Lecture Notes: Newton's Law of Universal Gravitation

Introduction to Newton's Law

• Newton's law of universal gravitation: A major scientific breakthrough.
• Observed planetary motion and its relation to gravitational force on Earth.
• Planets and objects in free fall toward larger masses due to gravity.

Thought Experiment

• Cannonball example:
  • Fired at different forces to understand orbit.
  • At immense force, it would never hit the ground, analogous to satellites and space stations.

Gravitational Force Characteristics

• Every object with mass experiences gravitational force.
• Near enormous objects (e.g., planets), gravity is noticeable.
• Even small objects (e.g., a car, a person) exert gravitational force, but it's negligible.

Newton's Gravitational Equation

• Formula: ( F = G \frac{m_1 m_2}{r^2} )
  • ( F ): Gravitational force.
  • ( G ): Constant of universal gravitation (6.67 x 10^-11 Nm²/kg²).
  • ( m_1, m_2 ): Masses of the objects.
  • ( r ): Distance between object centers.
• Henry Cavendish determined ( G ) experimentally.
• Gravitational force depends on mass, not volume.
  • Can treat objects as point masses.

Center of Mass in Systems

• Earth-Moon system:
  • Both exert gravitational force on each other.
  • Forces are equal in magnitude but produce different accelerations.
  • Earth's greater mass means the center of mass is within the Earth.
• Similar concept applies to falling objects on Earth.

Acceleration Due to Gravity

• All objects fall at the same rate (9.8 m/s²) without air resistance.
• Force of gravity imparts greater acceleration on more massive objects but also more inertia.
• Simplified by algebraic manipulation:
  • ( F = ma = G \frac{m_1 m_2}{r^2} )
  • Mass of falling object cancels out.
  • Acceleration due to gravity depends on Earth's mass and radius.

Gravity as a Field Force

• Newton couldn’t explain distance interaction.
• Gravity labeled as a field force by later scientists.
• Einstein's general theory of relativity advanced understanding of gravity.

Conclusion

• Newton’s work linked terrestrial and celestial motion.
• Understanding of gravity continues to evolve.
• Further exploration in modern physics.