Class 9 Science Notes | Gravitation Notes

Gravitation

Introduction to Gravitation

Gravitation is a fundamental force of nature that attracts any two objects with mass. It is one of the four fundamental interactions in nature, alongside electromagnetism, strong nuclear force, and weak nuclear force. Gravitation is responsible for keeping the planets in orbit around the sun, the moon in orbit around the Earth, and for objects falling to the ground when dropped.

Universal Law of Gravitation

The Universal Law of Gravitation was formulated by Sir Isaac Newton in 1687. This law states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:

$F = G \frac{m_1 m_2}{r^2}$

where:

• $F$ is the gravitational force between two masses,
• $G$ is the gravitational constant ($6.674 \times 10^{-11} \, \text{N} \, \text{m}^2 \, \text{kg}^{-2}$),
• $m_1$ and $m_2$ are the masses of the two objects,
• $r$ is the distance between the centers of the two masses.

Importance of Gravitation

Gravitation plays a crucial role in various natural phenomena and daily life activities:

1. Planetary Orbits: Keeps planets in orbit around the sun.
2. Tides: Causes tides due to the gravitational pull of the moon and the sun on Earth's water bodies.
3. Atmospheric Retention: Helps Earth retain its atmosphere, providing a stable environment for life.
4. Weight: The weight of an object is the force exerted on it due to Earth's gravitational pull.

Free Fall and Acceleration due to Gravity

When an object falls towards the Earth under the influence of gravitational force alone, it is said to be in free fall. The acceleration experienced by an object in free fall is called acceleration due to gravity, denoted by $g$. The standard value of $g$ on the surface of the Earth is approximately $9.8 \, \text{m/s}^2$.

Equations of Motion for Free Falling Objects

For objects in free fall, the equations of motion under uniform acceleration can be applied. These equations are:

1. $v = u + gt$
2. $s = ut + \frac{1}{2}gt^2$
3. $v^2 = u^2 + 2gs$

where:

• $u$ is the initial velocity,
• $v$ is the final velocity,
• $t$ is the time,
• $s$ is the displacement,
• $g$ is the acceleration due to gravity.

Mass and Weight

Mass is the amount of matter contained in an object and is measured in kilograms (kg). It is a scalar quantity and does not change with location. Weight is the force exerted by gravity on an object and is given by:

$W = mg$

where:

• $W$ is the weight,
• $m$ is the mass,
• $g$ is the acceleration due to gravity.

Weight is a vector quantity and varies depending on the location (e.g., it is different on the moon compared to Earth due to different values of $g$).

Gravitational Potential Energy

Gravitational potential energy is the energy possessed by an object due to its position in a gravitational field. It is given by:

$U = mgh$

where:

• $U$ is the gravitational potential energy,
• $m$ is the mass of the object,
• $g$ is the acceleration due to gravity,
• $h$ is the height above the reference point.

Satellites and Orbits

A satellite is an object that revolves around a planet in a circular or elliptical path. Satellites can be natural, like the moon, or artificial, like communication satellites. The gravitational force provides the necessary centripetal force to keep the satellite in orbit.

Orbital Velocity

The velocity required to keep a satellite in orbit is called orbital velocity. It is given by:

$v_o = \sqrt{\frac{GM}{R}}$

where:

• $v_o$ is the orbital velocity,
• $G$ is the gravitational constant,
• $M$ is the mass of the planet,
• $R$ is the radius of the orbit from the center of the planet.

Geostationary Satellites

Geostationary satellites have an orbital period equal to the Earth's rotational period (24 hours). They appear stationary relative to the Earth and are placed in a circular orbit at an altitude of approximately 35,786 km above the equator. These satellites are used for communication, weather monitoring, and broadcasting.

Escape Velocity

Escape velocity is the minimum velocity required for an object to escape the gravitational pull of a planet without further propulsion. It is given by:

$v_e = \sqrt{\frac{2GM}{R}}$

where:

• $v_e$ is the escape velocity,
• $G$ is the gravitational constant,
• $M$ is the mass of the planet,
• $R$ is the radius of the planet.

For Earth, the escape velocity is approximately 11.2 km/s.

Kepler's Laws of Planetary Motion

Johannes Kepler formulated three laws that describe the motion of planets around the sun:

1. First Law (Law of Orbits): Every planet moves in an elliptical orbit with the sun at one of the two foci.
2. Second Law (Law of Areas): A line segment joining a planet and the sun sweeps out equal areas during equal intervals of time.
3. 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.

Gravity and Shape of the Earth

The Earth is not a perfect sphere; it is an oblate spheroid. This means it is slightly flattened at the poles and bulging at the equator. The equatorial radius is larger than the polar radius due to the rotation of the Earth, which causes centrifugal force acting outward at the equator.

Variations in Gravitational Force

The gravitational force on the surface of the Earth is not uniform. It varies due to several factors:

1. Altitude: Gravitational force decreases with increasing altitude.
2. Latitude: Gravitational force is slightly stronger at the poles compared to the equator due to the oblate shape of the Earth.
3. Local Geological Structures: Variations in density and composition of Earth's crust can cause local variations in gravitational force.

Gravitational Force Inside the Earth

Inside the Earth, the gravitational force decreases with depth. At the center of the Earth, the gravitational force is zero because the mass of the Earth is symmetrically distributed around that point, resulting in no net gravitational pull.

Conclusion

Gravitation is a fundamental force that governs the motion of objects in the universe. Understanding the principles of gravitation helps explain various natural phenomena, from the falling of an apple to the motion of celestial bodies. The Universal Law of Gravitation, along with concepts like free fall, orbital velocity, and escape velocity, provide a comprehensive framework for studying gravitational interactions. Kepler's laws further enhance our understanding of planetary motion, while variations in gravitational force highlight the complex nature of Earth's gravitational field. Gravitation remains a crucial topic in physics, with applications ranging from space exploration to everyday life.