Gravitation

Gravitation

It is the force of attraction between any two bodies in the universe. 

- Everybody in the universe attracts every other body with a force know as force of attraction.

- The attraction between sun and moon.

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Gravity

It is the force of attraction between the earth and any object lying on or near it's surface.

- It is a special case of gravitation.

- A body thrown up falls back on the surface of the earth due to Earth's force of gravity.

Free fall

The motion of a body under the influence of gravity alone .

-If we neglect the resistance or friction offered by the air, the fall of a body in air is a free fall .

Acceleration due to gravity

The acceleration produced in a freely falling body under the gravitational pull of the earth .

- When a body falls freely towards the surface of the earth, it's velocity continuously increases.

- It is denoted by g.

Weight of the body

It is defined as the gravitational force with which a body is attracted towards the centre of the earth.

- The weight of a body is the measure of the gravitational pull exerted by the earth upon it.

- Weight is a vector quantity.

Newton's law of gravitation

It is found in 1665, while seeing an apple falling from a tree but it is published in 1687.

Newton published the universal law of gravitation in his book Principia. 

It states that 

Every particle in the universe attracts every other particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. 

F= G m1m2 / r^2

G is universal gravitational constant

F= G

The universal gravitational constant may be defined as the force of attraction between two bodies of unit mass each and placed unit distance apart.

Value of G

G = 6.67× 10^-11 Nm^2/kg^2

- The value of G does not depend on the nature and size of the bodies .

- It also doesn't depend on the nature of the medium between two bodies.

Main Characteristics of Gravitational Forces

The gravitational force is basically a central force, which works along the line joining the centers of two bodies. It is always a long range force. The gravitational force occurs even when we're talking about large distances. It is a conservative force.

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Importance of gravitational force

Gravity is a very important force. Every object in space exerts a gravitational pull on every other, and so gravity influences the paths taken by everything traveling through space. It is the glue that holds together entire galaxies. It keeps planets in orbit.

Newton's shell 🐚  theorem

This theorem gives gravitational force on a point mass due to a spherical shell.

- if a point mass lies outside a uniform spherical shell with a spherically symmetric internal mass distribution, the shell attracts the point mass as if the entire mass of the shell were concentrated at it's centre.

- if a point mass lies inside a uniform shell, the gravitational force on the point mass is zero. 

But if a point mass lies inside a homogeneous solid sphere, the force on the point mass acts towards the center of the sphere.

This force is exerted by the spherical mass situated interior to the point mass.

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Factors on which value of g depends

- altitude

- depth

- shape of Earth

- rotation of Earth

Variation of g with altitude 

Variation of g with depth

Variation of g with shape of Earth

Earth is not a perfect shape either circle or sphere. It is flattened at the poles and bulges out at the equator.

So the equatorial radius of the earth is greater than the polar radius by about 21 km.

g and R is inversely proportional to each other.

The value of g is minimum at the equator and maximum at the poles.

The variation of g between the poles and the equator is about 0.5 percentage.

Variation of g with latitude

The plane passing through the center of the earth and perpendicular to its axis of rotation is called it's equatorial plane..

The latitude of a plane defined be the angle which the line joining the place to the center of the earth makes with the equatorial plane.

-Such other factors are mountains, plateaus and valley's

Intensity of gravitational field

The gravitational field intensity at any point in the gravitational field due to a given mass be as the force experienced by a unit mass placed at that point provided the presence of unit mass doesn't disturb the original gravitational field.

- It is a vector quantity.

Gravitational field intensity is force per unit mass.

Gravitational Potential energy

The gravitational Potential energy of a body is the energy associated with it due to its position in the gravitational field of another body and is measured by the amount of work done in bringing a body from infinity to a given point in the gravitational field of the other.

For further explanation visit work, energy power .

Escape velocity

It is the minimum velocity with which a body must be projected vertically upwards in order that it may just escape the gravitational field of the earth.

v = √2gR

- Escape velocity doesn't depend on the mass of the body projected.

- As the escape velocity depends on the mass and radius of the planet from the surface of which the body is projected, so value of escape velocity is different for different planet.

- Escape velocity on the Earth's surface is 112 km per second.

Satellite

A satellite is a body which continuously resolves on its own around a much larger body in a stable orbit.

Natural satellite

A satellite created by nature .

- Moon is a natural satellite of the earth which in turns is a satellite of the sun.

Artificial satellite

A man made satellite.

- Russians were the first to put an artificial satellite.

- INSAT-IA, INSAT-IB etc.

 Kepler's three laws

There are actually three, Kepler's laws that is, of planetary motion:
1) every planet's orbit is an ellipse with the Sun at a focus.
2) a line joining the Sun and a planet sweeps out equal areas in equal times.
 3) the square of a planet's orbital period is proportional to the cube of the semi-major axis of its.

Weightlessness

When a body pressed against a supporting surface the supporting surface exerts a force of reaction on him. This force of reaction produces the feeling of weight in the body. If somehow the force of reaction becomes zero, the apparent weight of the body becomes zero.

A body is said to be in a state of weightlessness when the reaction of the supporting surface is zero or it's apparent weight is zero.

Inertial mass

The mass of a body which measures it's inertia 

It is equal to the ratio of applied force to acceleration produced.