Kara Sears
Kepler's laws of planetary motion describe how planetary bodies orbit the Sun. They were derived by the German astronomer Johannes Kepler, who published his first two laws in 1609, and his third law in 1619. Kepler's laws replaced circular orbits in the heliocentric theory of Nicolaus Copernicus with elliptical orbits and explained how planetary velocities vary. Isaac Newton computed in his Principia the acceleration of a planet moving according to Kepler's first and second laws, and his work was crucial in proving Kepler's laws.
| Characteristics | Values |
|---|---|
| Name | Johannes Kepler |
| Nationality | German |
| Profession | Astronomer, mathematician |
| Date of Birth | 1571 |
| Date of Death | 1630 |
| Known For | Kepler's laws of planetary motion, Kepler's first law, Kepler's second law, Kepler's third law |
| Education | N/A |
| Awards | N/A |
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What You'll Learn
Kepler's first law
The German astronomer Johannes Kepler derived his laws of planetary motion from the astronomical observations of Tycho Brahe. Kepler's first law reflected his discovery that he could not reconcile Brahe's precise observations with a circular fit to Mars' orbit, which has the highest eccentricity of all planets except Mercury.
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Kepler's second law
Kepler arrived at this law through a combination of accurate astronomical observations made by Tycho Brahe and assumptions that were either only approximately true or outright false. One such assumption was that planets are pushed around the Sun by a force from the Sun, which relies on the incorrect Aristotelian idea that an object needs to be pushed to maintain motion. Kepler also reasoned that the force from the Sun is inversely proportional to the distance from the Sun, believing that gravity spreading in three dimensions would be inefficient since the planets inhabited a plane. This led him to propose an inverse rather than the correct inverse square law.
The validity of Kepler's second law implies that a planet must have a higher than average velocity near perihelion (when it is closest to the Sun) and a lower than average velocity near aphelion (when it is farthest from the Sun). The angular velocity must also vary around the orbit in a similar way. Kepler's second law follows from the law of conservation of angular momentum, and it played a crucial role in Isaac Newton's formulation of his famous law of universal gravitation. Newton showed that the motion of bodies subject to central gravitational force need not always follow the elliptical orbits specified by Kepler's first law but can take paths defined by other open conic curves, such as parabolic or hyperbolic orbits.
It is worth noting that Kepler himself did not privilege his second law in any particular way, and he never numbered these laws or distinguished them from his other discoveries. The term "'Kepler's second law'" is, therefore, somewhat of a misnomer. It took nearly two centuries for the current formulation of Kepler's work to take on its settled form, and it was not until Voltaire's "Eléments de la philosophie de Newton" (Elements of Newton's Philosophy) in 1738 that the terminology of "laws" was first used in relation to Kepler's work.
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Kepler's third law
The law states that the square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit. In simpler terms, this means that a planet's orbital period is proportional to the size of its orbit. The orbital period is the amount of time it takes for a planet to complete one orbit around the Sun. The semi-major axis is half of the longest axis of the elliptical orbit.
This law, along with the other two laws of planetary motion, was formulated by Johannes Kepler based on the astronomical observations of Tycho Brahe. Kepler's laws replaced the circular orbits and epicycles of the heliocentric theory of Nicolaus Copernicus with elliptical orbits, providing a more accurate description of planetary motion in the Solar System.
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The work of Isaac Newton
Kepler's laws of planetary motion were derived by the German astronomer Johannes Kepler and published in 1609, except for the third law, which was published in 1619 (although one source says 1618). Kepler's laws describe the motion of planets in the solar system, stating that their orbits are elliptical with the Sun at one of the two foci, and explaining how planetary velocities vary.
Isaac Newton's work built upon Kepler's laws. In his Philosophiæ Naturalis Principia Mathematica, Newton computed the acceleration of a planet moving according to Kepler's first and second laws. He found that the direction of the acceleration is towards the Sun and that the magnitude of the acceleration is inversely proportional to the square of the planet's distance from the Sun (the inverse square law). This implied that the Sun may be the physical cause of the acceleration of planets.
However, Newton took an instrumentalist view, stating that he considered forces from a mathematical perspective rather than a physical one. He did not assign a cause to gravity. Instead, Newton defined the force acting on a planet as the product of its mass and the acceleration. This led to his understanding that every planet is attracted towards the Sun and that the force acting on a planet is directly proportional to the mass of the planet and inversely proportional to the square of its distance from the Sun.
Newton's work also showed that the motion of bodies subject to central gravitational force is not limited to the elliptical orbits specified by Kepler's first law but can follow other paths, including parabolic and hyperbolic orbits.
Newton's theory of gravitation, formulated nearly eighty years after Kepler's work, provided the unknown force behind Kepler's third law. Newton's work thus proved crucial in understanding the laws of planetary motion and gravitation between celestial bodies.
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The influence of Tycho Brahe
Kepler's laws of planetary motion, published in 1609, describe the orbits of planets around the Sun. These laws replaced the heliocentric theory of Nicolaus Copernicus, which stated that planets moved in circular orbits, with elliptical orbits.
In 1600, Kepler began working with Brahe, who asked him to define the orbit of Mars. After Brahe's death in 1601, Kepler inherited his mentor's data and worked with it for nine years. He struggled to reconcile Brahe's observations with a circular orbit for Mars but eventually discovered that the planet's orbit was elliptical. This discovery led to Kepler's first law of planetary motion, which states that planets move in elliptical orbits with the Sun at one focus.
Kepler's analysis of Brahe's data also led to his second law of planetary motion. He noticed that an imaginary line drawn from a planet to the Sun swept out equal areas of space in equal times, regardless of the planet's position in its orbit. This realization contradicted the contemporary belief that the circle was the Universe's perfect shape and that planetary orbits must be circular.
In summary, Tycho Brahe's influence on Kepler's laws was substantial. Brahe's accurate observations and extensive data provided the foundation for Kepler's analysis and discovery of the elliptical orbits of planets. Through his work with Brahe's data, Kepler formulated his three laws of planetary motion, revolutionizing our understanding of the solar system.
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