Universal Gravitation
The attractive force that governs planetary orbits and cosmic structures.
Gravity is the universal force of attraction acting between all masses. Sir Isaac Newton proved that the same force causing an apple to fall keeps the Moon in orbit.
This unit covers gravitational field strength, orbital velocities, Kepler's three laws of planetary motion, and the velocity required to escape planetary gravitational fields.
Key Takeaways
- •Gravitational force obeys the inverse-square law, dropping off rapidly with distance.
- •Orbits represent a state of perpetual free-fall where forward inertia balances gravitational pull.
- •Kepler's laws describe elliptical planetary orbits around the Sun.
Core Concepts & Definitions
1Newton's Law of Gravitation
Every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
•F = G * (m1 * m2) / r², where G = 6.6743 × 10⁻¹¹ N·m²/kg².
•Gravity is the weakest of the four fundamental forces but dominates at astronomical scales.
2Kepler's Laws of Planetary Motion
Three empirical laws describing planetary trajectories.
•First Law: Orbits are ellipses with the Sun at one focus.
•Second Law: A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
•Third Law: The square of the orbital period (T²) is proportional to the cube of the semi-major axis (r³).
Quick Revision Notes
- •G is the universal gravitational constant, which is the same everywhere in the universe. g is local acceleration due to gravity, which varies depending on location.
- •Escape velocity is exactly √2 times the circular orbital velocity at that same altitude.