Name: kepler’s planet distance law
Uploaded: 2023-04-30T11:07:15.000Z
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Kepler's Third Law of Planetary Motion

Consideriamo un pianeta in orbita attorno al Sole in un'orbita ellittica. Se il pianeta impiega il tempo T per completare un'orbita attorno al Sole, la sua velocità angolare è espressa come due pi greco diviso T.
La forza centripeta che agisce sul pianeta orbitante è espressa come il prodotto della sua massa, del quadrato della sua velocità angolare e della sua distanza media dal Sole.
Sostituendo omega, l'equazione della forza centripeta può essere ottenuta in termini di periodo orbitale del pianeta e semiasse maggiore dell'orbita.
La forza gravitazionale del Sole fornisce la forza centripeta per l'orbita del pianeta attorno al Sole. Sostituendo e riorganizzando i termini, il quadrato del periodo orbitale è uguale al prodotto di un termine costante e del cubo del semiasse maggiore dell'orbita.
Pertanto, il quadrato del periodo orbitale di un pianeta è proporzionale al cubo del semiasse maggiore dell'orbita. Questa è popolarmente conosciuta come la terza legge di Keplero del moto planetario. La costante di proporzionalità, che coinvolge la costante gravitazionale e la massa del Sole, è stata derivata più tardi quando Newton enunciò la sua legge di gravitazione.

terza legge di keplero del moto planetario

All'inizio del XVII secolo, l'astronomo e matematico tedesco Giovanni Keplero postulò tre leggi per il moto dei pianeti nel sistema solare. Nel 1609, egli formulò le sue prime due leggi basandosi sulle osservazioni dei suoi avi, Nicolò Copernico e Tycho Brahe. Tuttavia, nel 1618, egli pubblicò la sua terza legge del moto planetario, la quale fornisce una relazione matematica precisa tra la distanza media di un pianeta dal Sole e l'ammontare di tempo che esso impiega per girare intorno al Sole. Essa afferma che:

<img alt="Equation1" src="/files/ftp_upload/12756/12756_Equations_1.png" style="text-align: center; height: 15px;" />

La costante proporzionale per questa legge è stata derivata molto più tardi, dopo che Newton stabilì la legge di gravitazione universale. Tuttavia, Keplero strutturò la sua terza legge del moto planetario basandosi sulle osservazioni delle lune galileiane che orbitano intorno a Giove.

Questa legge ha stabilito i rapporti delle distanze medie di ogni pianeta dal Sole, alla distanza media della Terra dal Sole, come mostrato nella Tabella 1.

Table 1: Ratio of Planetary Distances from the Sun Compared to the Earth-Sun Distance.

<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;">Planetary Distance Ratio</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Mercury</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;">Earth</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;"> Mars</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;">Jupiter</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;">Saturn</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;">Uranus</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;">Neptune</td>
			<td style="color: black; border: 1px solid black; text-align: center;">30.180</td>
		</tr>
	</tbody>
</table>

Il valore effettivo per la distanza della Terra dal Sole è stato calcolato per la prima volta durante il transito di Venere usando il metodo del parallasse. Usando questo valore dell'unità astronomica, è stata ottenuta la distanza effettiva di tutti gli altri pianeti. Questa legge è molto utile per stimare le distanze di tutti i satelliti intorno ai pianeti giganti, semplicemente attraverso l'osservazione dei loro periodi di tempo.

Questo testo è adattato da <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>

Terza legge di Keplero del moto planetario

All'inizio del XVII secolo, l'astronomo e matematico tedesco Johannes Kepler postulò tre leggi per il moto dei pianeti nel sistema solare. In...

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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

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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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Kepler’s Planet Distance Law

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