# Details in calculations from 19th century astronomy

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• CPW
In summary, Urban LeVerrier used Newtonian mechanics to calculate the precession of Mercury's perihelion point in 1859. There are websites and papers available that show the calculation in detail. To decide on the distance between Mercury and other planets for the calculation, one can replace them with rings of equal mass. However, this is not enough to find Neptune's location in the night sky, as Uranus has a longer orbital period. A physics student armed with planetary data may not be able to perform this calculation by hand, as it is lengthy and may require advanced mathematical techniques. There may not be an online version of this calculation available.
CPW
TL;DR Summary
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?)

You replace the other planets by rings with the same mass, that makes the calculation accessible analytically. Here is a website doing this.

anorlunda
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.

## 1. What were the main methods used for astronomical calculations in the 19th century?

In the 19th century, astronomers primarily used mathematical equations and observations through telescopes to calculate details about celestial bodies and their movements.

## 2. How accurate were the calculations made in the 19th century compared to modern methods?

The accuracy of calculations made in the 19th century varied depending on the skill and resources of the astronomer. However, with the advancements in technology and understanding of physics, modern methods are generally more precise.

## 3. How did the 19th century calculations contribute to our understanding of the universe?

The 19th century calculations played a crucial role in expanding our knowledge of the universe. They helped determine the size, distance, and movements of celestial bodies, leading to breakthroughs in theories such as gravity and planetary motion.

## 4. How did the 19th century calculations impact future developments in astronomy?

The 19th century calculations laid the foundation for future developments in astronomy. They provided a starting point for further research and advancements in technology, leading to more accurate and detailed calculations in modern times.

## 5. What challenges did 19th century astronomers face when making calculations?

19th century astronomers faced challenges such as limited technology, lack of understanding of certain concepts, and the vastness of the universe. These factors often made calculations difficult and less accurate compared to modern methods.

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