Why do planets of our solar system orbit in rings not spheres?

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SUMMARY

The planets of our solar system, including Earth and Mars, orbit the Sun in a similar plane due to the initial conditions of the solar system's formation. The molecular cloud from which the Sun and planets formed had non-zero angular momentum, leading to the creation of a proto-planetary disk. This disk resulted from numerous collisions among particles, which coalesced into planets and asteroids. The gravitational pull of nearby objects also contributes to the stability of these orbits, explaining why structures like Saturn's rings are similarly aligned.

PREREQUISITES
  • Understanding of celestial mechanics
  • Familiarity with the concept of angular momentum
  • Knowledge of proto-planetary disk formation
  • Basic principles of gravitational interactions
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  • Research the formation of proto-planetary disks in astrophysics
  • Study the effects of angular momentum on celestial bodies
  • Explore the dynamics of gravitational interactions in multi-body systems
  • Learn about the characteristics and formation of Saturn's rings
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Astronomy enthusiasts, astrophysicists, and students studying planetary formation and celestial mechanics will benefit from this discussion.

Schoomy
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I was looking at this link: http://en.wikipedia.org/wiki/File:Universe_Reference_Map_%28Location%29_001.jpeg" and wondered to myself why the asteroid belt just outside of Mars is a ring...as opposed to a sphere.

Then I thought, why do all the planets seem to orbit the sun on a similar plane. For example, Earth and Mars have similar orbit planes. Why wouldn't one have a plane of orbit 90 degrees crossed of another?

I couldn't find a good answer online...it's probably simple! :p

Note: I say "sphere" but obviously it can only orbit in a ring. Just imagine, however, that each orbit path left a tracer line behind it. Their orbits wouldn't create spheres over a long timespan would they? Hope that makes sense!
 
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Another thought: this is probably a similar phenomenon to why Saturn's rings are on a very similar plane, yes? Does it have to do with the gravitational pull of nearby objects equalizing?
 
The molecular cloud from which the Sun and planets formed had some initial non-zero angular momentum. The protosun formed about some local concentration of mass. As more and more stuff fell into this protosun it began influencing the rest of the cloud gravitationally. The atoms/molecules with little angular momentum fell into the forming star. The stuff with non-zero angular momentum began orbiting the star. These initial orbits would have been quite random in nature, resulting in lots of collisions. The relative velocity between two particles in roughly the same orbit is quite small compared to the relative velocity between two particles in quite different orbits. The end result of all these collisions was to make the particles coalesce into a proto-planetary disk about the star. The planets (and asteroids) formed from this proto-planetary disk.
 

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