1.Gravitation

Gravitational Force:

• Definition: The gravitational force is an attractive force that acts between any two masses. It is the force that pulls objects toward each other.

• Law of Universal Gravitation: Proposed by Sir Isaac Newton, this law states that every mass attracts every other mass 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. The formula is given by: F=Gm1m2r2F = G \frac{m_1 m_2}{r^2}F=Gr2m1​m2​​ where FFF is the gravitational force, GGG is the gravitational constant, m1m_1m1​ and m2m_2m2​ are the masses of the objects, and rrr is the distance between their centers.

Gravitational Constant (G):

• Definition and Value: The gravitational constant is a fundamental constant in the universe, approximately equal to 6.674×10−11 N m2kg−26.674 \times 10^{-11} \, \text{N m}^2 \text{kg}^{-2}6.674×10−11N m2kg−2. It appears in the universal law of gravitation and quantifies the strength of the gravitational force.

Acceleration Due to Gravity (g):

• Concept: On the surface of the Earth, objects experience an acceleration due to gravity, denoted as ggg. This acceleration has a standard value of approximately 9.8 m/s29.8 \, \text{m/s}^29.8m/s2.

• Variation with Altitude and Depth: The value of ggg decreases with altitude and increases with depth within the Earth.

Free Fall:

• Definition: When an object is allowed to fall freely under the influence of gravity alone, it is said to be in free fall. The object experiences a uniform acceleration ggg downward.

Gravitational Potential Energy:

• Concept: Gravitational potential energy is the energy an object possesses because of its position in a gravitational field. It is given by: U=mghU = mghU=mgh where UUU is the potential energy, mmm is the mass of the object, ggg is the acceleration due to gravity, and hhh is the height above the reference point.

Kepler’s Laws of Planetary Motion:

• Introduction: The chapter also briefly touches on the laws formulated by Johannes Kepler, which describe the motion of planets around the Sun:

  1. First Law (Law of Ellipses): Planets move in elliptical orbits with the Sun at one of the foci.

  2. Second Law (Law of Equal Areas): A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.

  3. Third Law (Law of Harmonies): The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

Applications and Implications:

• Real-World Examples: The chapter often includes examples and applications of gravitational concepts, such as satellite orbits, weight of objects on different planets, and the effect of gravity on various objects and phenomena.