I imagine it to be Isaac Newton, who brought the discussion of "force" rather than "center" into the modeling of orbits. I imagine that prior to Newton's forces, one had to be either a geocentrist or a heliocentrist.
The answer depends on what is meant by "physics". If it is mathematical physics in the modern sense then the answer is perhaps Newton. But Newton's universe was static with stars performing only minor rotations around centers of mass of their planetary systems. There is a deeper sense in which Newton was first however. Before him mathematical modeling of celestial motions was always kinematic, although it was sometimes supported by a dynamical theory, as in the case of Aristotle or Kepler, but always a qualitative one, only kinematics was mathematized. Newton was first to mathematize the dynamics as well, and to derive kinematics from it. But if it is "physics" in the original sense of Aristotle, what is now called "natural philosophy", then it is most certainly not Newton.
In any case one did not have to be a geocentrist or a heliocentrist before Newton. The third most popular alternative is now called plurality of worlds, or cosmic pluralism, and it predates heliocentrism by at least two centuries. Anaximander speculated about the possibility of multiple worlds. Although he himself preferred geocentrism, the idea was whole heartedly embraced by early atomists, Leucippus, Democritus and Epicurus, the latter writing about an infinite universe filled with systems of worlds, "some like ours, some unlike it". This was accompanied by a developed system of "physics", but of qualitative nature. Since atoms were constantly on the move so presumably was everything made of them. A peculiarity of Epicurus is that he considered the Sun to be approximately of its visible size, and rejected contemporary geometric models in astronomy (homocentric spheres of Eudoxus). He even claimed that "all of geometry is wrong", because its principles were inconsistent with atomism.
During the Renaissence Nicolas of Kusa revived the infinite universe idea saying that the universe had "center nowhere and circumference everywhere". Later Giordano Bruno offered a more elaborate version of cosmic pluralism and was burned for it in 1600. Perhaps the most elaborate plural system prior to Newton was Descartes's vortex theory, where everything moves (although not according to Descartes' concept of "moving"). Universe is partioned into rotating vortices with stars in the middle, and planets circling around them. But like other natural philosophers before Newton Descartes did not provide a mathematical formulation of his dynamics, despite some important insights about the centrifugal force and momentum, which doomed it eventually. For a while in 18th century Cartesian physics and cosmology competed with Newton's, but as Newton's theory provided ever more precise numerical predictions Cartesian vortices remained only an attractive intuitive picture.
Galileo and Kepler used physics (whatever physics was available at that time) to prove that Earth moves around the Sun. This is the difference between Copernicus on one side and Galileo and Kepler on another side. For Copernicus, heliocentrism was a kinematic theory (probably kinematics does not belong to "physics", or does it?) But Galileo and Kepler used dynamical theories, attraction etc. in the case of Kepler, and other arguments like inertia in the case of Galileo. This is certainly physics.
Another question is that most of that physics was wrong. The correct physics was indeed discovered by Newton.
from wikipedia heliocentrism page:
In 1687, Isaac Newton published Philosophiæ Naturalis Principia Mathematica, which provided an explanation for Kepler's laws in terms of universal gravitation and what came to be known as Newton's laws of motion. This placed heliocentrism on a firm theoretical foundation, although Newton's heliocentrism was of a somewhat modern kind. Already in the mid-1680s he recognized the "deviation of the Sun" from the centre of gravity of the solar system. For Newton it was not precisely the centre of the Sun or any other body that could be considered at rest, but "the common centre of gravity of the Earth, the Sun and all the Planets is to be esteem'd the Centre of the World", and this centre of gravity "either is at rest or moves uniformly forward in a right line". Newton adopted the "at rest" alternative in view of common consent that the centre, wherever it was, was at rest.