What would happen if the earth did not move in space?
There are two movements of Earth in space- rotation and revolution.
The rotation of Earth occurs about its axis. The angle of the axis is approximately 23.5 degrees. The rotation of Earth means that Earth spins on an imaginary axis (or line) that stems from the North to South pole of the planet. The rotation of Earth on its axis is what causes day and night. The side of Earth that is facing the sun experiences day, while the side that faces away from the Sun experiences night.
As the Earth rotates on its axis, it also revolves around the Sun. The revolution of Earth entails it orbiting (circling) the Sun. The revolution of Earth is what causes the seasons. Since the Earth is tilted on its axis, one hemisphere (North or South) will lean toward the sun and the opposite hemisphere leans away from the Sun. The hemisphere that leans toward the Sun experiences summer or spring. The hemisphere that leans away from the Sun experiences winter or fall.
Therefore, if the earth did not move in space, there would also be no day or night. Likewise, seasons would not occur. This would result in extreme temperature differences between the sides (or hemispheres) of Earth that face the sun and that face away from the sun.