class-9-physics-gravitation

 

Gravitation Laws & Motion

class 9 gravitation lesson summary
Introduction:
Gravitation is one of the fundamental forces of nature that governs the motion of objects in the universe. It is the force of attraction between all masses and plays a crucial role in understanding the motion of celestial bodies, including planets, moons, and stars.
Universal Law of Gravitation:
Sir Isaac Newton formulated the Universal Law of Gravitation, which states that every object in the universe attracts every other object 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 equation for the force of gravitation is F = (G * m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers.
Gravitational Constant (G):
The gravitational constant, denoted by G, is a fundamental constant with a value of approximately 6.674 × 10^-11 N m²/kg². It determines the strength of the gravitational force between two objects with masses in kilograms and the distance in meters.
Weight and Mass:
Mass is the amount of matter present in an object and remains constant regardless of the object's location.
Weight is the force with which an object is attracted towards the center of the Earth (or any other celestial body) due to gravity. Weight is given by the formula W = m * g, where m is the mass of the object, and g is the acceleration due to gravity (approximately 9.8 m/s² on the Earth's surface).
Free Fall and Acceleration due to Gravity: When an object is falling under the sole influence of gravity (neglecting air resistance), it is said to be in free fall. The acceleration experienced by an object in free fall is called the acceleration due to gravity, denoted by 'g'.
On Earth, the value of 'g' is approximately 9.8 m/s². However, this value may vary slightly depending on the location and altitude.
Gravitational Potential Energy:
Gravitational potential energy is the energy possessed by an object due to its position in a gravitational field.
The gravitational potential energy (PE) is given by the equation PE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity, and h is the height (vertical distance) above a reference point.
Kepler's Laws of Planetary Motion:
Johannes Kepler formulated three laws that describe the motion of planets around the Sun: a. Kepler's First Law (Law of Orbits):
Planets move in elliptical orbits, with the Sun at one of the foci.
b. Kepler's Second Law (Law of Areas):
A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
c. Kepler's Third Law (Law of Periods):
The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
Conclusion:
Understanding gravitation is essential for comprehending the motion of objects in the universe. The Universal Law of Gravitation and Kepler's Laws of Planetary Motion provide valuable insights into the behavior of celestial bodies and their interactions due to the force of gravity. Gravitation continues to play a vital role in our exploration and understanding of the cosmos.

Physics - Gravitation Concepts and Formulas:

1. Orbital Velocity (v_orbit):

v_orbit = √(G * M / r)

Where:

• v_orbit: Orbital velocity.
• G: Universal gravitational constant (approximately 6.67 × 10^-11 N m²/kg²).
• M: Mass of the central body.
• r: Distance between the object and the center of the central body.

2. Escape Velocity (v_escape):

v_escape = √(2 * G * M / r)

Where:

• v_escape: Escape velocity.
• G: Universal gravitational constant.
• M: Mass of the celestial body.
• r: Distance between the object and the center of the celestial body.

3. Variation of Acceleration due to Gravity (g) with Altitude and Depth:

g' = (g * R_E²) / (R_E + h)²

Where:

• g': Acceleration due to gravity at height h above the Earth's surface or at depth h below the Earth's surface.
• g: Acceleration due to gravity at the Earth's surface (approximately 9.81 m/s²).
• R_E: Radius of the Earth (approximately 6,371 km).

Examples:

Example 1: Orbital Velocity

Calculate the orbital velocity of a satellite orbiting the Earth at a distance of 500 km from the Earth's center. (Mass of the Earth = 5.97 × 10²⁴ kg)

Solution:

Given data:

M = 5.97 × 10²⁴ kg

r = 500 km = 500,000 m

Using the formula for orbital velocity:

v_orbit = √(G * M / r)

Substitute the values:

v_orbit = √((6.67 × 10^-11 N m²/kg²) * (5.97 × 10²⁴ kg) / (500,000 m))

Calculate the result:

v_orbit ≈ 7,663 m/s

Example 2: Escape Velocity

Find the escape velocity from the surface of a planet with a mass of 3.2 × 10²³ kg and a radius of 4,000 km.

Solution:

Given data:

M = 3.2 × 10²³ kg

r = 4,000 km = 4,000,000 m

Using the formula for escape velocity:

v_escape = √(2 * G * M / r)

Substitute the values:

v_escape = √(2 * (6.67 × 10^-11 N m²/kg²) * (3.2 × 10²³ kg) / (4,000,000 m))

Calculate the result:

v_escape ≈ 5,019 m/s

Example 3: Variation of g with Altitude

Calculate the acceleration due to gravity at a height of 1,000 km above the Earth's surface.

Solution:

Given data:

h = 1,000 km = 1,000,000 m

g = 9.81 m/s²

R_E = 6,371 km = 6,371,000 m

Using the formula for variation of g with altitude:

g' = (g * R_E²) / (R_E + h)²

Substitute the values:

g' = (9.81 m/s² * (6,371,000 m)²) / (6,371,000 m + 1,000,000 m)²

Calculate the result:

g' ≈ 7.02 m/s²