Gravitation and Gravity

Gravitation and Gravity

Gravitation

Every body attracts every other body by a force called the force of gravitation.

Newton’s Law of Gravitation

• The force of gravitational attraction between two point bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

• Consider two point bodies of masses m₁ and m₂ placed at a distance r.

The force of gravitational attraction between them is:

• Here, G is a constant called the universal gravitational constant.

• The value of G = 6.67 × 10⁻¹¹ Nm²/kg².

Gravity

• The gravitational force of Earth is called gravity, i.e., gravity is the force by which Earth pulls a body towards its centre.

• The acceleration produced in a body due to the force of gravity is called acceleration due to gravity (denoted as g), and its value is 9.8 m/s².

• Acceleration due to gravity is independent of the shape, size, and mass of the body.

• If a man can jump with a velocity v from the surface of the Earth or/planet, the height attained by the man is given by the respective relation.

• The value of g on the moon is less than that on Earth. Hence, on the moon, a man can jump higher than on Earth.

Variation in g (Weight = mg)

1. The value of g decreases with height or depth from Earth's surface.

2. g is maximum at poles.

3. g is minimum at the equator.

4. g decreases due to the rotation of the Earth.

5. g decreases if the angular speed of the Earth increases, and increases if the angular speed of the Earth decreases.

If the angular speed of Earth becomes 17 times its present value, a body on the equator becomes weightless.

Weight of a Body in a Lift

• If the lift is stationary or moving with uniform speed (either upward or downward), the apparent weight of a body is equal to its true weight.

• If the lift is going up with acceleration, the apparent weight of a body is more than the true weight.

• If the lift is going down with acceleration, the apparent weight of a body is less than the true weight.

• If the cord of the lift is broken, it falls freely. In this situation, the weight of a body in the lift becomes zero — this is the situation of weightlessness.

• While going down, if the acceleration of lift is more than the acceleration due to gravity, a body in the lift comes in contact with the ceiling of the lift.

Kepler’s Laws of Planetary Motion

1. First Law:

• All planets move around the sun in elliptical orbits, with the sun being at rest at one focus of the orbit.

2. Second Law:

• The position vector of the planet with the sun at the origin sweeps out equal area in equal time, i.e., the areal velocity of a planet around the sun always remains constant.

• A consequence of this law is that the speed of the planet increases when it is closer to the sun and decreases when it is far away.

• Speed is maximum at perigee and minimum at apogee.

3. Third Law:

• The square of the period of revolution of a planet around the sun is directly proportional to the cube of the mean distance of the planet from the sun.

• If T is the period of revolution and r is the mean distance, then T² ∝ r³.

Clearly, distant planets have a longer period of revolution.

• Time period of Mercury = 88 days

• Time period of Pluto = 247.7 years

Satellite

Satellites are natural or artificial bodies revolving around a planet under its gravitational attraction.

• Moon is a natural satellite.

• INSAT-1B is an artificial satellite of Earth.

Orbital Speed of a Satellite

1. The orbital speed of a satellite is independent of its mass. Hence, satellites of different masses revolving in the orbit of the same radius have the same orbital speed.

2. Orbital speed of a satellite depends upon the radius of orbit (height of satellite from the surface of the earth). The greater the radius, the lesser the orbital speed.

The orbital speed of a satellite revolving near the surface of Earth is 7.9 km/sec.

Period of Revolution of a Satellite

The time taken by a satellite to complete one revolution in its orbit is called its period of revolution.

1. The period of revolution depends upon the height of the satellite from the surface of Earth — the greater the height, the longer the period.

2. The period of revolution is independent of its mass.

The period of revolution of a satellite revolving near the surface of the Earth is 1 hour 24 minutes (84 minutes).

Geo-Stationary Satellite

If a satellite revolves in the equatorial plane in the direction of Earth’s rotation (from west to east) with a period of revolution equal to 24 hours, then it will appear stationary relative to Earth.

• Such a satellite is called a Geostationary satellite.

• It revolves at a height of 36,000 km, and its orbit is called the parking orbit.

• Arthur C. Clarke was the first to predict that a communication satellite could be stationed in geosynchronous orbit.

Escape Velocity

Escape velocity is the minimum velocity with which a body should be projected from the surface of Earth so that it goes out of the gravitational field of Earth and never returns.

Escape velocity is independent of the mass, shape, and size of the body and its direction of projection.

It is also called the second cosmic velocity.

• For Earth: 11.2 km/s

• For Moon: 2.4 km/s

If R = radius of earth, then orbital velocity of a satellite and escape velocity are related such that:

Escape velocity = √2 × orbital velocity

Therefore, if the orbital velocity of a satellite is increased by √2 times (about 41%), the satellite will leave the orbit and escape.

Final Thoughts

Gravitation is the fundamental force that attracts every object in the universe toward another. Newton’s Law of Gravitation states that this force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

On Earth, this force is felt as gravity, causing objects to fall and giving them weight. The acceleration due to gravity (g = 9.8 m/s²) is nearly constant for all bodies. Variations in gravity explain why a person can jump higher on the Moon and why weight changes in a moving lift. Kepler’s Laws describe how planets move around the Sun in elliptical orbits with varying speeds. Satellites, whether natural or artificial, revolve around planets under gravitational attraction.

A geostationary satellite stays fixed relative to Earth, aiding communication. The escape velocity defines the minimum speed required for an object to break free from Earth’s gravity.