harmonic law
Definition
- Noun:
- Kepler's Third Law of Planetary Motion: A scientific law in astronomy formulated by Johannes Kepler. It states that for any planet orbiting the Sun, the square of its orbital period (the time it takes to complete one orbit) is directly proportional to the cube of the semi-major axis of its orbit (its average distance from the Sun). This means the ratio is constant for all planets in the solar system.
Usage Examples
- Noun:
- Kepler discovered the harmonic law by analyzing Tycho Brahe's astronomical data.
- The harmonic law allows astronomers to calculate a planet's distance from the Sun if its orbital period is known.
- According to the harmonic law, a planet farther from the Sun has a significantly longer year.
Advanced Usage
- Mathematical Expression: The harmonic law is commonly expressed as P² ∝ a³, where P is the orbital period and a is the semi-major axis. For objects orbiting the Sun, the constant of proportionality is 1 when using years and astronomical units (AU).
- Generalized Form: Newton later showed that a more general form of this law applies to any two orbiting bodies, where the constant depends on the sum of their masses.
Variants and Related Words
- Kepler's Third Law: The most common synonym for "harmonic law."
- Law of Periods: Another, less common, name for the same principle.
- Orbital Period (n): The time taken for one object to complete an orbit around another.
- Semi-major Axis (n): The longest radius of an elliptical orbit, representing the average distance.
Synonyms
- Kepler's Third Law
- Law of Periods
Related Phrases
- To obey/follow the harmonic law: To behave in accordance with this principle.
- The moons of Jupiter also obey a form of the harmonic law.
- To derive from the harmonic law: To be calculated or proven using this law.
- The relative distances of the planets were derived from the harmonic law.
Noun
-
a law stating that the ratio of the square of the revolutionary period (in years) to the cube of the orbital axis (in astronomical units) is the same for all planets
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