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

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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.
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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.
 

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

What is a space-time conic section?

A space-time conic section refers to the shape of the paths that objects follow through space-time under the influence of gravity. These paths, or orbits, are typically conic sections, which can be ellipses, parabolas, or hyperbolas, depending on the energy and velocity of the orbiting object.

Why are planetary orbits elliptical?

Planetary orbits are elliptical primarily due to the gravitational force exerted by the Sun, which follows an inverse-square law. According to Kepler's First Law, planets move in ellipses with the Sun at one focus. This can be derived from Newton's laws of motion and universal gravitation, and it also aligns with the solutions to Einstein's equations of general relativity in the weak-field approximation.

How does general relativity explain elliptical orbits?

General relativity explains elliptical orbits by describing gravity as the curvature of space-time caused by mass. Objects follow geodesics, or the straightest possible paths, in this curved space-time. For a planet orbiting a star, this geodesic is typically an ellipse, which is a type of conic section.

Are all planetary orbits perfect ellipses?

No, not all planetary orbits are perfect ellipses. While they are predominantly elliptical, they can be slightly perturbed by the gravitational influences of other bodies, leading to variations like precession or slight deviations from a perfect elliptical shape. Additionally, some objects may follow parabolic or hyperbolic trajectories, especially if they are not gravitationally bound to the star.

Can other factors besides gravity influence the shape of planetary orbits?

Yes, other factors can influence the shape of planetary orbits. These include the gravitational pull from other planets, relativistic effects near massive bodies, non-gravitational forces like radiation pressure or drag from interstellar medium, and the distribution of mass within the central star. However, gravity remains the dominant force shaping planetary orbits.

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