Orbit of planet have to be a conic section

In summary, the orbit of a planet can be proven to be a conic section through observations and the use of geometry, rather than differential equations. This can be seen in examples such as circular orbits of two bodies under the influence of their gravitational attraction, as shown in Halliday and Resnick's textbook. Newton also proved this in his book "Principia" using geometry, but a download of the book is not readily available.
  • #1
sorce
2
0
How we can prove (using geomtry and not differential equation) that the orbit of planet have to be a conic section.
 
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  • #2


I don't think you can "prove" such a thing...except maybe by observations.

Please take that as an opinion, not a firm statement, as I have been away from such things a looooong time...I surprised I even remembed there was an example of a the derivation from a textbook...


My old version of Halliday and Resnick has a derivation closely linked to your query, but not so general...for CIRCULAR orbits of two bodies m and M under the influence of each others gravitational attraction.

It starts with a center of mass of the combined bodies such that mr = MR, where r,R are the radial distances of bdoies m,M, from the center of mass, and noting the centripetal forces of the two bodies equal and figuring the gravitational attraction equal results in

GMm/(R+r)2 = mw2r...
 
  • #3


i saw in wikipedia that Newton prove it usinge geometry in his book "principia"
but i can't find download of the book/
 

What is a conic section?

A conic section is a curve that is formed when a plane intersects with a cone. There are four types of conic sections: circle, ellipse, parabola, and hyperbola.

Why do orbits of planets have to be a conic section?

According to Kepler's laws of planetary motion, a planet moves around the sun in an elliptical orbit with the sun at one of the two foci. This means that the orbit of a planet must be a conic section in order to follow Kepler's laws.

How does the shape of a conic section affect the orbit of a planet?

The shape of a conic section determines the eccentricity of the orbit. A circle has an eccentricity of 0, an ellipse has an eccentricity between 0 and 1, a parabola has an eccentricity of 1, and a hyperbola has an eccentricity greater than 1. The eccentricity of the orbit affects the speed and distance of the planet from the sun.

Can any object in space have a conic section orbit?

Yes, any object that orbits around another object in space will follow a conic section. This includes planets, moons, comets, and artificial satellites.

How do scientists determine the shape of a planet's orbit?

Scientists can determine the shape of a planet's orbit by observing its motion and calculating its eccentricity. This can be done through telescopic observations, mathematical calculations, and computer simulations.

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