Quantization Rule for Planetary Motion?

In summary, according to the Sommerfield quantization rule, any physical system with periodic coordinates in time has a quantum condition for each coordinate. However, in the case of planetary motion, the gaps between adjacent quantum levels are so small and there are so many of them that the motion can be treated as continuous and there is no need for a quantization rule.
  • #1
Mahasweta
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according to sommerfield quantization rule "for any physical system in which the co ordinates are periodin functions of time,there exist a quantum condition for each coordinate(e.g in bohrs heory angular momentum is quantised)" then why there is no quantization rule in planetary motion but the coordinates in this system is also periodic functions of time?
 
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  • #2
Mahasweta said:
why there is no quantization rule in planetary motion?

There would be, but the gaps between adjacent quantum levels are so small relative to the mass energy, and momentum of the planet, and there are so many of them, that we can treat the motion of planets as if it is continuous.
 
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What is the Quantization Rule for Planetary Motion?

The Quantization Rule for Planetary Motion is a mathematical principle proposed by German astronomer Johannes Kepler in the early 17th century. It states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. In other words, the farther a planet is from the sun, the longer its orbital period will be.

How was the Quantization Rule discovered?

Johannes Kepler discovered the Quantization Rule through his detailed observations of the planetary orbits made by his predecessor, Danish astronomer Tycho Brahe. Kepler spent years analyzing the data and eventually formulated his three laws of planetary motion, with the Quantization Rule being the third law.

Is the Quantization Rule applicable to all planets?

Yes, the Quantization Rule is applicable to all planets in our solar system, including the Earth. It also applies to other celestial bodies, such as moons and comets, orbiting larger bodies.

What are the implications of the Quantization Rule?

The Quantization Rule has significant implications for understanding the structure and dynamics of the solar system. It allows scientists to accurately predict the orbital periods of planets and other celestial bodies, and has been used to discover new planets and moons. It also played a crucial role in the development of the law of universal gravitation by Sir Isaac Newton.

Are there any exceptions to the Quantization Rule?

While the Quantization Rule holds true for most planets and celestial bodies, there are a few exceptions. For example, Mercury's orbit deviates slightly from the rule due to the gravitational influence of other planets. Additionally, the rule does not apply to objects in highly elliptical or irregular orbits.

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