At the end of the 1700s astronomers were searching for a planet between Mars and Jupiter because of a mathematical prediction made by a man named J.E. Bode. A relationship in position of the known planets in 1766 was noted by another man named Johann Titius; in 1778 Bode devised a math model to predict where other planets were likely to be found (details of the math are in the first link I have attached). In 1781 Uranus was discovered at a distance from the sun predicted by Bode's model. Because Bode's model predicted a planet in the orbit between Mars and Jupiter many scientists were looking for it in the late 1700s/early 1800s. A German group calling themselves the Celestial Police spent several years searching but the dwarf planet Ceres, the first object in the asteroid belt to be discovered, was found in 1801 by Giuseppe Piazzi, working in Palermo. At first scientists believed Ceres to be the predicted planet, but several other asteroids were discovered in the orbit over the next few years, and by the mid-1800s scientists considered the area to be an asteroid belt.
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