Orbit of planet have to be a conic section

AI Thread Summary
The discussion centers on proving that planetary orbits are conic sections using geometry rather than differential equations. One participant expresses skepticism about the possibility of such a proof, suggesting that observations are the primary means of validation. Another contributor references a derivation from Halliday and Resnick related to circular orbits influenced by gravitational attraction, highlighting the relationship between the bodies' distances from their center of mass. They mention Newton's geometric proof in "Principia" but struggle to locate a downloadable version of the text. The conversation emphasizes the historical and theoretical aspects of understanding planetary motion.
sorce
Messages
2
Reaction score
0
How we can prove (using geomtry and not differential equation) that the orbit of planet have to be a conic section.
 
Physics news on Phys.org


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...
 


i saw in wikipedia that Newton prove it usinge geometry in his book "principia"
but i can't find download of the book/
 
Thread 'Gauss' law seems to imply instantaneous electric field propagation'

Thread 'Gauss' law seems to imply instantaneous electric field propagation'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
View full post »
Thread 'A scenario of non-uniform circular motion'

Thread 'A scenario of non-uniform circular motion'

(All the needed diagrams are posted below) My friend came up with the following scenario. Imagine a fixed point and a perfectly rigid rod of a certain length extending radially outwards from this fixed point(it is attached to the fixed point). To the free end of the fixed rod, an object is present and it is capable of changing it's speed(by thruster say or any convenient method. And ignore any resistance). It starts with a certain speed but say it's speed continuously increases as it goes...
View full post »

Thread 'Do electron density waves accompany EM waves in coaxial cables?'

Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following transverse part $$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2} = \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$ and longitudinal part...
View full post »

Similar threads

I Hypatia, Elliptic orbits, conic sections
Replies
6
Views
3K
B Celestial mechanics: Why is my planet orbiting faster and faster?
Replies
22
Views
2K
B Can Jupiter gravitationally eject a pebble in orbit? A smaller mass?
Replies
2
Views
846
B Are planetary orbits elliptical because of a space–time conic section?
Replies
3
Views
1K
A Continuity of a quantity in a conical system to determine the velocity
Replies
0
Views
782
I Is a horseshoe orbit a hyperbolic orbit?
Replies
2
Views
1K
B Help Scaling Gravity Simulation
Replies
7
Views
2K
I Converse of focus-directrix property of conic sections
Replies
2
Views
1K
MHB How Do Conic Sections Relate to Orbital Mechanics?
Replies
3
Views
6K
I Kepler orbits for planets of similar masses
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top