Relation To Newton's Laws
Isaac Newton computed in his Philosophiæ Naturalis Principia Mathematica the acceleration of a planet moving according to Kepler's first and second law.
- The direction of the acceleration is towards the Sun.
- The magnitude of the acceleration is in inverse proportion to the square of the distance from the Sun.
This suggests that the Sun may be the physical cause of the acceleration of planets.
Newton defined the force on a planet to be the product of its mass and the acceleration. (See Newton's laws of motion). So:
- Every planet is attracted towards the Sun.
- The force on a planet is in direct proportion to the mass of the planet and in inverse proportion to the square of the distance from the Sun.
Here the Sun plays an unsymmetrical part which is unjustified. So he assumed Newton's law of universal gravitation:
- All bodies in the solar system attract one another.
- The force between two bodies is in direct proportion to the product of their masses and in inverse proportion to the square of the distance between them.
As the planets have small masses compared to that of the Sun, the orbits conform to Kepler's laws approximately. Newton's model improves Kepler's model and gives better fit to the observations. See two-body problem.
A deviation of the motion of a planet from Kepler's laws due to attraction from other planets is called a perturbation.
Read more about this topic: Kepler's Laws Of Planetary Motion
Famous quotes containing the words relation to, relation, newton and/or laws:
“There is the falsely mystical view of art that assumes a kind of supernatural inspiration, a possession by universal forces unrelated to questions of power and privilege or the artist’s relation to bread and blood. In this view, the channel of art can only become clogged and misdirected by the artist’s concern with merely temporary and local disturbances. The song is higher than the struggle.”
—Adrienne Rich (b. 1929)
“Much poetry seems to be aware of its situation in time and of its relation to the metronome, the clock, and the calendar. ... The season or month is there to be felt; the day is there to be seized. Poems beginning “When” are much more numerous than those beginning “Where” of “If.” As the meter is running, the recurrent message tapped out by the passing of measured time is mortality.”
—William Harmon (b. 1938)
“The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a description of the ruins of St Paul’s, like the editions of Balbec and Palmyra.”
—Horace Walpole (1717–1797)
“That man is a creature who needs order yet yearns for change is the creative contradiction at the heart of the laws which structure his conformity and define his deviancy.”
—Freda Adler (b. 1934)