Newton's Law of Gravitation and Space-Time Curvature

Newton's Law of Gravitation

Every object in the universe attracts every other object with a force.
Force between two objects is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance between their centers.
- Formula: F = G * (m1 * m2) / r^2
Gravitational force is easy to understand and applies to everyday life.
Limitations of Newtonian gravity: it does not account for variations in gravitational force deep inside the Earth or at very large distances.

Space-time curvature: Massive objects cause a curvature in the fabric of space-time.
Gravitational forces are interpreted as objects following the curved paths in space-time.
Example: A flat rubber sheet with a heavy object in the center, creating a dip.
- As objects move closer to the center, they experience stronger gravitational pull.
- Far from the center, the curvature and gravitational pull decrease.
Light also follows the curved paths created by massive objects, leading to gravitational lensing.

Formed when massive stars collapse under their own gravity after exhausting their nuclear fuel.
A black hole's gravity is so strong that not even light can escape from it.
Black holes lead to singularity, where known laws of physics break down.
Indirect detection methods include observing the effects of black holes on nearby objects and detecting specific signatures such as X-rays emitted by accreting matter.

Newton's law is suitable for simple gravitational interactions but has limitations.
Einstein's theory of general relativity provides a more comprehensive understanding, explaining gravity as the curvature of space-time.
Black holes are extreme examples of space-time curvature with significant gravitational effects.