Name: kepler's equal-area planet motion
Uploaded: 2025-05-22T09:05:41.000Z
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North Carolina K-12 Science Standard Course of Study

9-12

Earth and Environmental Science

Earth's Place in the Universe

ESS.EES.1.1

Kepler's Second Law of Planetary Motion

Considere un planeta en una órbita elíptica alrededor del sol que se mueve de A a A1 con un desplazamiento angular de dθ en el tiempo dt. Entonces, el área del sector dA cubierta en el tiempo dt sería la mitad del producto de la distancia radial del planeta y el arco rdθ. La velocidad del sector dA/dt sería entonces igual a la mitad de r2dθ/dt.
Aquí, dθ/dt es la velocidad angular del planeta. Por lo tanto, multiplicando la ecuación por la masa del planeta se obtiene la velocidad del sector en términos de la velocidad angular del planeta.
Sin embargo, mr2ω es el momento angular del planeta. Por lo tanto, la velocidad del sector es igual a la relación entre el momento angular del planeta y dos veces su masa.
La segunda ley de Kepler establece que si un planeta tarda el mismo tiempo dt en pasar de B a B1, entonces el área del sector bajo el arco BB1 sería igual al área bajo el arco AA1.
Por lo tanto, la velocidad del sector es constante, lo que implica que el momento angular permanece conservado.

la segunda ley del movimiento planetario de kepler

En el siglo XVII, el astrónomo y matemático alemán Johannes Kepler postuló tres leyes para el movimiento de los planetas en el sistema solar. Su primera ley establece que todos los planetas orbitan alrededor del Sol en una órbita elíptica, con el Sol en uno de los focos de la elipse. Por lo tanto, la distancia de un planeta al Sol varía a lo largo de su revolución alrededor del Sol. Mientras está en una órbita elíptica, la energía total del planeta se conserva. Por lo tanto, el planeta se desacelera cuando está en el apogeo y se acelera cuando está en el perigeo. Estas conclusiones llevaron a Kepler a enunciar su segunda ley, que el vector radio del planeta barre áreas iguales en tiempos iguales. Esto significa que si un planeta tarda el mismo tiempo en viajar de A a A1, y luego de B a B1, entonces las áreas AF1A1 y BF1B1 son iguales, como se muestra en la Figura 1. <img alt="Figure1" src="/files/ftp_upload/12755/12755_Figure_1.png" style="text-align: center; height: 350px;"> Desde que el área es constante en un intervalo de tiempo dado, la velocidad sectorial del planeta permanece constante. Dado que la velocidad sectorial es proporcional al momento angular del planeta, la segunda ley de Kepler implica que el momento angular de un planeta en una órbita elíptica se conserva. Este texto está adaptado de<a href="https://openstax.org/books/university-physics-volume-1/pages/13-5-keplers-laws-of-planetary-motion"> Openstax, University Physics Volume 1, Section 13.5 Kepler's Laws of Motion.</a>

La segunda ley del movimiento planetario de Kepler

A principios del siglo XVII, el astrónomo y matemático alemán Johannes Kepler postuló tres leyes para el movimiento de los planetas en el sistema solar. Suyos...

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kepler's equal-area planet motion

Kepler's second law explains how a planet moves faster and slower in its orbit around the Sun. Johannes Kepler, a German astronomer and mathematician in the early 17th century, developed three laws for planetary motion. His first law says that planets travel in elliptical orbits, with the Sun at one focus of the ellipse. Because the planet-Sun distance changes during the orbit, the planet does not move at the same speed all the time.

In an elliptical orbit, the total energy of the planet is conserved. As a result, the planet slows down at apogee, the point farthest from the Sun, and speeds up at perigee, the point closest to the Sun. Kepler used this idea to state his second law. The law says that the radius vector, the line from the Sun to the planet, sweeps out equal areas in equal times.

This means that if a planet takes the same time to travel from A to A1 and from B to B1, then the areas AF1A1 and BF1B1 are equal. Because the area swept out in a given time interval stays constant, the planet's sector velocity also remains constant. Sector velocity is linked to angular momentum. For that reason, Kepler's second law shows that the angular momentum of a planet in an elliptical orbit is conserved.

Kepler's Equal-Area Planet Motion

gravitation

Newton’s Law Behind Planet Motion

Newton’s law of gravitation links falling objects, the Moon’s orbit, and planetary motion. Before Newton, many people thought the sky and Earth followed different laws. Kepler later described the three laws of planetary motion, but their connection to a deeper force was still unclear. Isaac Newton made that connection in 1665 to 1666. He showed that the same phenomenon explains why objects fall to Earth and why the Moon moves around Earth. He also found that the Moon’s centripetal acceleration...

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kepler's second law of planetary motion

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kepler's third law of planetary motion

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key terms and concepts

Learn how Kepler's second law explains changing planet speed, equal areas in equal time, and why angular momentum stays conserved in an elliptical orbit.

Kepler's Equal-Area Planet Motion | JoVE K12

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JoVE Core Física presenta la teoría y la aplicación de conceptos físicos fundamentales, como la cinemática, dinámica, mecánica de fluidos, estática, ondas y acústica, mediante animaciones audiovisuales concisas y fáciles de entender. Además, los vídeos de científicos en acción muestran la aplicación de los conceptos relacionados en experimentos de investigación clásicos y originales, realizados en laboratorios de todo el mundo.

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Motion and Stability- Forces and Interactions

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Earth and Space Science

Space Systems

3.3.9-12.A

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Weather and Climate

3.3.9-12.E

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Earth’s Place In The Universe

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Earth’s Place in the Universe

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SC.912.E.5

SC.912.E.5.6

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South Carolina College and Career Ready Science Standards

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E-ESS1-4.

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New York State Science Learning Standards

Earth and Space Sciences

HS-ESS1-4.

Georgia Standards of Excellence

SAST1

SAST1.1

Kepler's First Law of Planetary Motion

In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. He ...

In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. His ...

Kepler's Third Law of Planetary Motion

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Nuclear Fusion

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First Law of Thermodynamics

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Use models to illustrate how the sun produces energy.

ESS.EES.1.3

Explain how Earth's position relative to the sun influences conditions on Earth.

Kepler's Equal-Area Planet Motion

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