Kepler's laws of planetary motion describe the motions of planets around the Sun, and they provide insights into the relationship between a planet's orbital velocity and its distance from the Sun.
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Kepler's First Law (Law of Orbits): This law states that planets move in elliptical orbits with the Sun at one focus of the ellipse.
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Kepler's Second Law (Law of Areas): This law states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This implies that a planet moves faster when it is closer to the Sun and slower when it is farther from the Sun.
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Kepler's Third Law (Law of Harmonies): This law provides a quantitative relationship between the period of a planet's orbit and its distance from the Sun. It states that the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (a) of its orbit. Mathematically, this is expressed as: \[ T^2 \propto a^3 \] where \(T\) is the orbital period (the time it takes for one complete orbit), and \(a\) is the average distance from the Sun (in astronomical units).
From the implications of these laws, particularly the second law, we can conclude that:
- A planet's orbital velocity is inversely related to its distance from the Sun. As a planet moves closer to the Sun (in a part of its orbit known as perihelion), it moves faster. Conversely, as it moves farther away (in a part of its orbit known as aphelion), it moves slower.
In summary, a planet's orbital velocity decreases with increasing distance from the Sun. This relationship is a fundamental aspect of planetary motion as described by Kepler.
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