Gavin Howe
Kepler's Second Law, also known as the ''area law', states that a line joining a planet and the Sun sweeps out equal areas during equal intervals of time. In other words, a planet is moving fastest when it is closest to the Sun and slowest when it is farthest away. This law was formulated by Johannes Kepler in the early 17th century and is one of three laws that describe the orbits of planets around the Sun. Kepler's laws replaced circular orbits in the heliocentric theory of Nicolaus Copernicus with elliptical orbits and explained how planetary velocities vary.
| Characteristics | Values |
|---|---|
| Name | Kepler's Second Law or the "area law" |
| Description | A planet is moving fastest when it is closest to the Sun (perihelion) and slowest when it is farthest from the Sun (aphelion) |
| Formula | The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit |
| Publication | 1609 |
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What You'll Learn
Planetary motion
Kepler's laws of planetary motion describe the orbits of planets around the Sun. These laws were published by German mathematician and astronomer Johannes Kepler in 1609, except for the third law, which was published in 1619. Kepler's laws replaced the heliocentric theory of Nicolaus Copernicus, which stated that the planetary orbit is a circle with epicycles and the Sun at its centre.
Kepler's three laws of planetary motion are as follows:
- The orbit of a planet is an ellipse with the Sun at one of the two foci.
- A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This is also known as the 'area law'.
- The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit.
Kepler's second law, the area law, states that the imaginary line joining a planet and the Sun sweeps out equal areas of space during equal time intervals as the planet orbits. This means that planets do not move with constant speed along their orbits. Instead, their speed varies, and they move fastest when they are closest to the Sun (perihelion) and slowest when they are farthest away (aphelion). Kepler arrived at this law through assumptions that were either only approximately true or outright false. One such assumption was that planets are pushed around the Sun by a force from the Sun, which relies on incorrect Aristotelian physics.
Kepler's laws were crucial in Isaac Newton's formulation of his theory of universal gravitation, which explains the unknown force behind Kepler's Third Law. Newton showed that the motion of bodies subject to central gravitational force need not always follow elliptical orbits, but can take paths defined by other, open conic curves.
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Orbital radius and angular velocity
Kepler's second law of planetary motion, also known as the "area law", states that a radius vector joining any planet to the Sun sweeps out equal areas in equal lengths of time. In other words, the areal velocity of a planet revolving around the Sun in an elliptical orbit remains constant, which implies that the angular momentum of a planet remains constant. This means that the angular velocity must vary around the orbit – a planet must have a higher than average velocity near perihelion (when it is closest to the Sun) and a lower than average velocity near aphelion (when it is farthest from the Sun).
The orbital radius and angular velocity of a planet in an elliptical orbit will vary. As the planet travels faster when it is closer to the Sun, and slower when it is farther away, the angular velocity will be higher near perihelion and lower near aphelion. This is because the planet's kinetic energy is not constant in its path – it has more kinetic energy near the perihelion and less kinetic energy near the aphelion, implying more speed at the perihelion and less speed at the aphelion.
Kepler's second law can be applied to the motion of planets around the Sun. It states that the orbit of a planet is an ellipse with the Sun at one of the two foci. This replaced the previous belief that planetary orbits were circular. Kepler's laws describe how planetary velocities vary, with the speed at which planets move in space continuously changing. The elliptical shape of the orbit means that the distance from the Sun is proportional to the time taken to cover a small piece of the orbit.
Kepler's second law is one of three laws of planetary motion, which describe the motions of the planets in the solar system. These laws were published by Johannes Kepler in 1609, based on the astronomical observations of Tycho Brahe. Kepler's second law was derived from the assumption that planets are pushed around the Sun by a force from the Sun, which is inversely proportional to the distance from the Sun.
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Planet's speed varies
Kepler's laws of planetary motion, published by Johannes Kepler in 1609, describe the orbits of planets around the Sun. Kepler's second law of planetary motion states that a radius vector joining any planet to the Sun sweeps out equal areas in equal lengths of time. This means that a planet's speed varies depending on its distance from the Sun. When a planet is closer to the Sun, it travels faster, and when it is farther from the Sun, it travels slower. This is because the propelling force from the Sun is inversely proportional to the distance from the Sun. Kepler reasoned that since the planets inhabited a plane, gravity spreading in three dimensions would be a waste. Thus, he proposed an inverse rather than the correct inverse square law.
Kepler's second law can be applied to understand the motion of planets in the solar system. For example, Earth moves the fastest when it is closest to the Sun, which occurs in early January when the Earth is about 147 million km (91 million miles) from the Sun. At this point, the Earth is travelling at a speed of 30.3 kilometres (18.8 miles) per second. Kepler's second law also established the concept of perihelion and aphelion. Perihelion refers to when a planet is closest to the Sun, and aphelion refers to when a planet is farthest from the Sun.
The validity of Kepler's second law was crucial to Isaac Newton's formulation of his famous law of gravitation between the Earth and the Moon and between the Sun and the planets. Newton showed that the motion of bodies subject to central gravitational force need not always follow the elliptical orbits specified by Kepler's first law. Instead, the motion can be in parabolic or hyperbolic orbits, depending on the total energy of the body. For example, a comet can enter and exit the solar system without returning. Kepler's second law also led to the observation that the angular momentum of any planet about an axis through the Sun and perpendicular to the orbital plane is unchanging.
Kepler's second law has two versions: the "distance law" and the "area law". The "area law" is the more widely accepted version and is considered one of three laws describing the motions of planets in the solar system. Kepler himself never numbered these laws or distinguished them from his other discoveries. It was not until nearly two centuries after Kepler's work that the current formulation of his laws took on its settled form. Voltaire's Eléments de la philosophie de Newton (Elements of Newton's Philosophy) of 1738 was the first publication to use the terminology of "laws".
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Planet's distance from the Sun
Kepler's second law of planetary motion describes the motions of planets in the solar system. The law states that a radius vector joining any planet to the Sun sweeps out equal areas in equal lengths of time. In other words, the law establishes that a planet will travel faster when it is closer to the Sun and slower when it is farther away. This is because the angular velocity of the planet in its elliptical orbit will vary. Kepler's second law can be applied to understand the relationship between a planet's distance from the Sun and its velocity.
Kepler's laws of planetary motion, published by Johannes Kepler in 1609, describe the orbits of planets around the Sun. Kepler's laws replaced the heliocentric theory of Nicolaus Copernicus, which stated that planetary orbits were circular with the Sun at the center. Instead, Kepler's laws introduced elliptical orbits, with the Sun at one of the two foci. This was a significant advancement in the study of planetary motion, as it provided a mathematical foundation for understanding the solar system.
Kepler's second law can be applied to any planet in the solar system to understand its motion around the Sun. For example, when a planet is near perihelion (the point in its orbit closest to the Sun), the distance between the Sun and the planet is smaller. To conserve angular momentum, the planet must increase its tangential velocity. Similarly, when the planet is near aphelion (the point in its orbit farthest from the Sun), the distance between the Sun and the planet is larger, and the planet's tangential velocity must decrease to maintain the same angular momentum.
Kepler's second law also has implications for the shape of planetary orbits. By studying the orbit of Mars, Kepler inferred that other bodies in the solar system, including those farther away from the Sun, also have elliptical orbits. This was a breakthrough discovery, as it contradicted the previous belief that circular orbits were "perfect" and that all planets followed circular paths. Kepler's laws introduced the concept of elliptical orbits and explained how planetary velocities vary based on their distance from the Sun.
In summary, Kepler's second law of planetary motion is applicable to understanding the relationship between a planet's distance from the Sun and its velocity. The law states that a planet's velocity will vary depending on its distance from the Sun, with faster speeds when closer to the Sun and slower speeds when farther away. Kepler's laws revolutionized our understanding of planetary motion by introducing elliptical orbits and providing a mathematical framework for describing the solar system.
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Calculation of orbits
Kepler's laws of planetary motion, published by Johannes Kepler in 1609, describe the orbits of planets around the Sun. Kepler's three laws state that:
- The orbit of a planet is an ellipse with the Sun at one of the two foci: This is the first property of an ellipse, defined by two points called foci. The Sun is located at one focus of the orbital ellipse, with the planet following the ellipse in its orbit, resulting in a constantly changing planet-to-Sun distance.
- A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time: This law, known as the "area law", states that planets do not move at a constant speed along their orbits. Instead, their speed varies so that the imaginary line joining the centres of the Sun and the planet covers equal areas in equal amounts of time. As a result, a planet is moving fastest when it is closest to the Sun (perihelion) and slowest when it is farthest from the Sun (aphelion).
- The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit: This law implies that the time it takes for a planet to orbit the Sun increases with the radius of its orbit. For example, Mercury, being the innermost planet, takes only 88 days to orbit the Sun, while Saturn requires 10,759 days.
These laws replaced the previous concept of circular orbits and epicycles in the heliocentric theory of Nicolaus Copernicus with elliptical orbits, providing a more accurate description of planetary velocities and orbits within the Solar System.
Kepler's laws have practical applications in calculating the orbits of planets and other celestial bodies. By utilising these laws, scientists can determine the orbital period, radius, and angular velocity of a planet in its elliptical orbit. Additionally, Kepler's Third Law enables the calculation of the masses of two objects in space when their distance and orbital period are known. This law is not limited to the Solar System but can be applied to any two objects in space.
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Frequently asked questions
Kepler's 2nd law can be applied when observing the motion of planets in orbit around the Sun.
Kepler's 2nd law states that a line joining a planet and the Sun sweeps out equal areas during equal intervals of time. In other words, a planet is moving fastest when it is closest to the Sun (perihelion) and slowest when it is at its furthest from the Sun (aphelion).
Previous theories, such as those proposed by Aristotle and Ptolemy, suggested that planets orbit the Sun in a circular motion. Kepler's laws of planetary motion replaced these circular orbits with elliptical orbits.
Kepler's 2nd law has several implications. Firstly, it implies that planets do not move with a constant speed along their orbits. Secondly, it suggests that the speed of a planet is influenced by its distance from the Sun, with the planet travelling faster when closer to the Sun and slower when farther away.
