Which Newton work gave a mathematical basis for Kepler's laws and heliocentric dynamics?

Newton’s work that gave a mathematical basis for Kepler’s laws and heliocentric dynamics was Principia Mathematica, formally titled Philosophiæ Naturalis Principia Mathematica.

First published in 1687, the Principia set out Newton’s laws of motion and universal gravitation. In its third book, Newton applied those principles to the Solar System, showing how an inverse-square gravitational force could produce the orbital behavior described empirically by Kepler.

Newton demonstrated that Kepler’s second law follows from a central force and that inverse-square attraction leads to conic-section orbits, including ellipses. His framework also explained tides, lunar irregularities, planetary masses, Earth’s shape, and cometary trajectories.

The work is often shortened to Principia, while Principia Mathematica is a widely used shortened form of its Latin title. It should not be confused with Arithmetica Universalis, Newton’s mathematical textbook, or Opticks, his major work on light and color.