Elliptical Orbits and Resonance of Eccentricities

In summary: Over time, the forces of gravity pulled the planets towards that plane, and the orbits of the planets stayed relatively close to it.
  • #1
Ian J.
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Hi,

Dumb Question #1251:

What I understand so far (which maybe incomplete or wrong): in any system with multiple objects orbiting a larger body (either star+planets or planet+moons) each body can have an influence on the others, such that large bodies such as stars and big gas giants have a common barycenter for their elliptical orbits (e.g. Sun - Jupiter), and that there can be resonance in the orbits such that the orbital periods are related (2:1; 3:2; 5:1; etc).

What I want to know is:

1. How much of an effect does the eccentricity of anyone body's orbit affect the eccentricity of the other bodies' orbits, significantly or insignificantly?

2. In the evolution of a system, does any resonance for the eccentricities of the orbits settle down to an observable pattern (similar to the resonance of the orbit periods)?

TIA

Ian
 
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  • #2
Any body that is significantly different in eccentricity from all the others will tend to end up unhappy - flung out of the system or into a new orbit. This is why the Solar System features mostly near-circular orbits. Objects in random elliptical orbits would keep interacting until they settled down into something similar. Even if the major axes of all the ellipses were in one exact line, they would soon be scattered by mutual interactions.

As far as how much each object affects the others, hard to say without specifying exact circumstances - and then you are getting deep into celestial mechanics.
 
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  • #3
:thumbs: Thanks for that, that's actually quite a reassuring answer :smile:
 
  • #4
tfr000 said:
Any body that is significantly different in eccentricity from all the others will tend to end up unhappy - flung out of the system or into a new orbit. This is why the Solar System features mostly near-circular orbits. Objects in random elliptical orbits would keep interacting until they settled down into something similar. Even if the major axes of all the ellipses were in one exact line, they would soon be scattered by mutual interactions.

I'm happy with that answer. How do you explain that most orbits in the solar system are in the same plane, is it a similar argument?
 
  • #5
Devils said:
How do you explain that most orbits in the solar system are in the same plane, is it a similar argument?
It's got more to do with the way the cloud of gas that ended up as our Solar System collapsed. By the time planets started to form, most of the material was already orbiting close to a single plane(the protoplanetary disc).
 

1. What is an elliptical orbit?

An elliptical orbit is a type of orbit in which an object, such as a planet or satellite, moves around another object in an oval-shaped path. This path is called an ellipse, and the object being orbited is located at one of the two focal points of the ellipse.

2. How do elliptical orbits differ from circular orbits?

Elliptical orbits differ from circular orbits in that they are not perfectly round. In a circular orbit, the distance between the orbiting object and the object being orbited remains the same at all times. In an elliptical orbit, the distance varies, with the object being closer to the other object at one point in the orbit and farther away at another point.

3. What is resonance of eccentricities?

Resonance of eccentricities is a phenomenon that occurs when two objects with elliptical orbits have their orbital paths influenced by each other's gravitational pull. This can cause the eccentricity, or the degree of deviation from a perfect circle, of one object's orbit to match or align with the eccentricity of the other object's orbit. This can result in the objects orbiting in a synchronized pattern or even colliding.

4. How does resonance of eccentricities affect the stability of orbits?

The resonance of eccentricities can greatly affect the stability of orbits. Depending on the specific circumstances, it can either lead to the objects being locked in a stable, synchronized orbit, or it can cause the objects to collide and potentially be destroyed. In some cases, resonance of eccentricities can also cause an object to be ejected from its orbit entirely.

5. What are some examples of resonance of eccentricities in our solar system?

Some examples of resonance of eccentricities in our solar system include the three inner Galilean moons of Jupiter (Io, Europa, and Ganymede), which are in a 1:2:4 resonance, meaning their orbital periods are in a ratio of 1:2:4. Another example is Pluto's orbit, which is in a 3:2 resonance with Neptune, meaning it completes three orbits around the sun in the same amount of time that Neptune completes two orbits.

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