Birth of Modern Astronomy
In 1543, Copernicus' ideas that the sun is at the center of the solar system was published in "De Revolutionibus." The "unorthodox" idea came to be known as the heliocentric model of cosmology thereby changing the way the universe is viewed.
Tycho Brahe
Tycho Brahe, under the patronage of Frederick II, established an astronomical observatory on the Danish island of Hveen in approximately 1576. There he extensively observed and recorded the positions of the sun, moon and planets.
Johannes Kepler
However, it wasn't until after Brahe died that Kepler was able to obtain the majority of Brahe's research, thereby developing Kepler's laws of planetary motion.
Kepler's First Law
Using algebra, he found a relation between the periods of revolution about the sun and the planets length of the semimajor axis. According to the law, "Each planet moves about the Sun in an orbit that is an ellipse, with the Sun at one focus of the ellipse."
Gravity and Orbit
This elliptical orbit is a closed kind of curve where the sum of the distances to two points are equal. In the case of planetary motion, because the sun acts as a foci, the gravitational pull of the sun speeds up the momentum of the planet on its approach and as the planet recedes from the sun it slows down. Consequently, gravity keeps the planets in their elliptical orbit.