CBSE Class 11th Kepler’s laws Details & Preparations Downloads
Motion is always relative. Based on the energy of the particle under motion, motions are classified into two types:
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.
Kepler’s First Law – The Law of Orbits
Kepler's First Law, also known as the Law of Ellipses, describes the shape of the orbits followed by planets around the Sun. Johannes Kepler formulated this law in the early 17th century, and it represents a departure from the traditional belief that planetary orbits were perfect circles. Here's a detailed explanation of Kepler's First Law:
The orbit of a planet around the Sun is an ellipse, with the Sun situated at one of the two foci of the ellipse.
Key Concepts:
Ellipse: An ellipse is a geometric shape resembling a flattened circle, characterised by two points called foci. In the case of planetary orbits, the Sun is located at one of these foci.
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Eccentricity: The degree of "flattening" of the ellipse is described by a parameter called eccentricity. An eccentricity of 0 corresponds to a perfect circle, while an eccentricity between 0 and 1 represents an elliptical orbit. The greater the eccentricity, the more elongated the ellipse.
Kepler’s Second Law – The Law of Equal Areas
Kepler's Second Law, also known as the Law of Equal Areas, describes the rate at which a planet moves along its elliptical orbit. This law was formulated by Johannes Kepler in the early 17th century and is one of the three laws that collectively describe the motion of planets around the Sun. Here's an explanation of Kepler's Second Law:
A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
Key Concepts:
Equal Areas: As a planet moves along its elliptical orbit, the area it sweeps out in space during a specific time interval is constant. This means that the rate at which a planet covers an area is uniform throughout its orbit.
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Variable Orbital Speed: Since the distance between a planet and the Sun changes as it moves along its elliptical orbit (per Kepler's First Law), the planet's orbital speed varies. The planet travels faster when it is closer to the Sun (at perihelion) and slower when it is farther away (at aphelion).
Kepler’s Third Law – The Law of Periods
Kepler's Third Law, also known as the Law of Harmonies, establishes a relationship between the orbital periods and the average distances of planets from the Sun. This law, formulated by Johannes Kepler in the early 17th century, provides insights into the quantitative aspects of planetary motion. Here's an explanation of Kepler's Third Law:
The square of the orbital period (the time it takes for a planet to complete one orbit around the Sun) is directly proportional to the cube of the semi-major axis of its orbit (the average distance from the planet to the Sun).
Mathematical Expression:
T2∝a3
Where:
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T is the orbital period of the planet.
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a is the semi-major axis of the planet's orbit.
Key Concepts:
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Proportional Relationship: The mathematical relationship implies that if you square the orbital period of any planet and compare it with the cube of its average distance from the Sun, the result will be the same for all planets in the solar system.
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Harmonic Pattern: The law reveals a harmonic pattern in the solar system, indicating that there is a systematic and predictable relationship between the time it takes for a planet to orbit the Sun and its average distance from the Sun.
CBSE Class 11th Downloadable Resources:
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SAMPLE PRACTICE QUESTIONS OF SIGNIFICANT FIGURES:
Q1. What are Kepler's laws of planetary motion?
Answer 1 Kepler's laws are three fundamental principles describing the orbits of planets around the sun. They were formulated by the German astronomer Johannes Kepler in the early 17th century.
Q2. What is Kepler's First Law, the Law of Ellipses?
Answer 2 Kepler's First Law states that the orbit of a planet around the sun is an ellipse, with the sun at one of the two foci. This law revolutionised our understanding of planetary orbits, moving away from the circular orbits proposed by earlier models.
Q3. Why is the Law of Ellipses important?
Answer 3 The Law of Ellipses helps explain variations in a planet's distance from the sun during its orbit, providing a more accurate description of the paths of planets.
Q4. What is Kepler's Second Law, the Law of Equal Areas?
Answer 4 Kepler's Second Law states that a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time. This law reflects the unequal speed of a planet at different points in its orbit.
Q5. How does the Law of Equal Areas explain planetary motion?
Answer 5 The Law of Equal Areas implies that a planet moves faster when closer to the sun (perihelion) and slower when farther away (aphelion). This idea is based on the conservation of angular momentum.