Name: kepler’s planet distance law
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K12 Standards

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NC 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 Third Law of Planetary Motion

Consideremos un planeta que orbita alrededor del Sol en una órbita elíptica. Si el planeta tarda T en completar una órbita alrededor del Sol, su velocidad angular se expresa como dos pi divididos por T.
La fuerza centrípeta que actúa sobre el planeta en órbita se expresa como el producto de su masa, el cuadrado de su velocidad angular y su distancia media al Sol.
En sustitución de omega, la ecuación de la fuerza centrípeta se puede obtener en términos del período orbital del planeta y el semieje mayor de la órbita.
La fuerza gravitacional del Sol proporciona la fuerza centrípeta para que el planeta orbite alrededor del Sol. Sustituyendo y reorganizando los términos, el cuadrado del período orbital es igual al producto de un término constante y el cubo del semieje mayor de la órbita.
Por lo tanto, el cuadrado del período orbital de un planeta es proporcional al cubo del semieje mayor de la órbita. Esto se conoce popularmente como la tercera ley de Kepler del movimiento planetario. La constante de proporcionalidad, que involucra la constante gravitacional y la masa del Sol, se derivó más tarde cuando Newton estableció su ley de gravitación.

la tercera 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. En 1909, formuló sus dos primeras leyes basadas en las observaciones de sus predecesores, Nikolaus Copernicus y Tycho Brahe. Sin embargo, en 1918, publicó su tercera ley del movimiento planetario, la cual establece una relación matemática precisa entre la distancia promedio de un planeta al Sol y el tiempo que tarda en orbitar alrededor del Sol. Esta ley establece que: <img alt="Equation1" src="/files/ftp_upload/12756/12756_Equations_1.png" style="text-align: center; height: 15px;"> El valor constante de proporcionalidad para esta ley se obtuvo mucho después de que Newton estableció la ley universal de la gravedad. Sin embargo, Kepler formateó esta tercera ley del movimiento planetario basándose en la observación de las lunas galileanas orbitando a Júpiter. Esta ley establece las proporciones de las distancias promedio de cada planeta al Sol en comparación con la distancia promedio de la Tierra al Sol, como se muestra en la Tabla 1. Tabla 1: Proporción de Distancias Planetarias desde el Sol Comparadas con la Distancia Tierra-Sol. <table style="margin-left: auto; margin-right: auto;"> <tbody style="border: 1px solid black;"> <tr> <td style="color: black; border: 1px solid black; text-align: center;">Material</td> <td style="color: black; border: 1px solid black; text-align: center;">Proporción de Distancia Planetaria</td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">Mercurio</td> <td style="color: black; border: 1px solid black; text-align: center;">0.387</td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">Venus</td> <td style="color: black; border: 1px solid black; text-align: center;">0.723</td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">Tierra</td> <td style="color: black; border: 1px solid black; text-align: center;">1.000</td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;"> Marte</td> <td style="color: black; border: 1px solid black; text-align: center;">1.520</td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">Júpiter</td> <td style="color: black; border: 1px solid black; text-align: center;">5.200</td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">Saturno</td> <td style="color: black; border: 1px solid black; text-align: center;">9.570</td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">Urano</td> <td style="color: black; border: 1px solid black; text-align: center;">19.170</td> </tr> <tr> <td style="color: black; border: 1px solid black; text-align: center;">Neptuno</td> <td style="color: black; border: 1px solid black; text-align: center;">30.180</td> </tr> </tbody> </table> El valor real de la distancia entre la Tierra y el Sol fue calculado por primera vez durante un tránsito de Venus utilizando el método de paralaje. Utilizando este valor de la unidad astronómica, se obtuvieron las distancias reales a todos los demás planetas. Esta ley es muy útil para estimar las distancias de todos los satélites alrededor de los planetas jovianos, solo con observar sus períodos de tiempo. 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 Tercera 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. En...

Education

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JoVE Core

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Unit 1

Unidad 1

Gravitation

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KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

kepler’s planet distance law

Kepler’s third law links a planet’s average distance from the Sun to the time it takes to orbit the Sun. This rule gives a clear mathematical relationship between orbital distance and orbital period, which is the time for one full revolution. Johannes Kepler developed this law in the early 17th century after building on the observations of Nicolaus Copernicus and Tycho Brahe.

Kepler first formed his first two laws from those earlier observations. He later published the third law of planetary motion in 1918. The proportionality constant for the law was found much later, after Newton established the universal law of gravitation. Kepler also shaped this third law from observations of the Galilean moons orbiting Jupiter.

The law helped establish the ratios of the average distances of the planets from the Sun compared with Earth’s average distance from the Sun. For example, the distance ratios are 0.387 for Mercury, 0.723 for Venus, 1.000 for Earth, 1.520 for Mars, 5.200 for Jupiter, 9.570 for Saturn, 19.170 for Uranus, and 30.180 for Neptune. These ratios show how planetary orbits can be compared using Earth as the reference point.

The actual Earth-Sun distance was first calculated during a transit of Venus using the parallax method, which measures distance from an observed shift in position. Once this astronomical unit was known, the actual distances to the other planets could be found. The same law is also useful for estimating the distances of satellites around the Jovian planets by observing their time periods.

Kepler’s Planet Distance Law

gravitation

Newton’s Law Behind Planet Motion

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acceleration due to gravity on other planets

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kepler's third law of planetary motion

Kepler’s third law links a planet’s average distance from the Sun to the time it takes to orbit the Sun. This rule gives a clear mathematical relationship between orbital distance and orbital period, which is the time for one full revolution. Johannes Kepler developed this law in the early 17th century after building on the observations of Nicolaus Copernicus and Tycho Brahe. Kepler first formed his first two laws from those earlier observations. He later published the third law of planetary...

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key terms and concepts

Explore how Kepler’s third law connects a planet’s orbit time with its average distance from the Sun, using Earth as the reference for planet distances.

Kepler’s Planet Distance Law | 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

PS.Phy.2.4

Pennsylvania State Academic Standards

Earth and Space Science

Space Systems

3.3.9-12.A

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HS-ESS1-4

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SC.912.E.5

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South Carolina College and Career Ready Science Standards

Earth and Space Science (ESS)

E-ESS1-4.

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New York State Science Learning Standards

Earth and Space Sciences

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Georgia Standards of Excellence

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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 ...

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ESS.EES.1.3

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Kepler’s Planet Distance Law

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