Keplers Law of Planetary Motion?

[fzshinobi]

Can someone briefly explain to me how Kepler's law of planetary motion uses differential calculus?
I'm searching for a topic for a 7 page report on a mathematical concept that uses differential calculus. I thought about Kepler's law on planetary motion, but I have a very vague understanding on the concept of his laws. So, if someone could briefly fill me in on how the two are related, that will really help me get started (and confirm it as my topic).

Any help is appreciated.

If you have any other ideas for a research topic for me, please feel free to list them here.
Thanks :)

 

[fzshinobi]

Keplers Law of Planetary Motion using Differential Calculus?

Can someone briefly explain to me how Kepler's law of planetary motion uses differential calculus?
I'm searching for a topic for a 7 page report on a mathematical concept that uses differential calculus. I though about Keplers law on planetary motion, but I have a very vague understanding on the concept of his laws. So, if someone could breifly fill me in on how the two are related, that will really help me get started (and confirm it as my topic).

Any help is appreciated.

If you have any other ideas for a research topic for me, please feel free to list them here.
Thanks :)

 

[Nabeshin]

I guess you could say Kepler's laws use differential calculus in that they can be derived from Newton's laws with the aid of some calculus. The laws themselves, nor their applications, really involve differential calculus, but certain derivations do (not the original ones, however. I think Newton proved things using geometry, even though he had some rudimentary differential calculus).

Refer to the link for a some derivations, although there are many others.

Link: http://en.wikipedia.org/wiki/Kepler...s_of_motion_and_Newton.27s_law_of_gravitation

 

[Chronos]

You don't need differential equations, see
http://arxiv.org/PS_cache/arxiv/pdf/0810/0810.4246v1.pdf

 

[HallsofIvy]

Strictly speaking, Kepler's law do NOT use Calculus because Kepler died before Calculus was invented. It IS true that Newton used Calculus to show that an inverse square law of gravitation will give planetary orbits obeying Kepler's laws.

See: http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion

 

[berkeman]

Two threads merged into one.

 

[JazzFusion]

As others have mentioned, Kepler did NOT use differential calculus to derive his laws. He made observations from the years of data taken by his teacher and mentor, Tycho Brahe.

If you are looking for some ideas from basic physics using differential calculus, you might try:
Simple Harmonic Motion: a = -ω² x, where 'a' is the acceleration and ω² is a constant.

Impulse-Momentum Theorem: Can be used in the kinetic theory of ideal gases to relate the pressure in a container to the temperature and r.m.s. speed.

Conservation of Momentum/Conservation of Angular Momentum: Lots of great examples here, but starting from the Impulse-Momentum Theorem, if ΔF is zero (no external forces), then momentum must be conserved.

Gradient: For anything that can be expressed as a potential (such as gravitational potential energy or electric potential), the gradient can be used to determine the field.

 

[erkumud]

keplers law is about the law realate to planet motio
this about the

Spoiler

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