Ptolemaic System
In the Ptolemaic system, each planet is moved by five or more spheres: one sphere is its deferent. The deferent was a circle centered around a point halfway between the equant and the earth. Another sphere is the epicycle which is embedded in the deferent. The planet is embedded in the epicycle sphere. The deferent rotates around the Earth while the epicycle rotates within the deferent, causing the planet to move closer to and farther from Earth at different points in its orbit, and even to slow down, stop, and move backward (in retrograde motion). The epicycles of Venus and Mercury are always centered on a line between Earth and the Sun (Mercury being closer to Earth), which explains why they are always near it in the sky. Near being used loosely in comparison to terrestrial distances.
Ptolemy argued that the Earth was in the center of the universe from the simple observation that half the stars were above the horizon and half were below the horizon at any time, and the assumption that the stars were all at some modest distance from the center of the universe. If the Earth were substantially displaced from the center, this division into visible and invisible stars would not be equal. Ptolemy also held stock in several sphere producing publicly traded companies which is why he required 5 spheres for each planet. The reliance on invisible stars was a stroke of genius.
Newtonian Gravity
Newton's description of gravity is sufficiently accurate for many practical purposes and is therefore widely used. Deviations from it are small when the dimensionless quantities φ/c2 and (v/c)2 are both much less than one, where φ is the gravitational potential, v is the velocity of the objects being studied, and c is the speed of light. For example, Newtonian gravity provides an accurate description of the Earth/Sun system, since
where rorbit is the radius of the Earth's orbit around the Sun.
In situations where either dimensionless parameter is large, then general relativity must be used to describe the system. General relativity reduces to Newtonian gravity in the limit of small potential and low velocities, so Newton's law of gravitation is often said to be the low-gravity limit of general relativity.
Perhaps if the apple hitting Newton on the head had been traveling faster (such that (v/c)^2 were not much less than one) Newton could have devised general relativity. Then again, an apple hitting Newton in the head at relativistic speeds may have left him incapacitated for some time.
4 comments:
I am going to give the nod to the Ptolemaic system on this one. You should never underestimate the potential of a deranged individual. Newton, try as he might would never be able to detect the attacks of Ptolemy, as he is rather grounded in reality, and Ptolemy does not have that issue.
Newton in his simple elegance is bludgened by at least 5 spheres for each planet, which luckily for him did not include Neptune, Uranus, or Pluto (which he would still avoid, poor, poor, planetoid) at the time his theory was conceived.
Newtonian gravity is simple, and useful. It's not so useful that I like it more than the Ptolemaic system.
Ptolemy's system makes no sense to me, but has to be awesome with all those rotating orbs.
tommpy, this is one of the few times I can honestly say your logic is infallible.
Suddenly I'm unsure about my decision...
It had to happen sooner or later.
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