Johannes Kepler was the successor to Tycho Brahe. Armed with Brahe's accurate measurements, Kepler was able to determine the shape of the planetary orbits. It turned out that all objects in orbit travel in the same shape, an ellipse. An ellipse is an elongated circle with, which has two foci, outside the center point. Kepler formulate three laws to describe the orbits of the planets. Kepler's used scientific methods to determine with certainty that the Sun was the center of the solar system, not the Earth.
Kepler's first law states that every planet orbits the Sun in the shape of an ellipse, with the Sun at on of the foci.
Kepler's second law states that a planet sweeps out equal area in equal times throughout its orbit. In one month time, a certain amount of area is swept out, which will be equal to the area swept out at any other month. This means that a planet speeds up as it nears the Sun, and slows down when it is further from the Sun.
Kepler determined that the square of the orbital period is proportional to the cube of the radius. This meant that all the planets had a common feature. The distance was related to the time required to orbit the Sun. With this information a planet's distance from the Sun could be measured simply by measuring the time required for the planet to go around the Sun.