The geocentric theory is a system for describing the universe with Earth-centered coordinates. It was extremely popular from ancient times until the 1600s, as it was particularly effective at cosmological predictions.
The work of Galileo and Kepler began to change this (see Copernican Revolution). The idea that planets move around the sun, in nearly circular ellipses, gradually took hold. The difficulty of calculating the orbits was one factor which militated against quick acceptance of Kepler's laws of motion.
By the 1800s, the spectacular successes of Newtonian theory convinced everyone that the Sun is a preferred frame of reference, and that the laws of physics must be applied in that frame. The geocentric theory was considered to be profoundly mistaken, and the heliocentric theory correct. However, this view is based more on a philosphical. rather than a scientific position. Bartosz Milewski (2006) states in reference to the Geocentric Theory: "Looking at the predictions it made of planetary movements, it is pretty good. One could probably derive it nowadays from the heliocentric theory by changing the system of coordinates (since the system attached to the Earth is not inertial, one would have to use Einstein's general relativity to do that correctly). Maybe physicists would be forced to introduce more cycles upon cycles to account for all the anomalies—maybe infinitely many. So even though the two theories differ in complexity, they are presumably equivalent in their predictive power." 
Scripture Quoted to justify Geocentric Theory
A small number of people still accept the Geocentric theory. They interpret the Bible as saying that the geocentric theory is correct.
"He has fixed the earth firm, immovable." (1 Chronicles 16:30)
"Thou hast fixed the earth immovable and firm ..." (Psalm 93:1)
"Thou didst fix the earth on its foundation so that it never can be shaken." (Psalm 104:5)
"...who made the earth and fashioned it, and himself fixed it fast..." (Isaiah 45:18)
"The sun also ariseth, and the sun goeth down, and hasteth to his place where he arose." (Ecclesiastes 1:5)
"Then spake Joshua to the LORD in the day when the LORD delivered up the Amorites before the children of Israel, and he said in the sight of Israel, Sun, stand thou still upon Gibeon; and thou, Moon, in the valley of Ajalon. And the sun stood still, and the moon stayed, until the people had avenged themselves upon their enemies. Is not this written in the book of Jasher? So the sun stood still in the midst of heaven, and hasted not to go down about a whole day." (Joshua 10, 12-13)