The paper concludes with sugestions for further research into the geometry of planetary orbits. 2004-10-01T20:36:57Z 2004-10-01T20:36:57Z 1974-12-01 AIM-320 http://hdl.handle.net/1721.1/5788 en_US AIM-320 58 p. 2835824 bytes 2193477 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | Abelson, Harold diSessa, Andrea Rudolph, Lee Velocity Space and the Geometry of Planetary Orbits |
| title | Velocity Space and the Geometry of Planetary Orbits |
| title_full | Velocity Space and the Geometry of Planetary Orbits |
| title_fullStr | Velocity Space and the Geometry of Planetary Orbits |
| title_full_unstemmed | Velocity Space and the Geometry of Planetary Orbits |
| title_short | Velocity Space and the Geometry of Planetary Orbits |
| title_sort | velocity space and the geometry of planetary orbits |
| url | http://hdl.handle.net/1721.1/5788 |
| work_keys_str_mv | AT abelsonharold velocityspaceandthegeometryofplanetaryorbits AT disessaandrea velocityspaceandthegeometryofplanetaryorbits AT rudolphlee velocityspaceandthegeometryofplanetaryorbits |