Physics of Gravitation Explained | Chapter 13 of University Physics

Chapter 13 of University Physics unifies Newton’s laws with celestial mechanics to reveal how gravitation governs everything from falling apples to orbiting planets and black holes. In this summary, we explore the universal law of gravitation, weight and gravitational acceleration, potential energy and escape speed, satellite motion, Kepler’s laws, and the physics of extreme objects like black holes.

Newton’s Universal Law of Gravitation

Every mass attracts every other mass with a force given by:

F_g = G (m₁ m₂) / r²

• G is the gravitational constant (6.674×10⁻¹¹ N·m²/kg²).
• The force acts along the line connecting the masses and obeys Newton’s Third Law.
• Superposition lets you sum gravitational forces from multiple bodies.

Weight & Acceleration Due to Gravity

On or near Earth’s surface, the gravitational force on a mass m is:

w = G m_E m / R_E² = m g

• g ≈ 9.80 m/s² but varies slightly with latitude and altitude.
• Apparent weight differs from true weight when accelerating or in rotating frames.

Gravitational Potential Energy & Escape Speed

The potential energy between two masses is:

U = – G m M / r

Because U → 0 as r → ∞, it is negative closer to the mass. The escape speed from radius R is:

v_esc = √(2GM / R)

Satellite Motion & Orbits

• Orbital speed: v = √(GM / r)
• Orbital period: T = 2π √(r³ / GM)
• Total energy: E = – GMm / (2r)

Weightlessness in orbit arises because satellites are in continuous free fall around Earth.

Kepler’s Laws from Newtonian Gravitation

• First law: Orbits are ellipses with the sun at one focus.
• Second law: Equal areas in equal times—reflecting angular momentum conservation.
• Third law: T² ∝ a³—period squared proportional to semi-major axis cubed.

Spherical Mass Distributions

For a spherically symmetric body:

• Outside, the gravitational field is as if all mass were at the center.
• Inside a thin shell, net force is zero.
• Within a solid sphere, only the mass enclosed within radius r contributes to the force.

Apparent Weight & Earth’s Rotation

Earth’s rotation reduces apparent weight at the equator by providing part of the centripetal force needed for circular motion.

Black Holes & the Event Horizon

A black hole forms when mass collapses within its Schwarzschild radius:

R_S = 2GM / c²

• The event horizon marks the boundary beyond which nothing can escape.
• Black holes are detected by their gravitational influence and radiation from in-falling matter.

Conclusion

Chapter 13 shows how the universal gravitational interaction shapes planetary orbits, satellite dynamics, and the most extreme objects in the universe. By mastering these concepts, you’ll be equipped to explore astrophysics, orbital mechanics, and space mission design.

Watch the full video summary here for detailed examples and derivations. Dive into more chapters to deepen your physics knowledge and practical problem-solving skills.

If you found this breakdown helpful, be sure to subscribe to Last Minute Lecture for more chapter-by-chapter textbook summaries and academic study guides.