Chapter 3.2 - 3.3

Newton's Great Synthesis

• Newton was a pivotal thinker who mathematically explained the observations of planetary and stellar motion.

• He formulated three laws of motion and introduced the gravitational force responsible for the geometries of motion in the universe.

Three Laws of Motion

1. First Law (Law of Inertia)

   • An object at rest remains at rest unless acted upon by a force.

   • Example: A book on a table stays still until someone pushes it.

2. Second Law (Law of Acceleration)

   • A force is required to change the motion of an object, affecting its speed or direction.

   • An object in motion continues to move at a constant velocity unless acted upon by a force.

   • Example: If a spacecraft is moving in space, it will keep moving unless a force stops or accelerates it.

3. Third Law (Action and Reaction)

   • For every action, there is an equal and opposite reaction.

   • Example: In rockets, the explosive forces push down, resulting in an upward thrust.

   • Figure 3.7 illustrates this principle with rocket propulsion: the force of explosion pushes the rocket upward while expelling gases downwards.

Conservation of Angular Momentum

• Angular momentum must be conserved in a closed system, meaning that the total amount of spin remains constant unless acted upon by an external force.

• Example: A skater spins faster when pulling her arms inward due to conservation of angular momentum.

• Understanding angular momentum is essential for grasping orbits and formation processes in the solar system.

Newton's Law of Gravitation

• Newton's most significant insight linked terrestrial motion (like a jumping person falling back to Earth) with celestial mechanics (like the Moon's orbit around Earth).

• Gravitational attraction is responsible for holding planets and moons in their orbits around celestial bodies.

Gravitational Force

• Defined mathematically: F = G * (m1 * m2) / r^2

  • F: gravitational force

  • G: gravitational constant (weak force)

  • m1, m2: masses of the two objects

  • r: distance between the centers of the two masses

• The law states that gravity is always attractive and how the force strengthens with increased mass but weakens with greater distance.

Effects of Distance on Gravity

• The force of gravity decreases rapidly as the distance increases:

  • At twice the Earth's radius, the force is 1/4.

  • At three times the Earth's radius, it becomes 1/9 (or 1/nth).

  • This illustrates the R squared effect: as distance (r) increases, the force diminishes significantly.

Understanding Mass

• Mass measures the amount of matter in an object, represented by the periodic table of elements (e.g., hydrogen and oxygen in water).

• Future discussions may include dark matter, which also follows gravitational laws but is not yet fully understood.

Conclusion

• Newton's law of gravitational attraction was groundbreaking, capable of predicting the Moon's orbit and applicable to all masses in the universe.