Details in calculations from 19th century astronomy

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Discussion Overview

The discussion revolves around the historical calculations performed by Urban LeVerrier regarding the precession of Mercury's perihelion and the prediction of Neptune's location. Participants explore the methodologies used in 19th-century astronomy, particularly focusing on the application of Newtonian mechanics and the challenges involved in performing these calculations by hand.

Discussion Character

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

Main Points Raised

  • One participant inquires about the details of LeVerrier's calculations for Mercury's perihelion precession and the necessary distance measurements between Mercury and other planets for gravitational force calculations.
  • Another participant suggests using rings to represent other planets, which could simplify the calculations analytically and provides a link to a relevant website.
  • A participant expresses interest in calculating the position of Neptune and asks for starting points for the calculations, as well as additional resources.
  • One participant argues that calculating Neptune's position cannot be done solely from the perihelion precession and suggests focusing on the Sun, Saturn, and Jupiter to explain the differences in observed motion, noting the complexity of such calculations.
  • A later reply appreciates the explanation of the calculation methodology, indicating a better understanding of the historical context.

Areas of Agreement / Disagreement

Participants express varying views on the methodologies for calculating the precession of Mercury's perihelion and the prediction of Neptune's location. There is no consensus on the best approach or the feasibility of performing these calculations by hand.

Contextual Notes

Participants mention the complexity of calculations involved and the potential reliance on modern computational methods, highlighting the limitations of performing these calculations manually.

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TL;DR
Is there a website or paper that shows the calculation in detail?
I’ve read that Urban LeVerrier was able to calculate using Newtonian mechanics the precession of the perihelion point of Mercury’s orbit (1859). Is there a website or paper that shows the calculation in detail?

In particular:

  • How would one decide on the distance between Mercury and the other planets to perform the calculation of the gravitational force?
  • (Can a physics student perform this calculation armed with just the planetary data in the back of the textbook?)
  • A related question: is there a website or paper that shows details of LeVerrier’s calculation to predict the location of the planet Neptune?
  • (I’ve read that this problem would be an inverse problem in modern mathematics and solved with computers, but can someone provide the starting point of this calculation on paper?)
 
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You replace the other planets by rings with the same mass, that makes the calculation accessible analytically. Here is a website doing this.
 
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Thank you for the suggestion and the weblink. I've been interested in doing this calculation by hand for the precession of the perihelion points.

If I want to calculate where to find Neptune in the night sky (famous by-hand calculation of Adams and LeVerrier for the discovery of this planet), what would be the starting point for the calculation?
And is there another website for that calculation?
 
You can't do that just from the perihelion precession - and Uranus has an orbital period of 84 years, longer than the time difference between the discovery of Uranus and Neptune. You can calculate the motion assuming there is only the Sun and Saturn and Jupiter (the rest doesn't matter), compare that to the actual motion, and then look what could explain the difference. The calculations are lengthy if you do this by hand and I don't know if there is an online version of them.
 
Thank you for explaining the methodology of the calculation. That makes this famous bit of science history more understandable to me.
 

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