Gravitation - Physics (Undergraduate Foundation)

This course provides a complete treatment of Newton's law of universal gravitation. It covers the principles governing the attractive force between masses, the concepts of gravitational fields and potential energy, and culminates in the application of these laws to the orbital mechanics of planets and satellites. The law of gravitation is a fundamental principle of the cosmos. It is essential for understanding the motion of celestial bodies, launching and maintaining artificial satellites for communications and Earth observation, and for calculating interplanetary trajectories. This is the physics that governs the structure of the solar system and the universe. By the end of this course, you will be able to apply Newton's law of universal gravitation to calculate the force between two masses, determine the gravitational potential energy of a system, explain Kepler's laws of planetary motion, and solve problems involving the orbital velocity and period of satellites. This course is a mandatory part of the curriculum for first-year university students of physics and engineering. It directly builds upon the principles of rotational motion and dynamics and is a critical prerequisite for the study of astrophysics and celestial mechanics.

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Enrolment valid for 12 months
This course is also part of the following learning track. You may join the track to gain comprehensive knowledge across related courses.
[NUC Core] PHY 101: General Physics I - Mechanics
[NUC Core] PHY 101: General Physics I - Mechanics
This learning track provides a complete and rigorous treatment of introductory classical mechanics as specified by the NUC Core Curriculum. It is structured to build a comprehensive analytical framework, starting with the mathematical description of motion (kinematics) and progressing through its causes (Newtonian dynamics), the powerful conservation laws, the dynamics of rotating systems, and finally, the principles of universal gravitation. Mastery of this material is the non-negotiable foundation for all subsequent study in physics and engineering. The principles of classical mechanics are the operational language for analysing the physical world. This track provides the essential toolset for solving problems in every field of engineering, from aerospace to civil, and for understanding phenomena from the trajectory of a projectile to the orbits of planets. By the end of this track, you will be able to analyse motion using vectors and calculus, apply Newton's laws to solve any standard dynamics problem, use conservation laws to analyse complex systems and collisions, analyse rotational motion, and solve problems in celestial mechanics. This learning track is a mandatory prerequisite for all first-year university students of physics, engineering, and related physical sciences. It provides the foundational knowledge required for all subsequent courses in mechanics, electromagnetism, thermodynamics, and modern physics.

This learning track provides a complete and rigorous treatment of introductory classical mechanics as specified by the NUC Core Curriculum. It is structured to build a comprehensive analytical framework, starting with the mathematical description of motion (kinematics) and progressing through its causes (Newtonian dynamics), the powerful conservation laws, the dynamics of rotating systems, and finally, the principles of universal gravitation. Mastery of this material is the non-negotiable foundation for all subsequent study in physics and engineering. The principles of classical mechanics are the operational language for analysing the physical world. This track provides the essential toolset for solving problems in every field of engineering, from aerospace to civil, and for understanding phenomena from the trajectory of a projectile to the orbits of planets. By the end of this track, you will be able to analyse motion using vectors and calculus, apply Newton's laws to solve any standard dynamics problem, use conservation laws to analyse complex systems and collisions, analyse rotational motion, and solve problems in celestial mechanics. This learning track is a mandatory prerequisite for all first-year university students of physics, engineering, and related physical sciences. It provides the foundational knowledge required for all subsequent courses in mechanics, electromagnetism, thermodynamics, and modern physics.

Course Chapters

1. Introduction
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This chapter introduces the law of universal gravitation. It defines the scope of the course, which covers the force between masses, gravitational fields, potential energy, and the orbital mechanics of planets and satellites. Key objectives include understanding the course structure and the historical and scientific importance of Newton's law of gravitation.

Chapter lessons

1-1. Welcome

A direct statement of the course's purpose and structure. This lesson outlines the progression from Newton's law to Kepler's laws and satellite motion.

2. Newton's Law of Universal Gravitation
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This chapter provides a full treatment of Newton's law of universal gravitation. It establishes the mathematical relationship for the attractive force between any two objects with mass, a foundational principle of physics. Key topics include the inverse square law, the universal gravitational constant G, the concept of a gravitational field, and the distinction between gravitational mass and inertial mass.

Chapter lessons

2-1. The law of universal gravitation

Formally states Newton's law of gravitation, F = Gm₁m₂/r². It defines each term in the equation and establishes the inverse square relationship for the force.

2-2. The gravitational field

Introduces the concept of a gravitational field as a way to describe the influence that a massive object extends into the space around it.

2-3. Gravitational potential energy

Defines gravitational potential energy for a two-particle system. It establishes the formula U = -Gm₁m₂/r and clarifies the convention of setting zero potential at infinite separation.

3. Kepler's Laws and Orbital Motion
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This chapter covers Kepler's three laws of planetary motion. These laws provide a complete description of the orbits of planets around a star and are a direct consequence of the law of universal gravitation. Key topics include Kepler's law of orbits, law of areas, and law of periods. The relationship between these empirical laws and Newton's gravitational theory is established.

Chapter lessons

3-1. Kepler's first law of orbits

States Kepler's First Law: the orbit of every planet is an ellipse with the Sun at one of the two foci. This establishes the geometric shape of planetary orbits.

3-2. Kepler's second law of areas

States Kepler's Second Law: a line joining a planet and the Sun sweeps out equal areas during equal intervals of time. This is a direct consequence of the conservation of angular momentum.

3-3. Kepler's third law of periods

States Kepler's Third Law: the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. This relates the orbital size to its period.

4. Conclusion
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This chapter consolidates the principles of universal gravitation. It provides a structured summary of Newton's gravitational law and Kepler's laws of planetary motion, reinforcing the core concepts of celestial mechanics. The conclusion summarises the key laws and their applications in orbital mechanics. It also provides a forward look to how this theory was superseded by Einstein's general relativity.

Chapter lessons

4-1. Summary of gravitation

A concise review of Newton's law of gravitation and Kepler's laws. This lesson ensures the foundational principles of celestial mechanics are consolidated.

4-2. Beyond Newton: A look at general relativity

Provides a brief, conceptual overview of how Einstein's theory of general relativity provides a more complete description of gravity, particularly in strong gravitational fields.