Name: kepler's equal-area planet motion
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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 Second Law of Planetary Motion

Güneşin etrafında eliptik bir yörüngede bulunan, A'dan A'yahareket eden, 1 zamanda dθ açısal yer değiştirmesine sahip bir gezegen düşünün. Daha sonra, dt zamanında kapsanan dA sektör alanı, gezegenin radyal mesafesinin ve rdθ yayının yarısı olacaktır. Sektör hızı dA/dt daha sonra r2dθ/dt'nin yarısına eşit olacaktır.
Burada, dθ/dt gezegenin açısal hızıdır. Böylece, denklemin gezegenin kütlesi ile çarpılması, gezegenin açısal hızı cinsinden sektör hızını verir.
Ancak, mr2ω gezegenin açısal momentumudur. Bu nedenle, sektör hızı, gezegenin açısal momentumunun kütlesinin iki katına oranına eşittir.
Kepler'in ikinci yasası, bir gezegenin B'den B1'e hareket etmesi için dt ile aynı süreyi alırsa, BB1 yayının altındaki sektör alanının, AA1 yayının altındaki alana eşit olacağını belirtir.
Bu nedenle, sektör hızı sabittir, bu da açısal momentumun korunduğunu ima eder.

kepler'in gezegen hareketinin İkinci yasası

17. yüzyılın başlarında, Alman astronom ve matematikçi Johannes Kepler, güneş sistemi içindeki gezegenlerin hareketi için üç yasa önerdi. İlk yasası, tüm gezegenlerin bir elips yörüngesinde Güneş etrafında döndüğünü ve Güneş'in elipsin bir odak noktasında olduğunu belirtir. Bu nedenle, bir gezegenin Güneş'e olan mesafesi, Güneş etrafındaki devrimi sırasında değişir.

Elips yörüngesindeyken, gezegenin toplam enerjisi korunur. Bu nedenle, gezegen apoapsis noktasında yavaşlar ve perigee noktasında ivme kazanır. Bu sonuçlar, Kepler'ı ikinci yasasını belirtmeye yönlendirdi, yani gezegenin yarıçap vektörü eşit zaman aralıklarında eşit alanları süpürür. Bu, bir gezegenin A noktasından A1 noktasına seyahat etmek için aynı süreyi aldığını ve ardından B noktasından B1 noktasına seyahat ettiğini varsayarsak, AF1A1 ve BF1B1 alanlarının eşit olduğu anlamına gelir, şekil 1'de gösterildiği gibi.

<img alt="Figure1" src="/files/ftp_upload/12755/12755_Figure_1.png" style="text-align: center; height: 350px;" />

Bir zaman aralığında alan sabit olduğu için, gezegenin sektör hızı sabit kalır. Sektör hızı, gezegenin açısal momentumuyla orantılı olduğundan, Kepler'in ikinci yasası bir gezegenin eliptik yörüngede açısal momentumunun korunduğunu ima eder.

Bu metin, <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> sitesinden uyarlanmıştır.

Kepler'in Gezegen Hareketinin İkinci Yasası

17. yüzyılın başlarında, Alman gökbilimci ve matematikçi Johannes Kepler, güneş sistemindeki gezegenlerin hareketi için üç yasa öne sürdü. Onun...

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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

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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 Temel Fizik, kinematik, dinamik, akışkanlar mekaniği, statik, dalgalar ve akustik dahil olmak üzere temel fizik konularının teorisini ve uygulamasını kısa ve anlaşılması kolay animasyonlu videolarla tanıtıyor. Ek olarak, sektör içindeki bilim insanı videoları, dünya çapındaki günümüz laboratuvarlarında gerçekleştirilen klasik ve orijinal araştırma deneylerinde ilgili kavramların uygulanmasını göstermektedir.

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Motion and Stability- Forces and Interactions

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Earth and Space Science

Space Systems

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Weather and Climate

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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

HS-ESS1-4.

Georgia Standards of Excellence

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Kepler's Equal-Area Planet Motion

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