Are planetary orbits elliptical because of a space–time conic section?

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Discussion Overview

The discussion revolves around the nature of planetary orbits, specifically whether they can be understood as elliptical due to a space-time conic section. Participants explore the relationship between conic sections, orbits, and the implications of relativity.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant presents a graph involving triangles or cones in a space-time context, questioning the nature of a planet's world line and its relation to timelines.
  • Another participant clarifies that the cones described likely represent past and future lightcones, which are relevant in relativity but do not directly relate to the conic sections of orbits in Newtonian gravity.
  • It is noted that orbits are conic sections only in Newtonian gravity, and that relativistic models do not yield perfect conic sections, as evidenced by Mercury's orbit.
  • A historical perspective is provided, mentioning Kepler's discovery of elliptical orbits and Newton's mathematical proof, asserting that this is unrelated to relativity.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between conic sections and the nature of orbits in different gravitational frameworks. There is no consensus on the implications of relativity for the shape of orbits.

Contextual Notes

The discussion highlights the distinction between Newtonian and relativistic models of gravity, as well as the historical context of the discovery of elliptical orbits. There are unresolved assumptions regarding the interpretation of space-time diagrams and their relevance to orbital mechanics.

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TL;DR
Planetary orbits look like they're part of a conic section where the cone is some kind of higher-dimensional part of space–time. I'm wondering about world lines and time lines, and if this is true or not.
Hi. I saw a 2D graph of two triangles, or maybe cones, one standing straight up, the other one "resting" on top of the other one but upside down with the two pointy ends touching others. The horizontal axis was labeled "space," the vertical axis was labeled "time." I'm sorry for my ignorance of this graph. So since the ellipse is a conic section, does that mean the world line that the planet traces out won't be centered on a vertical axis? Is this a timeline that isn't centered? To me, at least, it seems like the timeline of a planet orbiting a star is moving away from something. Perhaps away from another timeline? Can anyone explain this, especially about the timeline and about the helical world line not being centered vertically?
 
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You are confusing several things. What I think you are describing with two cones is the past and future lightcone of an event. This is the surface that separates the parts of spacetime that can influence or be influenced by that event from the rest of spacetime that is too far away for causal influences to propagate in the time available.

This has nothing to do with the conic sections of orbits. In fact, orbits are only conic sections in Newtonian gravity. When you switch to a full relativistic model of gravity (and lightcones are only relevant in relativity), not even idealised orbits are perfect conic sections. In fact, the failure of Mercury to be exactly where Newtonian gravity said it would be was one of the earliest tests of relativity.
 
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The elliptical shape of orbits was discovered from data by Kepler (Kepler's first law) in the early 1600's and was mathematically proven by Newton (and Liebnitz?) in the late 1600's. It is unrelated to relativity.
 
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Okay, thanks for clearing that up.
 

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