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

[Vectronix]

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?

 

[Ibix]

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.

 

[FactChecker]

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.

 

[Vectronix]

Okay, thanks for clearing that up.