Predicting orbits and masses of as-yet-unknown bodies

  • Context: Graduate 
  • Thread starter Thread starter gulfcoastfella
  • Start date Start date
  • Tags Tags
    bodies Orbits
Click For Summary

Discussion Overview

The discussion revolves around the methods used to predict the orbits and masses of undiscovered celestial bodies, particularly in the context of Hamiltonian and Lagrangian dynamics. Participants explore the historical and theoretical implications of these dynamics in relation to known bodies and their unexplained orbits.

Discussion Character

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

Main Points Raised

  • One participant questions the relationship between unexplained orbits of known bodies and the prediction of orbits and masses of unknown bodies, suggesting a connection to Hamiltonian Dynamics.
  • Another participant discusses the relative benefits of using Lagrangian mechanics versus Hamiltonian mechanics in solving mechanics problems, particularly in the context of planetary systems.
  • A participant clarifies their focus on Hamilton's Principle and Lagrangian Dynamics, referencing their studies and suggesting that variational methods may be applicable in predicting orbits of undiscovered bodies.
  • Historical examples are cited, such as the predictions of Neptune and Pluto, highlighting the methods used in their discovery.
  • A participant raises a question about the role of perturbation methods in the discovery of Neptune and whether variational methods were involved.
  • Another participant notes the historical context of the prediction of Neptune, indicating uncertainty about the specific calculations used at that time.

Areas of Agreement / Disagreement

Participants express varying views on the methods and historical context of predicting celestial bodies, with no consensus reached on the specific techniques or their applications.

Contextual Notes

There are limitations regarding the historical accuracy of the methods used in the discovery of Neptune and Pluto, as well as the specific roles of Hamiltonian and Lagrangian dynamics in these predictions. The discussion reflects a mix of theoretical exploration and historical inquiry.

gulfcoastfella
Gold Member
Messages
99
Reaction score
1
I read an article on Phys.org (The Strange Case of the Missing Dwarf), and as I'm in the middle of reading and studying Hamiltonian Dynamics, the article made me wonder how the unexplained orbits of existing bodies are used to determine the orbits and masses of as-yet-undiscovered bodies. It sounds suspiciously like Hamiltonian Dynamics. Am I right in thinking so?
 
Astronomy news on Phys.org
Has one done Lagrangian mechanics before Hamiltonian mechanics?

Here is an interesting point: there is rarely any benefit from using a Hamiltonian instead of a Lagrangian to solve a standard mechanics problem.
http://www.people.fas.harvard.edu/~djmorin/chap15.pdf

I find examples of both Lagrangian and Hamiltonian dynamics with respect to planetary systems or binary star systems to globular clusters.
 
Thanks for the reply, Astronuc. When I said Hamiltonian Dynamics, I really meant Hamilton's Principle and Lagrangian Dynamics/Mechanics. I'm currently reading through chapter 7 (Hamilton's Principle - Lagrangian and Hamiltonian Dynamics) of Marion & Thornton's "Classical Dynamics of Particles and Systems, 5th Ed." I've also put a dent in Robert Weinstock's "Calculus of Variations: with Applications to Physics and Engineering."

In Weinstock's text, I've already read about the use of Variational methods to find curves that begin or end at points, but end or begin on curves, respectively. It was this indication that Variational methods can be used with more constraints than just points that got me wondering if similar methods can be used to predict orbits (varied functions) of as-yet-undiscovered bodies based on unexplained motions in already-known bodies.
 
Neptune and Pluto were predicted that way, with a nice precision for Neptune and a bit more messy search for Pluto.
 
mfb, I read that Neptune was discovered through the application of perturbation methods. Does this mean a combination of perturbation and variational methods, or did variational methods not enter into the discovery?
 
The prediction is over 150 years old - all those concepts were quite new back then (Hamilton was 41 at the time Neptune was discovered), I don't know how exactly they did the calculations. It looks like the references here have more details.
 

Similar threads

Replies
17
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 10 ·
Replies
10
Views
5K
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
10K
  • · Replies 21 ·
Replies
21
Views
6K
  • · Replies 9 ·
Replies
9
Views
6K
  • · Replies 31 ·
2
Replies
31
Views
3K
  • · Replies 40 ·
2
Replies
40
Views
23K