Newton and Kepler's Laws | |
Newton recognized that the velocity of any object is changed when it is acted upon by a unbalanced force. In fact, he postulated that the acceleration (the rate of change of its velocity) is proportional to this unbalanced force. Now an acceleration can involve a change in the size or in the direction of the velocity. Since a planet's orbit is a curved path, certainly the direction of its velocity is changing, which means that it is indeed being acted upon by an unbalanced force. What is the unbalanced force acting on a speeding planet? Newton argued that a planet travels in an curved orbit about the Sun because the Sun exerts a force of gravitational attraction on it. The gravitational force of the Sun causes the planet's path -- its orbit -- to be continuously deflected from a straight line, so that the orbit bends about the Sun. Newton proposed that any two objects -- for example the Sun and a planet -- attract each other with a gravitational force. His Universal Law of Gravitation states that the gravitational force between two objects is proportional to the mass of each object and inversely proportional to the square of the distance between them. The gravitational force is apparent on the Earth -- things fall to the ground because they are attracted by the Earth. Newton's insight was that the same force operating between the Earth and the Moon could explain the Moon's orbit or, operating between the Sun and a planet, explain the planet's orbit. Furthermore, Newton was able
to combine the Law of Universal Gravitation with his understanding of
motion (acceleration proportional to unbalanced force) to find what orbital
motion must look like. In fact, he showed that all three of Kepler's laws
follow mathematically from the Law of Universal Gravitation, and that
in general orbits may be described as conic sections. |