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

  • B
  • Thread starter Vectronix
  • Start date
In summary: The world line traced out by a planet orbiting a star will be curved, but it will always be centered on the vertical axis. This is because the curvature of spacetime is always proportional to the distance from the center of the galaxy.
  • #1
Vectronix
64
2
TL;DR Summary
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?
 
Physics news on Phys.org
  • #2
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.
 
Last edited:
  • Like
Likes vanhees71, FactChecker, PeterDonis and 1 other person
  • #3
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.
 
  • Like
Likes vanhees71
  • #4
Okay, thanks for clearing that up.
 

1. What is a space-time conic section?

A space-time conic section is a curve that is formed by the intersection of a cone and a plane in a four-dimensional space-time. It is a mathematical concept that is used to describe the shape of planetary orbits.

2. How does a space-time conic section affect planetary orbits?

A space-time conic section determines the shape of a planetary orbit. If the orbit is elliptical, it means that the cone and the plane intersect at an angle, resulting in a curved path for the planet.

3. Why are planetary orbits elliptical?

Planetary orbits are elliptical because of the influence of gravity. According to Newton's laws of motion, objects in space are attracted to each other by the force of gravity. This force causes the planet to follow a curved path around the sun, resulting in an elliptical orbit.

4. Are all planetary orbits elliptical?

No, not all planetary orbits are elliptical. Some planets, such as Mercury and Venus, have nearly circular orbits. This is because their orbits are closer to the sun and are less affected by the gravitational pull of other planets.

5. How does the shape of a planetary orbit affect the planet's motion?

The shape of a planetary orbit affects the planet's motion by determining its speed and distance from the sun. When a planet is closer to the sun, it moves faster and has a shorter orbital period. On the other hand, when a planet is farther from the sun, it moves slower and has a longer orbital period.

Similar threads

I Michelson & Morley in Space-Time Diagram: Can't Make it Work
    • Special and General Relativity
Replies
18
Views
1K
I Hypatia, Elliptic orbits, conic sections
    • Classical Physics
Replies
6
Views
2K
I Length contraction viewed with Heaviside equations
    • Special and General Relativity
2
Replies
42
Views
4K
I Request for Input: 2D Minkowski Spacetime Diagram Generator
    • Special and General Relativity
Replies
6
Views
1K
I "Unexpected" Symmetry in Elliptical Orbit
    • Other Physics Topics
Replies
11
Views
2K
Understanding Conic Sections: Exploring the Plane-Cone Intersection
    • General Math
Replies
1
Views
3K
Is my fictional Solar System stable and realistic?
    • Sci-Fi Writing and World Building
Replies
21
Views
1K
I I need some support, please, for a gravity assist analysis
    • Classical Physics
3
Replies
86
Views
4K
Solving Linear-Nonlinear Systems
    • Precalculus Mathematics Homework Help
Replies
4
Views
1K
MHB Proof and tutorial on conic sections
    • Math Guides, Tutorials and Articles
Replies
5
Views
8K

Hot Threads

Recent Insights

Back
Top