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Newton_area_law_derivation.gif (256 × 256 pixels, file size: 15 KB, MIME type: image/gif, looped, 7 frames, 28 s)

Summary

Description
English: Newton's derivation of the area law from the laws of motion: as an object orbits the Sun it sweeps out equal areas in equal intervals of time.


An object (not shown) is in orbit around the Sun (Point S). The effect of the Sun's gravitational attraction is represented as a sequence of impulses, always directed towards point S. In the limit of infinitely many small impulses the representation approaches infinitely close to smooth gravitational attraction.

When the object is at point B it receives an impulse towards point S. Without that impulse the object would proceed to point c. The actual displacement BC follows from the rules for velocity composition; the displacement BC is the vector sum of the displacements BV and Bc. The triangles SBc and SBC have the same base and the same height, hence they have the same surface area.

At point C the object receives another impulse towards point S. Without that impulse the object would have proceeded to point d in an equal interval of time. The impulse towards point S makes the object proceed to point D.

The triangles SBc, SBC, SCd, SCD, SDe, SDE all have the same surface area.

In the limit of the time intervals going to infinitisimally small the sequence of lines connecting the points B, C, D, E, etc approaches infinitely close to the actual smooth trajectory.
العربية: إثبات نيوتن الهندسي لقانون المساحات
Date (UTC)
Source Own work
Author Cleonis

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Original upload log

The original description page was here. All following user names refer to en.wikipedia.
  • 2009-04-28 21:17 Cleonis 256×256× (15224 bytes) A 256x256 px version of the animated GIF.
  • 2009-04-28 21:16 Cleonis 512×512× (23490 bytes) A 512x512 px version of the animated GIF.
  • 2009-04-28 21:14 Cleonis 1024×1024× (35918 bytes) Instead of a still image this is a sequence of images, that are exchanged every 4 seconds. The format is animated GIF. The sequence shows the steps in the mathematical reasoning.
  • 2009-04-28 21:05 Cleonis 1024×1024× (15083 bytes) {{Information |Description = Newton's derivation of the area law from the laws of motion: as an object orbits the Sun it sweeps out equal areas in equal intervals of time.<br> <br> An object (not shown) is in orbit around the Sun (Point '''S''''). The eff

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Date/TimeThumbnailDimensionsUserComment
current03:46, 1 July 2017Thumbnail for version as of 03:46, 1 July 2017256 × 256 (15 KB)OgreBot(BOT): Reverting to most recent version before archival
03:46, 1 July 2017Thumbnail for version as of 03:46, 1 July 2017512 × 512 (23 KB)OgreBot(BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2009-04-28 21:16:08 by Cleonis
03:46, 1 July 2017Thumbnail for version as of 03:46, 1 July 20171,024 × 1,024 (35 KB)OgreBot(BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2009-04-28 21:14:21 by Cleonis
03:46, 1 July 2017Thumbnail for version as of 03:46, 1 July 20171,024 × 1,024 (15 KB)OgreBot(BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2009-04-28 21:05:44 by Cleonis
20:41, 29 June 2017Thumbnail for version as of 20:41, 29 June 2017256 × 256 (15 KB)PavlyHUser created page with UploadWizard

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