dorsal/arxiv
View SchemaBallistic trajectory: parabola, ellipse, or what?
| Authors | Lior M. Burko, Richard H. Price |
|---|---|
| Categories | |
| ArXiv ID | physics/0310049 |
| URL | https://arxiv.org/abs/physics/0310049 |
| DOI | 10.1119/1.1866097 |
| Journal | Am. J. Phys. 73, 516-520 (2005) |
Abstract
Mechanics texts tell us that a particle in a bound orbit under gravitational central force moves on an ellipse, while introductory physics texts approximate the earth as flat, and tell us that the particle moves in a parabola. The uniform-gravity, flat-earth parabola is clearly meant to be an approximation to a small segment of the true central-force/ellipse orbit. To look more deeply into this connection we convert earth-centered polar coordinates to ``flat-earth coordinates'' by treating radial lines as vertical, and by treating lines of constant radial distance as horizontal. With the exact trajectory and dynamics in this system, we consider such questions as whether gravity is purely vertical in this picture, and whether the central force nature of gravity is important only when the height or range of a ballistic trajectory is comparable to the earth radius. Somewhat surprisingly, the answers to both questions is ``no,'' and therein lie some interesting lessons.
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"abstract": "Mechanics texts tell us that a particle in a bound orbit under gravitational\ncentral force moves on an ellipse, while introductory physics texts approximate\nthe earth as flat, and tell us that the particle moves in a parabola. The\nuniform-gravity, flat-earth parabola is clearly meant to be an approximation to\na small segment of the true central-force/ellipse orbit. To look more deeply\ninto this connection we convert earth-centered polar coordinates to\n``flat-earth coordinates\u0027\u0027 by treating radial lines as vertical, and by\ntreating lines of constant radial distance as horizontal. With the exact\ntrajectory and dynamics in this system, we consider such questions as whether\ngravity is purely vertical in this picture, and whether the central force\nnature of gravity is important only when the height or range of a ballistic\ntrajectory is comparable to the earth radius. Somewhat surprisingly, the\nanswers to both questions is ``no,\u0027\u0027 and therein lie some interesting lessons.",
"arxiv_id": "physics/0310049",
"authors": [
"Lior M. Burko",
"Richard H. Price"
],
"categories": [
"physics.class-ph",
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"physics.gen-ph"
],
"doi": "10.1119/1.1866097",
"journal_ref": "Am. J. Phys. 73, 516-520 (2005)",
"title": "Ballistic trajectory: parabola, ellipse, or what?",
"url": "https://arxiv.org/abs/physics/0310049"
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