Name: kepler’s planet distance law
Uploaded: 2023-04-30T11:07:15.000Z
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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

Güneş'in etrafında eliptik bir yörüngede dönen bir gezegen düşünün. Gezegenin Güneş etrafındaki bir yörüngesini tamamlaması T zamanını alırsa, açısal hızı iki pi'nin T'ye bölünmesiyle ifade edilir.
Yörüngedeki gezegene etki eden merkezcil kuvvet, kütlesinin, açısal hızının karesinin ve Güneş'e olan ortalama uzaklığının çarpımı olarak ifade edilir.
Omega yerine, merkezcil kuvvet denklemi, gezegenin yörünge periyodu ve yörüngenin yarı ana ekseni cinsinden elde edilebilir.
Güneş'in yerçekimi kuvveti, gezegenin Güneş etrafında dönmesi için merkezcil kuvveti sağlar. Terimleri yerine koyarsak ve yeniden düzenlersek, yörünge periyodunun karesi, sabit bir terimin çarpımına ve yörüngenin yarı ana ekseninin küpüne eşittir.
Bu nedenle, bir gezegenin yörünge periyodunun karesi, yörüngenin yarı ana ekseninin küpü ile orantılıdır. Bu, halk arasında Kepler'in gezegensel hareketin üçüncü yasası olarak bilinir. Yerçekimi sabitini ve Güneş'in kütlesini içeren orantılılık sabiti, daha sonra Newton'un yerçekimi yasasını ifade etmesiyle türetilmiştir.

kepler'in gezegen hareketlerinin Üçüncü yasası

17. yüzyılın başlarında, Alman astronom ve matematikçi Johannes Kepler, güneş sistemindeki gezegenlerin hareketleri için üç yasa önerdi. 1909'da, Nikolaus Copernicus ve Tycho Brahe'nin gözlemlerine dayanarak ilk iki yasasını ortaya koydu. Ancak 1918'de, gezegenlerin hareketleriyle Güneş etrafında tam bir devri için bir gezegenin ortalama uzaklığı ile geçen süre arasında kesin matematiksel bir ilişki veren üçüncü yasasını yayınladı. Bu yasa şunu ifade eder:

<img alt="Equation1" src="/files/ftp_upload/12756/12756_Equations_1.png" style="text-align: center; height: 15px;" />

Bu yasanın orantı sabiti çok daha sonra, Newton evrensel çekim yasasını oluşturduktan sonra türetilmiştir. Ancak Kepler, gezegen hareketinin bu üçüncü yasasını Jüpiter'in yörüngesindeki Galile uydularının gözlemine dayanarak biçimlendirmiştir.

Bu yasanın orantı sabiti daha sonra, Newton evrensel kütleçekim yasasını kuranıktan sonra türetilmiştir. Ancak Kepler, bu üçüncü gezegen hareketi yasasını, Jüpiter'in etrafında dönen Galileia uydularının gözlemine dayanarak formatladı.

Bu yasa, her bir gezegenin Güneş'e ortalama uzaklık oranlarını, Güneş'e olan Dünya'nın ortalama uzaklık oranıyla karşılaştıran Tablo 1'de gösterildiği gibi belirler.

Tablo 1: Dünyanın Güneş'e olan Uzaklık Oranına Karşı Gezegen Uzaklık Oranı.

<table style="border-collapse: collapse; width: 20%; margin: 20px auto; text-align: center;">
	<thead>
		<tr>
			<th style="border: 1px solid #000; padding: 8px;">Malzeme</th>
			<th style="border: 1px solid #000; padding: 8px;">Gezegen Uzaklık Oranı</th>
		</tr>
	</thead>
	<tbody>
		<tr>
			<td style="border: 1px solid #000; padding: 8px;">Merkür</td>
			<td style="border: 1px solid #000; padding: 8px;">0.387</td>
		</tr>
		<tr>
			<td style="border: 1px solid #000; padding: 8px;">Venüs</td>
			<td style="border: 1px solid #000; padding: 8px;">0.723</td>
		</tr>
		<tr>
			<td style="border: 1px solid #000; padding: 8px;">Dünya</td>
			<td style="border: 1px solid #000; padding: 8px;">1.000</td>
		</tr>
		<tr>
			<td style="border: 1px solid #000; padding: 8px;">Mars</td>
			<td style="border: 1px solid #000; padding: 8px;">1.520</td>
		</tr>
		<tr>
			<td style="border: 1px solid #000; padding: 8px;">Jüpiter</td>
			<td style="border: 1px solid #000; padding: 8px;">5.200</td>
		</tr>
		<tr>
			<td style="border: 1px solid #000; padding: 8px;">Satürn</td>
			<td style="border: 1px solid #000; padding: 8px;">9.570</td>
		</tr>
		<tr>
			<td style="border: 1px solid #000; padding: 8px;">Uranüs</td>
			<td style="border: 1px solid #000; padding: 8px;">19.170</td>
		</tr>
		<tr>
			<td style="border: 1px solid #000; padding: 8px;">Neptün</td>
			<td style="border: 1px solid #000; padding: 8px;">30.180</td>
		</tr>
	</tbody>
</table>

Dünyanın Güneş'ten olan gerçek uzaklık değeri, paralaks yöntemini kullanarak ilk kez Venus'un geçişi sırasında hesaplandı. Astronomik birim değerini kullanarak, diğer tüm gezegenlere olan gerçek uzaklıklar elde edildi. Bu yasa, sadece zaman sürelerini gözlemleyerek Jüpiter'in etrafındaki tüm uyduların uzaklıklarını tahmin etmek için çok yararlıdır.

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'in Hareket Yasaları'ndan uyarlama yapılmıştır.</a>

Kepler'in Gezegen Hareketlerinin Üçüncü Yasası

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

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KEY TERMS AND CONCEPTS

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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

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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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South Carolina College and Career Ready Science Standards

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Kepler’s Planet Distance Law

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