Kepler's Laws of Planetary Motion are three scientific laws that describe the motion of planets around the Sun. They were formulated by the German astronomer Johannes Kepler in the early 17th century based on the extensive observations made by Danish astronomer Tycho Brahe.
1. Kepler's First Law, also known as the Law of Ellipses, states that the orbit of a planet is an ellipse with the Sun at one of the two foci. This means that the path of a planet is not a perfect circle but a slightly elongated shape.
2. Kepler's Second Law, also known as the Law of Equal Areas, states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means that a planet moves faster when it is closer to the Sun and slower when it is farther away.
3. Kepler's Third Law, also known as the Law of Harmonies, states that the square of the orbital period of a planet is directly proportional to the cube of its average distance from the Sun. This means that the farther a planet is from the Sun, the longer its orbital period.
Kepler's Laws revolutionized our understanding of the motion of planets and laid the foundation for Isaac Newton's laws of motion and gravitation. They are fundamental principles in the field of celestial mechanics and have greatly contributed to our understanding of the solar system and the universe.
Motion is always relative. Based on the energy of the particle under motion, motions are classified into two types:
Bounded Motion
Unbounded Motion
In bounded motion, the particle has negative total energy (E < 0) and has two or more extreme points where the total energy is always equal to the potential energy of the particle, i.e., the kinetic energy of the particle becomes zero.
For eccentricity 0 ≤ e <1, E < 0 implies the body has bounded motion. A circular orbit has eccentricity e = 0, and an elliptical orbit has eccentricity e < 1.
In unbounded motion, the particle has positive total energy (E > 0) and has a single extreme point where the total energy is always equal to the potential energy of the particle, i.e., the kinetic energy of the particle becomes zero.
For eccentricity e ≥ 1, E > 0 implies the body has unbounded motion. The parabolic orbit has eccentricity e = 1, and the hyperbolic path has eccentricity e > 1.
Also Read:
Gravitational Potential Energy
Gravitational Field Intensity
Kepler’s laws of planetary motion can be stated as follows:
Kepler’s First Law – The Law of Orbits
According to Kepler’s first law, “All the planets revolve around the sun in elliptical orbits having the sun at one of the foci”. The point at which the planet is close to the sun is known as perihelion (about 147 million kilometres from the sun), and the point at which the planet is farther from the sun is known as aphelion (152 million kilometres from the sun). It is characteristic of an ellipse that the sum of the distances of any planet from two foci is constant.
Kepler's Laws of Planetary Motion
Kepler’s First Law – The Law of Orbits
Kepler’s Second Law – The Law of Equal Areas
Kepler’s second law states, “The radius vector drawn from the sun to the planet sweeps out equal areas in equal intervals of time”.
As the orbit is not circular, 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 implies more speed at the perihelion and less speed (vmin) at the aphelion. If r is the distance of the planet from the sun at perihelion (rmin) and at aphelion (rmax), then,
rmin + rmax = 2a × (length of the major axis of an ellipse) . . . . . . . (1)
Keplers Second Law
Kepler’s Second Law – The Law of Equal Areas
Using the law of conservation of angular momentum, the law can be verified. At any point of time, the angular momentum can be given as L = mr2ω.
Now, consider a small area ΔA described in a short time interval Δt and the covered angle is Δθ. Let the radius of curvature of the path be r, then the length of the arc covered = r Δθ
ΔA = 1/2[r.(r.Δθ)]= 1/2r2Δθ
Therefore, ΔA/Δt = [ 1/2r2]Δθ/dt
Taking limits on both sides as, Δt→0, we get,
Now, by conservation of angular momentum, L is a constant.
Thus, dA/dt = Constant
The area swept in equal intervals of time is a constant.
Kepler’s second law can also be stated as, “The areal velocity of a planet revolving around the sun in elliptical orbit remains constant, which implies the angular momentum of a planet remains constant”. As the angular momentum is constant, all planetary motions are planar motions, which is a direct consequence of central force.
Check: Acceleration Due to Gravity
Kepler’s Third Law – The Law of Periods
According to Kepler’s law of periods,”The square of the time period of revolution of a planet around the sun in an elliptical orbit is directly proportional to the cube of its semi-major axis”.
T2 ∝ a3
The shorter the orbit of the planet around the sun, the shorter the time taken to complete one revolution. Using the equations of Newton’s law of gravitation and laws of motion, Kepler’s third law takes a more general form.
P2 = 4π2 /[G(M1+ M2)] × a3
Where M1 and M2 are the masses of the two orbiting objects in solar masses.
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Frequently Asked Questions on Kepler’s Law
Q1
What does Kepler’s first law state?
According to Kepler’s first law, all the planets revolve around the Sun in elliptical orbits, with the Sun as one of the foci.
Q2
What does Kepler’s second law state?
According to Kepler’s second law, the speed at which the planets move in space continuously changes. The second law helps to explain that when the planets are closer to the Sun, they will travel faster.
Q3
What is Kepler’s third law?
Kepler’s third law, also called the law of periods, states that the square of the orbital period is proportional to the cube of its mean
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Explanation:
Kepler's Laws of Planetary Motion are three scientific laws that describe the motion of planets around the Sun. They were formulated by the German astronomer Johannes Kepler in the early 17th century based on the extensive observations made by Danish astronomer Tycho Brahe.
1. Kepler's First Law, also known as the Law of Ellipses, states that the orbit of a planet is an ellipse with the Sun at one of the two foci. This means that the path of a planet is not a perfect circle but a slightly elongated shape.
2. Kepler's Second Law, also known as the Law of Equal Areas, states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means that a planet moves faster when it is closer to the Sun and slower when it is farther away.
3. Kepler's Third Law, also known as the Law of Harmonies, states that the square of the orbital period of a planet is directly proportional to the cube of its average distance from the Sun. This means that the farther a planet is from the Sun, the longer its orbital period.
Kepler's Laws revolutionized our understanding of the motion of planets and laid the foundation for Isaac Newton's laws of motion and gravitation. They are fundamental principles in the field of celestial mechanics and have greatly contributed to our understanding of the solar system and the universe.
Introduction to Kepler’s Laws
Motion is always relative. Based on the energy of the particle under motion, motions are classified into two types:
Bounded Motion
Unbounded Motion
In bounded motion, the particle has negative total energy (E < 0) and has two or more extreme points where the total energy is always equal to the potential energy of the particle, i.e., the kinetic energy of the particle becomes zero.
For eccentricity 0 ≤ e <1, E < 0 implies the body has bounded motion. A circular orbit has eccentricity e = 0, and an elliptical orbit has eccentricity e < 1.
In unbounded motion, the particle has positive total energy (E > 0) and has a single extreme point where the total energy is always equal to the potential energy of the particle, i.e., the kinetic energy of the particle becomes zero.
For eccentricity e ≥ 1, E > 0 implies the body has unbounded motion. The parabolic orbit has eccentricity e = 1, and the hyperbolic path has eccentricity e > 1.
Also Read:
Gravitational Potential Energy
Gravitational Field Intensity
Kepler’s laws of planetary motion can be stated as follows:
Kepler’s First Law – The Law of Orbits
According to Kepler’s first law, “All the planets revolve around the sun in elliptical orbits having the sun at one of the foci”. The point at which the planet is close to the sun is known as perihelion (about 147 million kilometres from the sun), and the point at which the planet is farther from the sun is known as aphelion (152 million kilometres from the sun). It is characteristic of an ellipse that the sum of the distances of any planet from two foci is constant.
Kepler's Laws of Planetary Motion
Kepler’s First Law – The Law of Orbits
Kepler’s Second Law – The Law of Equal Areas
Kepler’s second law states, “The radius vector drawn from the sun to the planet sweeps out equal areas in equal intervals of time”.
As the orbit is not circular, 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 implies more speed at the perihelion and less speed (vmin) at the aphelion. If r is the distance of the planet from the sun at perihelion (rmin) and at aphelion (rmax), then,
rmin + rmax = 2a × (length of the major axis of an ellipse) . . . . . . . (1)
Keplers Second Law
Kepler’s Second Law – The Law of Equal Areas
Using the law of conservation of angular momentum, the law can be verified. At any point of time, the angular momentum can be given as L = mr2ω.
Now, consider a small area ΔA described in a short time interval Δt and the covered angle is Δθ. Let the radius of curvature of the path be r, then the length of the arc covered = r Δθ
ΔA = 1/2[r.(r.Δθ)]= 1/2r2Δθ
Therefore, ΔA/Δt = [ 1/2r2]Δθ/dt
Taking limits on both sides as, Δt→0, we get,
Now, by conservation of angular momentum, L is a constant.
Thus, dA/dt = Constant
The area swept in equal intervals of time is a constant.
Kepler’s second law can also be stated as, “The areal velocity of a planet revolving around the sun in elliptical orbit remains constant, which implies the angular momentum of a planet remains constant”. As the angular momentum is constant, all planetary motions are planar motions, which is a direct consequence of central force.
Check: Acceleration Due to Gravity
Kepler’s Third Law – The Law of Periods
According to Kepler’s law of periods,”The square of the time period of revolution of a planet around the sun in an elliptical orbit is directly proportional to the cube of its semi-major axis”.
T2 ∝ a3
The shorter the orbit of the planet around the sun, the shorter the time taken to complete one revolution. Using the equations of Newton’s law of gravitation and laws of motion, Kepler’s third law takes a more general form.
P2 = 4π2 /[G(M1+ M2)] × a3
Where M1 and M2 are the masses of the two orbiting objects in solar masses.
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Frequently Asked Questions on Kepler’s Law
Q1
What does Kepler’s first law state?
According to Kepler’s first law, all the planets revolve around the Sun in elliptical orbits, with the Sun as one of the foci.
Q2
What does Kepler’s second law state?
According to Kepler’s second law, the speed at which the planets move in space continuously changes. The second law helps to explain that when the planets are closer to the Sun, they will travel faster.
Q3
What is Kepler’s third law?
Kepler’s third law, also called the law of periods, states that the square of the orbital period is proportional to the cube of its mean
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