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# The discovery of Neptune: the science overcomes itself

**Hello everyone!**

For those who don’t know us, a very brief introduction on who we are and where we go! **MathIsInTheAir** is an italian blog of Applied Maths and surroundings and here are the links: english version and italian version. Although our english blog contains not so many posts, we would like to expand it in the very near future. I don’t want you to get bored, so if you like you may visit our websites or you may read the “not so quick introduction” to MathIsInTheAir I did last year.

Today I just want to present our second english mathematical post, called “**The discovery of Neptune: the science overcomes itself**” written by Andrea Capozio. As it can be understood by the name, the post goes throught the steps that brought to the discovery of the planet Neptune. It is a very fashinating story, so read it!

We hope you like it!

**by MathIsInTheAir**

# The discovery of Neptune: the science overcomes itself

# 1. Introduction.

Mathematics has always had a tremendous impact on reality, bigger than you might think, lowering itself perfectly in the present but also anticipating and outlining the future. Even with less advanced than today’s technological means, past discoveries changed our perception of the world, simply using theories and formulations.

In this post we won’t see complicated formulas (or at least nothing that we haven’t already seen at high school) or theorems on the limit of human understanding, I would rather tell a story that struck me deeply: how humans discovered Neptune. It’s a story explaining what scientific activity is: a constant challenge to extend the boundaries of our understanding and our knowledge of reality.

# 2. Newton, Laplace and Lagrange.

Without starting from Adam and Eve (although even there at the beginning there was an apple), I would say that our story can start in 1687 with the publication of the formula of universal gravitation by Isaac Newton: in the universe every material point attracts every other material point with a force that is directly proportional to the product of their masses and inversely proportional to the square of their distance.

###### *Isaac Newton (1642 – 1727)*

From this result, it was immediately clear that the motion of the planets of the Solar System is largely determined by the attraction of the sun (just think that the mass of the Sun is 1,000 times the mass of Jupiter, the largest planet of the Solar System).

No time to celebrate this historic achievement, which criticism of Newton’s law immediately set off; substantially, this formula gave a good approximation for the motion of the planets, but to describe correctly the dynamics of the Solar System it’s needed to take into account the Forces of mutual attraction between all the planets, thus extending the gravitational problem to the case of n-bodies. Newton himself could not resist the obvious objections, feeling so necessary that God put sometimes planetary orbits into place.

Eighteenth century Physicists and mathematicians dedicated themselves to the study of “perturbations” exerted by the planets in the n-body problem:

• Laplace introduced mathematical methods able to treat the problem of planetary perturbations and to show that the observed motion of Jupiter and Saturn could be explained by the mutual attraction of the two planets.

• Although he did considerable simplifications to the overall problem, Joseph Louis Lagrange in 1772 demonstrated the existence of a stable system for the case of three bodies.

These and other achievements in the late 700 and early 800 have laid the foundation for the discovery of the planet Neptune.

### …Continue reading our post:

**English version: here**

**Italian version: here**

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