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Astronomy and Space Sciences

Astrodynamics

Laws of Planetary Motion

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Kepler's 3rd Law

Kepler's 3rd Law, known as the Law of Harmonies, describes the relationship between the time it takes for a planet to orbit the Sun (orbital period) and its average distance from the Sun. Mathematically, it can be expressed as

T^2 \propto a^3

where

T

is the orbital period and

a

is the semi-major axis of the orbit. This law allows the comparison of the relative distances and periods of planets in the solar system.

Kepler's 1st Law

Kepler's 1st Law, also known as the Law of Ellipses, states that all planets move in elliptical orbits, with the Sun at one of the two foci. This law challenged the long-standing belief in perfect circular orbits and showed that planetary motions are more complex, leading to more accurate models of the solar system.

Kepler's 2nd Law

Kepler's 2nd Law, often referred to as the Law of Equal Areas, states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means that a planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun, reflecting the conservation of angular momentum.

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