Overview
This lecture explains the concept of gravity, its historical understanding, the laws that describe it, and how it affects objects differently depending on mass and distance.
Historical Theories of Gravity
- Aristotle believed heavier objects fall faster than lighter ones.
- Galileo demonstrated that, ignoring air friction, all objects fall at the same rate regardless of mass.
Newton’s Law of Universal Gravitation
- Newton proposed gravity as a universal force every mass exerts on other masses.
- Gravitational force depends on the product of two masses and inversely on the square of their distance.
- The gravitational force formula also includes the universal gravitational constant, a very small value.
Gravity on Celestial Bodies
- Objects experience gravity from all bodies, but the Earth's gravity is most significant for us due to its mass and proximity.
- The gravitational acceleration on Earth is 9.81 m/s², represented by "g."
- Weight is the gravitational force on an object at a planet's surface; it changes with location, though mass remains constant.
- On the Moon, gravity is about one-sixth that of Earth; on the Sun, nearly 30 times stronger.
Action and Reaction Forces
- Any two bodies exert equal and opposite gravitational forces on each other (Newton's third law).
- The difference in observed motion is due to differences in mass (large masses show negligible acceleration).
Free Fall and Acceleration
- In free fall (ignoring air resistance), all objects accelerate at the same rate under gravity.
- Experiments on the Moon proved this by dropping a feather and a hammer, showing simultaneous fall.
Gravity in Space and the Limits of Classical Theory
- Far from other bodies, gravity becomes negligible, and objects travel at constant speed.
- Compressing a mass like the Sun into a small radius leads to black holes; gravity becomes so strong that classical mechanics fails.
- Changes in gravity (such as if the Sun disappeared) cannot affect Earth instantly due to the speed-of-light limit; general relativity is required for such cases.
Key Terms & Definitions
- Gravity — A force that attracts two bodies toward each other due to their masses.
- Gravitational Force — The attractive force between any two masses, described by Newton’s law.
- Universal Gravitational Constant (G) — The constant value in Newton's law determining gravity’s strength.
- Gravitational Acceleration (g) — The acceleration due to gravity at a planet’s surface.
- Weight — The force on a mass due to gravity at a specific location.
- Mass — The amount of matter in an object, which does not change with location.
Action Items / Next Steps
- Review Newton’s law of universal gravitation and its formula.
- Understand the difference between mass and weight.
- Prepare questions about gravity’s limits and Einstein’s solution for next class.