Help in explaining a question on gravity

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Discussion Overview

The discussion revolves around the mechanics of gravitational orbits, specifically why larger mass bodies, like the Sun, influence smaller bodies, such as planets, to orbit around them. Participants explore concepts related to the center of mass, barycenters, and the mathematical explanations behind these phenomena.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions why larger mass bodies cause smaller ones to orbit them, seeking clarification on the underlying principles.
  • Another participant asserts that bodies orbit around a common center of mass, introducing the concept of barycenters.
  • A follow-up question is posed regarding whether the Sun also orbits around a center that is not its own, indicating a need for clarification on the solar system's dynamics.
  • Mathematical explanations are sought, with a suggestion to research the concept of barycenter to understand momentum conservation in orbital mechanics.
  • It is noted that in systems with significant mass differences, the barycenter is close to the larger mass, making it reasonable to state that "Earth orbits the Sun" for practical purposes.
  • One participant emphasizes that the heliocentric model is an approximation and that the barycenter is not located at the Sun's center.
  • The distinction between the two-body problem and systems with multiple bodies is raised, with the latter requiring numerical solutions.
  • A participant highlights the Earth-Moon system, noting that their masses are closer in comparison, which makes the barycenter's effect more noticeable, and discusses the implications of this wobble.

Areas of Agreement / Disagreement

Participants express varying views on the implications of the barycenter concept and the accuracy of the heliocentric model. There is no consensus on the extent to which these models represent reality, and the discussion remains unresolved regarding the implications of these dynamics.

Contextual Notes

Participants mention limitations in understanding the mathematical explanations for multi-body systems and the approximations involved in describing orbital mechanics.

trees and plants
Hello. I have this question: do you know why a physical body with bigger mass makes another one orbit around it like the sun does in the solar system and not the opposite of this? Thank you.
 
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The bodies actually orbit around the common center of mass.
 
You mean the sun also orbits around the center of the solar system which is different than the sun?
 
How is this explained mathematically? Do you know?
 
Google "barycenter". A planet orbiting a stationary Sun violates conservation of momentum because the Sun has zero momentum and the planet's momentum is changing. Both need to orbit a common center.

In the case of objects with large mass differences, the barycenter is very close to the center of the larger mass. So "Earth orbits the Sun" is close enough to the truth for most purposes.
 
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So saying heliocentric system is not correct, center of the solar system is correct which is not the sun. I understand now that they were approximations so far, scientists were trying to describe it and so far this is the latest correct view of the orbits of the solar system?
 
universe function said:
You mean the sun also orbits around the center of the solar system which is different than the sun?
Yes, the Solar system's barycenter is not located in Sun's center.
https://spaceplace.nasa.gov/barycenter/en/
universe function said:
How is this explained mathematically? Do you know?
I think only two-body problem can be solved analytically. System with multiple bodies need to be solved numerically.
https://en.m.wikipedia.org/wiki/Two-body_problem
 
The masses of the Earth and Moon are nearer equal to each other and the phenomenon is more appreciable. The Earth has a definite 'wobble' as it 'orbits' the barycentre, once a month and there are no other large bodies in Earth orbit to spoil the effect. The barycentre is about 3/4 of the distance from the centre of the Earth to its surface - pretty significant, eh?
I don't think that amount of wobble is great enough for it to cause enough parallax to affect observations of other objects in the Solar System, though.
 

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