Gravitation and Newton's Law

Gravitation

What is Gravitation? Gravitation is a fundamental force of nature that causes objects with mass to attract each other.

History of Gravitation

• Ancient Greeks: Aristotle and Epicurus proposed theories of gravitation
• Galileo Galilei: first to study gravity experimentally
• Sir Isaac Newton: developed the Law of Universal Gravitation (1687)
• Albert Einstein: developed the Theory of General Relativity (1915)

Newton's Law of Universal Gravitation

• Formula: F = G * (m1 * m2) / r^2
• Variables:
  • F: gravitational force
  • G: gravitational constant (6.67408e-11 N m^2 kg^-2)
  • m1 and m2: masses of objects
  • r: distance between centers of objects
• Key Points:
  • Every point mass attracts every other point mass
  • Force is proportional to product of masses and inversely proportional to square of distance

Gravitational Fields

• Definition: a region around a mass where gravitational force can be detected
• Properties:
  • Gravitational field strength: g = F / m
  • Gravitational potential: V = -G * m / r
• Gravitational Field Lines:
  • Imaginary lines that emerge from a mass and enter into another mass
  • Direction of field lines: from higher to lower potential

Gravity and Motion

• Free Fall: acceleration of an object under gravity (g = 9.8 m/s^2 on Earth)
• Orbital Motion: circular motion of an object under gravity (e.g., planets around the Sun)
• Escape Velocity: minimum velocity required for an object to escape gravitational pull

Gravitational Phenomena

• Tides: periodic rising and falling of sea levels due to gravitational pull of Moon and Sun
• Gravitational Waves: ripples in spacetime produced by massive, accelerating objects (e.g., black holes)
• Black Holes: regions of spacetime where gravity is so strong, not even light can escape

What is Gravitation?

• Gravitation is a fundamental force of nature that causes objects with mass to attract each other.

History of Gravitation

• Ancient Greeks, such as Aristotle and Epicurus, proposed theories of gravitation.
• Galileo Galilei was the first to study gravity experimentally.
• Sir Isaac Newton developed the Law of Universal Gravitation in 1687.
• Albert Einstein developed the Theory of General Relativity in 1915.

Newton's Law of Universal Gravitation

• The formula for the law is F = G × (m1 × m2) / r^2.
• F is the gravitational force.
• G is the gravitational constant (6.67408e-11 N m^2 kg^-2).
• m1 and m2 are the masses of objects.
• r is the distance between the centers of objects.
• Every point mass attracts every other point mass.
• The force is proportional to the product of the masses and inversely proportional to the square of the distance.

Gravitational Fields

• A gravitational field is a region around a mass where the gravitational force can be detected.
• Gravitational field strength is g = F / m.
• Gravitational potential is V = -G × m / r.
• Gravitational field lines are imaginary lines that emerge from a mass and enter into another mass.
• The direction of the field lines is from higher to lower potential.

Gravity and Motion

• Free fall is the acceleration of an object under gravity (g = 9.8 m/s^2 on Earth).
• Orbital motion is the circular motion of an object under gravity (e.g., planets around the Sun).
• Escape velocity is the minimum velocity required for an object to escape the gravitational pull.

Gravitational Phenomena

• Tides are the periodic rising and falling of sea levels due to the gravitational pull of the Moon and Sun.
• Gravitational waves are ripples in spacetime produced by massive, accelerating objects (e.g., black holes).
• Black holes are regions of spacetime where gravity is so strong that not even light can escape.