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
Famous quotes containing the words newton, law and/or gravitation:
“Where the statue stood
Of Newton with his prism and silent face,
The marble index of a mind for ever
Voyaging through strange seas of thought, alone.”
—William Wordsworth (1770–1850)
“Nature’s law says that the strong must prevent the weak from living, but only in a newspaper article or textbook can this be packaged into a comprehensible thought. In the soup of everyday life, in the mixture of minutia from which human relations are woven, it is not a law. It is a logical incongruity when both strong and weak fall victim to their mutual relations, unconsciously subservient to some unknown guiding power that stands outside of life, irrelevant to man.”
—Anton Pavlovich Chekhov (1860–1904)
“I look for the new Teacher that shall follow so far those shining laws that he shall see them come full circle; shall see their rounding complete grace; shall see the world to be the mirror of the soul; shall see the identity of the law of gravitation with purity of the heart; and shall show that the Ought, that Duty, is one thing with Science, with Beauty, and with Joy.”
—Ralph Waldo Emerson (1803–1882)