Constants of Change
Thinking about nature often shifts between two ideas:
Fixed Laws: This idea states that the universe follows unchanging rules, much like Newton's laws in classical physics.
There are specific laws that is under Newton’s law about physics which will be discussed later. The laws shows unchanging rules because if all variables are known it can provide an accurately predictable results, which shows stability and consistency. Just like the fixed law, it follows unchanging rules.
Flux and Change: This view claims that everything is always changing, reflecting Heraclitus's saying that you cannot step into the same river twice.
Flux in simple terms means it is constantly changing. And based on the Greek philosopher Heraclitus, it means that the water is always changing and flowing and it is not the same river you stepped into last time and that somewhat explains the idea of flux and change.
Isaac Newton's Contribution
Isaac Newton is known for merging rational thinking with mystical ideas. He used math to describe motion and set the stage for classical mechanics with his laws of motion.
Dynamics of Motion
Before Newton, math was based on static models. Galileo and Kepler discovered that planets move in elliptical orbits, which leads to Newton's ideas:
Cannonball Example: Newton broke down motion into simple horizontal and in complex ways.
Galileo discovered that the path of such a projectile is a parabola, a curve known to the ancient Greeks and related to the ellipse, it forms an inverted U shape. Then, in Newton’s view- The cannonball's motion in the horizontal direction, parallel to the ground, It occurs at a constant speed.
Calculus: Developed during Newton's time, calculus helped us understand motion by measuring how things change and how much they move over time.
This way also helped with the cannonball study, it was determined by height, velocity, and acceleration. He used the basic operations of calculus, the differentiate and integrate.
then, these dynamics of motion lead into these question.
How can we explain this constant that is hiding among the dynamic variables? When all else is changing? why is the acceleration fixed?
to answer that when we go back the cannonball study, the Earth must be pulling the ball downward; there is a gravitational force that acts on the ball. Just like us, we feel weight because gravity pulls our bodies downward, and we still weigh the same if we stand at the top of a tall building.
All of the laws of physics that were discovered by Isaac Newton's basic insight-that change in nature can be described by mathematical processes and methods.
Newton's Laws of Motion
First Law: An object stays at rest when it is still, or if in motion it is at a constant velocity unless influenced by an external factor.
Second Law: Force is equals to mass times acceleration.
Third Law: when there is interactions with two objects, there's an equal and opposite reaction. In the opposite direction and with equal magnitude, they produce forces on one another.
These laws help explain how gravity influences motion.
Evolution of Mathematical Physics
Differential Equations: This shows us to describe how to find the position at any time, as long as we know the values
The Three-Body Problem, Moon/Earth/Sun system is said to be this problem. Newton explained that a standard closed-form equation was unable to solve the system because of the complex relationship of their gravitational forces.
The Moon and Earth are an ideal example of the three-body problem since their motion are significantly affected by the gravity of the Sun.
Conclusion
Our understanding of motion has moved from seeking exact solutions to recognizing complexities, stressing the balance between stability and change in how we see reality.