Newton's Law of Gravitation
By Newton's second law, the gravitational force that acts on the planet is:
where only depends on the property of the Sun. According to Newton's third Law, the Sun is also attracted by the planet with a force of the same magnitude. Now that the force is proportional to the mass of the planet, under the symmetric consideration, it should also be proportional to the mass of the Sun. So the form of the gravitational force should be
where is a universal constant. This is Newton's law of universal gravitation.
The acceleration of solar system body no i is, according to Newton's laws:
where is the mass of body no j, and is the distance between body i and body j, and is the unit vector from body i pointing towards body j, and the vector summation is over all bodies in the world, besides no i itself. In the special case where there are only two bodies in the world, Planet and Sun, the acceleration becomes
which is the acceleration of the Kepler motion.
Read more about this topic: Kepler's Laws Of Planetary Motion
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