Всемирный закон тяготения

• The universal law of gravitation states that every particle of matter in the Universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
• This force acts along the line joining the two particles.

Mathematical Formulation

• F = G * (m1 * m2) / r^2
• F is the gravitational force between two masses
• G is the gravitational constant
• m1 and m2 are the masses of the two objects
• r is the distance between the centers of the two objects

Gravitational Constant (G)

• G is the universal gravitational constant, approximately 6.674 × 10^-11 N⋅m²/kg².
• G is the same throughout the universe.
• G was first accurately measured by Henry Cavendish in 1798 using a torsion balance.

Key Concepts

• The force is always attractive.
• The force is proportional to the product of the masses.
• Greater masses result in a stronger gravitational force.
• The force is inversely proportional to the square of the distance.
• As distance increases, the gravitational force decreases rapidly.
• The force acts along the line connecting the centers of the two masses.

Implications

• Explains why objects fall to the ground.
• Explains the orbits of planets around the Sun.
• Explains the orbits of moons around planets.
• Explains the tides on Earth (due to the gravitational pull of the Moon and Sun).
• Describes motion of celestial bodies.

Gravity vs. Weight

• Gravity is the force of attraction between any two objects with mass.
• Weight is the force of gravity acting on an object.
• Weight = m * g, where g is the acceleration due to gravity.

Acceleration due to Gravity (g)

• g is the acceleration experienced by an object due to the force of gravity.
• Near the Earth's surface, g is approximately 9.8 m/s².
• g varies slightly depending on location (altitude and latitude).

Orbital Motion

• Planets orbit the Sun due to gravity.
• The gravitational force provides the centripetal force required for circular motion.
• Satellites orbit the Earth due to gravity.
• Kepler's laws of planetary motion are consequences of the law of gravitation.

Kepler's Laws of Planetary Motion

• Law of Ellipses: The orbit of each planet is an ellipse with the Sun at one of the two foci.
• Law of Equal Areas: A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.
• Law of Harmonies: The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

Gravitational Potential Energy

• Gravitational potential energy (U) is the potential energy an object has due to its position in a gravitational field.
• U = -G * (m1 * m2) / r
• The zero point of gravitational potential energy is typically defined as infinity (infinite separation).

Gravitational Field

• A gravitational field is a field of force that surrounds a mass.
• Any other mass placed in this field will experience a gravitational force.
• Gravitational field strength (g) is the force per unit mass.

Limitations

• It is an inverse-square law and works well for describing gravitational forces at moderate distances.
• It does not accurately describe gravity in very strong gravitational fields or at very high speeds.
• Einstein's theory of general relativity provides a more accurate description of gravity under these extreme conditions.
• It doesn't explain dark matter or dark energy.