Name: planet orbits as ellipses
Uploaded: 2025-05-22T09:05:41.000Z
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K12 Standards

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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 First Law of Planetary Motion

Johannes Kepler stwierdził w swoim pierwszym prawie, że każda planeta porusza się po eliptycznej orbicie, a Słońce znajduje się w jednym ze swoich ognisk.
Na orbicie eliptycznej planeta znajduje się najbliżej Słońca w punkcie peryhelium A i najdalej od Słońca, gdy znajduje się w punkcie aphelium B. Średnia odległość planety od Słońca jest równa półosi wielkiej elipsy.
W peryhelium energia potencjalna planety jest mniejsza niż w aphelium, ponieważ odległość rA jest mniejsza niż odległość rB.
Zgodnie z zasadą zachowania energii, całkowita energia planety na zamkniętej orbicie jest zachowywana. Dlatego energia kinetyczna planety w peryhelium jest wyższa niż w aphelium.
Ponieważ energia kinetyczna jest równa połowie iloczynu masy planety i kwadratu jej prędkości orbitalnej, planeta porusza się szybciej po swojej orbicie, gdy jest bliżej Słońca w peryhelium i zwalnia, gdy znajduje się z dala od Słońca.

pierwsze prawo keplera dotyczące ruchu planet

Na początku XVII wieku niemiecki astronom i matematyk Johannes Kepler postulował trzy prawa ruchu planet w Układzie Słonecznym. Swoje dwa pierwsze prawa sformułował na podstawie obserwacji swoich przodków, Mikołaja Kopernika i Tycho Brahe.

Polski astronom Mikołaj Kopernik przedstawił teorię stwierdzającą heliocentryczny model Układu Słonecznego. Zgodnie z tą teorią heliocentryczną wszystkie planety, w tym Ziemia, krążą wokół Słońca po orbitach kołowych.

Z drugiej strony duński astronom Tycho Brahe, pracodawca Johannesa Keplera, skrupulatnie i szczegółowo zapisał położenie każdej planety. W przypadku większości widocznych planet obserwacje te były zgodne z teorią heliocentryczną Kopernika, z wyjątkiem planety Mars.

Analizując dane Tycho Brahe dotyczące Marsa, Johannes Kepler zdał sobie sprawę, że teoria Kopernika jest dokładna, z tym wyjątkiem, że planety krążą wokół Słońca po orbitach eliptycznych, a nie kołowych. To doprowadziło go do pierwszej zasady ruchu planet, która stwierdza, że ​​każda planeta porusza się po elipsie, a Słońce znajduje się w jednym z jej ognisk.

Elipsa to wydłużony okrąg. Stopień wydłużenia elipsy wyraża się za pomocą parametru zwanego mimośrodem.

<img alt="Równanie1" src="/files/ftp_upload/12754/12754_Figure_1.png" style="text-align: center; height: 500px; width: 700px;" />

Oś elipsy wzdłuż wydłużenia nazywana jest osią wielką a, a prostopadła do niej osią małą b. Dlatego mimośród elipsy wyraża się jako

<img alt="Równanie1" src="/files/ftp_upload/12754/12754_Equations_1.png" style="text-align: center; height: 50px;" />

Od b < a, mimośród elipsy jest zawsze mniejszy od jedności. Dla okręgu a = b, stąd mimośród koła wynosi zero.

Mimośród orbity Marsa wynosi 0,0935. Uważa się, że ma najbardziej ekscentryczną orbitę po Merkurym, którego ekscentryczność wynosi 0,21. Orbita Ziemi ma mimośród 0,0167.

Ponieważ planety krążą po orbitach eliptycznych, a Słońce jest w jednym z ognisk, ich odległości radialne zmieniają się w ciągu roku. Najbliższa odległość od Słońca nazywana jest perygeum, a dalsza odległość nazywana jest apogeum.

Ten tekst jest adaptacją <a href="https://openstax.org/books/university-physics-volume-1/pages/13-5-keplers-laws-of- planetary-motion">Openstax, University Physics, tom 1, sekcja 13.5 Prawa ruchu Keplera.</a>

Pierwsze prawo Keplera dotyczące ruchu planet

Na początku XVII wieku niemiecki astronom i matematyk Johannes Kepler postulował trzy prawa ruchu planet w Układzie Słonecznym. On...

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planet orbits as ellipses

Planet orbits are not perfect circles. Johannes Kepler used planet data from Tycho Brahe to show that each planet follows an ellipse, with the Sun at one focus. This idea came from studying Mars, which did not fit the circular path expected in the Copernican heliocentric model.

Copernicus had proposed that the solar system is heliocentric, meaning the Sun is at the center and the planets, including Earth, move around it. His model treated those paths as circles. Brahe later recorded the positions of the planets in great detail, and most of the visible planets matched the Copernican picture. Mars was the major exception.

An ellipse is an elongated circle. Its longest axis is the major axis, marked a, and the shorter axis across it is the minor axis, marked b. The amount of stretch is called eccentricity. Because b is less than a, the eccentricity of an ellipse is always less than 1, and a circle has an eccentricity of zero because its sides are equal.

Kepler’s orbit model also explains why a planet’s distance from the Sun changes during the year. The closest point is called perigee, and the farthest point is called apogee. Mars has an eccentricity of 0.0935, which is the most eccentric orbit after Mercury at 0.21. Earth’s orbit is much closer to a circle, with an eccentricity of 0.0167.

Planet Orbits as Ellipses

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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Center of Mass in the Two-Body Problem

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acceleration due to gravity on other planets

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Measuring Gravity on Distant Planets

Gravity near Earth’s surface is measured as acceleration due to gravity. On Earth, students can test it with simple experiments. On other planets, that kind of direct experiment is not possible. Instead, astronomers use observations to find a planet’s gravity. They study how the planet affects nearby objects, especially its satellite. The key idea is that the acceleration depends on the planet’s gravity, not on the object’s mass. To make the calculation, scientists track a satellite’s path...

apparent weight and the earth's rotation

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variation in acceleration due to gravity near the earth's surface

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the principle of superposition and the gravitational field

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Adding Gravitational Forces with Superposition

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circular orbits and critical velocity for satellites

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Orbital Speed and Period in Circular Paths

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energy of a satellite in a circular orbit

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Satellite Orbits and Energy in Space

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kepler's first law of planetary motion

Planet orbits are not perfect circles. Johannes Kepler used planet data from Tycho Brahe to show that each planet follows an ellipse, with the Sun at one focus. This idea came from studying Mars, which did not fit the circular path expected in the Copernican heliocentric model. Copernicus had proposed that the solar system is heliocentric, meaning the Sun is at the center and the planets, including Earth, move around it. His model treated those paths as circles. Brahe later recorded the...

kepler's second law of planetary motion

Kepler's Equal-Area Planet Motion

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kepler's third law of planetary motion

Kepler’s Planet Distance Law

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detection of black holes

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Einstein’s Gravity and Mercury’s Orbit

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key terms and concepts

Learn how Kepler used Mars data to show that planets move in ellipses, not perfect circles, and why eccentricity changes a planet’s distance from the Sun.

Planet Orbits as Ellipses | JoVE K12

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

Kepler's Second 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. His ...

Kepler's Third 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. In ...

Detection of Black Holes

Although black holes were theoretically postulated in the 1920s, they remained outside the domain of observational astronomy until the 1970s.
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Tidal Forces

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Light as Energy

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First Law of Thermodynamics

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Energy Dynamics

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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.

Planet Orbits as Ellipses

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