# Kepler's laws with introduction to differential calculus

## TL;DR

This paper derives Kepler's laws from Newton's laws and explains the mathematical techniques involved, providing a clear connection between physics and differential calculus for scholars interested in these fields.

## Contribution

It offers a detailed derivation of Kepler's laws from Newton's laws and introduces higher mathematical techniques used in the proofs.

## Key findings

- Derivation of Kepler's laws from Newton's laws
- Explanation of the gravitational law as a consequence of Kepler's laws
- Educational insights into mathematical techniques used in physics

## Abstract

We explain the solution of the following two problems: obtaining of Kepler's laws from Newton's laws (so called two bodies problem) and obtaining the fourth Newton's law (the formula for gravitation) as a corollary of Kepler's laws. This small book is devoted to the scholars, who are interested in physics and mathematics. We also make a series of digressions, where explain some technique of the higher mathematics, which are used in the proofs.