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What pushes planets along?

By the 17th century, people like Descartes and Newton were questioning the Greek view that the circular motions of celestial objects were natural.

For Aristotle, the answer to the question 'why does an object go on moving?' had been 'Because a force continues to push it along'. Galileo suggested that no force is needed to keep an object moving with constant velocity. Newton took this as his first law of motion. 
Newton's answer to 'What force pushes a planet along?' was 'No force is necessary, the motion simply continues'. At the time, this was a revolutionary idea. Newton's explanation: an inward force is needed for a curved orbit, continually pulling the planet away from simple straight line motion. Any satellite must fall inward from the tangent to its circular orbit, again and again and again. That falling constitutes an inward acceleration. 
Gravity, Newton argued, provides the inward pull acting on every satellite. The acceleration due to gravity is v2/ R, where v is the satellite’s orbital speed and R is the radius of its circular orbit.