The *ideas* as to *why do different planets orbit the Sun faster?* goes back to the geocentric solar system of Claudius Ptolemy (motion around the Earth in circles, including the Sun moving around the Earth in a circle), later Copernicus (heliocentric solar system still used circles but around the Sun). The observations of Tycho Brahe using Mars (Tycho geocentric-heliocentric model), Galileo telescope observations, Kepler formulating the laws of planetary motion (elliptical motion, not circles) based upon Tycho Brahe study of Mars, and Isaac Newton.
"In the 1660s, Isaac Newton (1642-1727), armed with calculus, of which he was a co-inventor, developed laws of motion and gravitation, which encompassed the entire universe, more or less subsuming Kepler and Galileo. Kepler's laws retained a flavor of mutual independence, but with the new mathematics, Newton was able to derive enhanced versions of and unite the three. In his 1687 book, Principia Mathematica, he verified, as Kepler had strongly suspected, that they apply to all the solar system planets and by implication to everything everywhere. Newton modestly told the world that he stood on the shoulders of giants, and Johannes Kepler was certainly one of the giants.", ref - Governing the Planets, Sky & Telescope 138(2):58-62, 2019
My note - Newton's law of gravity and motion allowed mathematical modeling of the planets, elliptical orbits around the Sun and accurate position change predictions that Kepler developed from Tycho observations of the motion of Mars.
MS WWT has videos to watch, one is on Galileo. One of the arguments used against Copernicus to claim the Earth did not move, if the Earth moved around the Sun, the Moon would be left behind and not keep up. Galileo telescope observations of the small lights moving around Jupiter showed Jupiter could move as it did yet the tiny lights always kept up with Jupiter. Isaac Newton neatly explained all of this with the universal law of gravity. Thus the Earth could move around the Sun and the Moon be kept in place moving around the Earth, just like the moons of Jupiter do.