How does the Earth stay in orbit around the Sun?
The Earth is not actually orbiting the Sun on its own power; it is perpetually falling into the Sun's gravity well. The mass of the Earth, plus its distance from the Sun, plus the extreme speed at which it is traveling (about 30km/s) keep it from falling into the surface of the Sun itself. This is an example of centripetal force. Because of the Sun's enormous gravity, the Earth is attracted to its surface. The power of that attraction keeps the Earth moving at a constant speed, and that speed is enough to keep the planet from actually moving from its relative position in space. This orbit is not a perfect circle, but an elliptical orbit, with the Earth reaching its "farthest" point from the sun during the Northern Hemisphere's summer months.
The Earth is not revolving just like that, it is revolving because of the gravitational pull of the sun. Mass of the earth, distance and the force allows it to stay in its orbit.
Read Kepler's and Newton's laws and formulas.
The Earth stays in orbit by the massive tug of the gravity of the sun. The sun's mass equals its gravity power, and the sun has many times the amount of mass then the Earth, causing the Earth to be tugged into orbit around the sun. This is much like the way a space shuttle is pulled in orbit around the Earth.