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

Giovanni Keplero affermò nella sua prima legge che ogni pianeta traccia un'orbita ellittica, con il Sole in uno dei suoi fuochi.
Nell'orbita ellittica, un pianeta è il più vicino al Sole nel punto del perielio A e il più lontano dal Sole quando si trova nel punto dell'afelio B. La distanza media del pianeta dal Sole è uguale al semiasse maggiore dell'ellisse.
Al perielio, l'energia potenziale del pianeta è inferiore a quella dell'afelio, poiché la distanza rA è minore della distanza rB.
Seguendo il principio di conservazione dell'energia, l'energia totale del pianeta in un'orbita chiusa viene conservata. Pertanto, l'energia cinetica del pianeta al perielio è superiore a quella all'afelio.
Poiché l'energia cinetica è pari alla metà del prodotto della massa del pianeta e del quadrato della sua velocità orbitale, il pianeta si muove più velocemente nella sua orbita quando è più vicino al Sole al perielio e rallenta quando è lontano dal Sole.

la prima legge di keplero del moto planetario

All'inizio del diciassettesimo secolo, l'astronomo e matematico tedesco Giovanni Keplero postulò tre leggo per il moto dei pianeti nel sistema solare. Egli formulò le prime due leggi basandosi sulle osservazioni dei suoi antenati, Nicolò Copernico e Tycho Brahe.

L'astronomo polacco Nicolò Copernico ideò una teoria che presentava un modello eliocentrico per il sistema solare. Secondo questa teoria eliocentrica, tutti i pianeti, compresa la Terra, orbitano in modo circolare attorno al Sole.

Dall'altro lato, l'astronomo danese Tycho Brahe, il datore di lavoro di Giovanni Keplero, aveva meticolosamente registrato la posizione dettagliata di ogni pianeta. Per i pianeti più visibili, queste osservazioni erano in accordo con la teoria eliocentrica copernicana, eccetto per il pianeta Marte.

Mentre analizzava i dati di Tycho Brahe riguardo a Marte, Giovanni Keplero realizzò che la teoria copernicana era accurata eccetto che per il fatto che i pianeti orbitavano attorno al Sole in orbite ellittiche e non circolari. Questo lo portò alla sua prima legge del moto planetario, la quale affermava che ogni pianeta viaggia lungo un'ellisse, con il Sole situato in uno dei fuochi dell'ellisse.

Un'ellisse è un cerchio allungato. Il grado di elongazione di un'ellisse è espresso usando un parametro chiamato eccentricità.

<img alt="Equation1" src="/files/ftp_upload/12754/12754_Figure_1.png" style="text-align: center; height: 500px;" />

L'asse di un ellisse lungo l'elongazione è chiamato asse maggiore a, e quello perpendicolare ad esso è l'asse minore b. Di conseguenza l'eccentricità di un'ellisse è espressa come:

<img alt="Equation1" src="/files/ftp_upload/12754/12754_Equations_1.png" style="text-align: center; height: 50px;" />

Siccome b < a, l'eccentricità di un ellisse è sempre minore dell'unità. Per un cerchio, a = b, quindi l'eccentricità di un cerchio è zero.

L'eccentricità dell'orbita marziana è di 0,0935. Esso è considerato avere la maggiore eccentricità dopo Mercurio, il quale ha eccentricità uguale a 0.21. L'orbita della Terra ha un'eccentricità di 0.0167.

Visto che i pianeti sono in orbite ellittiche con il sole in uno dei fuochi, le loro distanze radiali cambiano durante l'anno. Quando la loro distanza è più vicina al sole si chiama perigeo, mentre quando è più distante si chiama apogeo.

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>

La prima 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. Lui...

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Gravitation

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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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newton's law of gravitation

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gravitation between spherically symmetric masses

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Gravitational Potential Inside a Shell

Gravitational potential energy for spherically symmetric bodies depends on their masses and the distance between them. The idea is to treat each body as if its mass were concentrated at its center of mass. This makes the calculation easier for high school physics. A spherically symmetric mass can be thought of as many concentric spherical shells. Now place a point mass at a distance r from the center of one shell. Every particle on a given spherical ring is the same distance from that point...

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Point-Mass Approximation in Spherical Gravity

Newton’s law of gravitation gives the force between two point masses. For large spherical objects, such as the Earth, the Moon, and other planets, the same law can be used by treating each body as if its mass were concentrated at its center. This idea can be proven by comparing gravitational potential energy. The transcript shows that a hollow sphere of mass M and a point mass m give the same energy result as two extended solid spherical objects. To set up the proof, a tiny ring on the shell...

reduced mass coordinates: isolated two-body problem

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Center of Mass in the Two-Body Problem

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acceleration due to gravity on earth

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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

Earth's Spin and Apparent Weight

Earth’s spin changes how weight is measured on the surface. Because the Earth turns once every 24 hours, objects on the surface move in a circle. That motion requires a net centripetal force, which points toward the center of the circle. The north and south poles are the only exception. At the equator, the force that provides this inward pull comes from Earth’s gravity. It is the difference between an object’s true weight and the normal force from the ground. The normal force is the support...

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

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How Earth’s Shape Affects Apparent Weight

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potential energy due to gravitation

Gravitational Binding and Potential Energy

Gravitational potential energy describes how gravity stores energy between two masses. Because gravity is a conservative force, the work needed to move an object between two points depends on the starting and ending positions, not on the path taken. That is why a gravitational potential energy function can be written in terms of spatial coordinates. For a mass bound by gravity to another object, the potential energy is negative near the attracting body and rises toward zero as the distance...

the principle of superposition and the gravitational field

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Adding Gravitational Forces with Superposition

Gravitational forces can be added using the principle of superposition. For objects that are sufficiently far apart, the net gravitational force on a point object is the vector sum of the forces from each mass. This means each force is found first, and then the forces are added as vectors. Superposition is useful because gravity from more than one object can combine in ways that are not always easy to see. One force may be increased or reduced by another force, or the final effect may be a...

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escape velocity

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circular orbits and critical velocity for satellites

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Orbital Speed and Period in Circular Paths

Orbital speed and period in circular paths explain how the Moon, planets, and satellites stay in motion around larger bodies. The Moon orbits Earth. Earth and the other planets orbit the Sun. The space above our atmosphere also contains many artificial satellites. A circular orbit is the simplest orbit to study. It helps show how an object’s speed and its period, or the time for one full orbit, depend on where it is and what it circles. Nicolaus Copernicus first suggested that Earth and the...

energy of a satellite in a circular orbit

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Satellite Orbits and Energy in Space

Satellite orbits and energy in space depend on altitude, orbit shape, and gravity. Thousands of artificial satellites circle Earth every day at many different distances. Satellites below 1,600 km are in low-Earth orbit, or LEO. Research satellites and Earth observation satellites are usually placed in LEO. They mostly move in elliptical orbits, which are oval-shaped paths. Navigation satellites are placed in medium-Earth orbit, or MEO, which ranges from 2,000 km to 36,000 km above Earth’s...

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

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...

kepler's third law of planetary motion

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...

tidal forces

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detection of black holes

How Astronomers Find Black Holes

Black holes are found through indirect astronomical evidence. They were first proposed in the 1920s, but they stayed outside observational astronomy until the 1970s. Their closest known cousins are neutron stars, which are made mostly of packed neutrons and are extremely dense. A neutron star can have the mass of the Sun while its diameter is only a few kilometers. Because of that, the escape velocity from its surface is close to the speed of light. Interest in black holes rose again in the...

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Weightlessness and Einstein’s Equivalence

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space-time curvature and the general theory of relativity

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Einstein’s Gravity and Mercury’s Orbit

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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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South Carolina College and Career Ready Science Standards

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New York State Science Learning Standards

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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.
Their ...

Tidal Forces

The origin of Earth&#39;s ocean tides has been a subject of continuous investigation for over 2000 years. However, the work of Newton is considered to be ...

Circular Orbits and Critical Velocity for Satellites

The Moon orbits around the Earth. In turn, the Earth (and other planets) orbit the Sun. The space directly above our atmosphere is filled with artificial ...

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Newton&#39;s law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, ...

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First Law of Thermodynamics

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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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