Science 1 (1. Gravitation )

• Gravitation is a universal force that acts not only between two objects on the earth but also between any two objects in the universe
• Gravitation was discovered by Sir Isaac Newton after observing an apple fall from a tree
• Newton concluded that the earth attracts objects towards itself with an attractive force directed towards the center of the earth
• Circular motion and centripetal force are related to the gravitational force
• Kepler's laws describe planetary motion, including the fact that the orbit of a planet is an ellipse with the Sun at one of the foci
• Kepler's third law states that the square of a planet's period of revolution around the Sun is directly proportional to the cube of the mean distance of the planet from the Sun
• Newton made significant contributions in various areas including light, heat, sound, and mathematics. He invented calculus and constructed a reflecting telescope
• The value of G is the gravitational force acting between two unit masses kept at a unit distance away from each other
• In SI units, the value of G is equal to the gravitational force between two masses of 1 kg kept 1 m apart
• In SI units, the unit of G is Newton m^2 kg^-2
• The value of G was first experimentally measured by Henry Cavendish
• In SI units, the value of G is 6.673 x 10^-11 N m^2 kg^-2
• This force is directly proportional to the product of the masses of the two objects and is inversely proportional to the square of the distance between them
• Newton's universal law of gravitation states that every object in the Universe attracts every other object with a definite force
• If the mass of one object is doubled, the force between the two objects also doubles
• G is the constant of proportionality and is called the Universal gravitational constant
• The direction of the force is always along the line joining the centres of the two bodies
• If the distance is doubled, the force decreases by a factor of 4
• The distance between the centres is taken to be d
• The centre of mass of a spherical object having uniform density is at its geometrical centre
• The centre of mass of any object having uniform density is at its centroid
• The centre of mass of an object is the point inside or outside the object at which the total mass of the object can be assumed to be concentrated
• The centripetal force acting on a planet revolving around the Sun in a circular orbit is F = mv^2/r
• The speed of the planet can be expressed in terms of the period of revolution T as v = 2πr/T
• The gravitational force is much weaker than other forces in nature but it controls the Universe and decides its future
• Newton postulated the inverse square law of gravitation based on the centripetal force acting on the planet towards the Sun
• There is a gravitational force between two objects kept on a table or between you and your friend sitting next to you
• The gravitational force due to the earth on Mahendra is 1.83 x 10^9 times larger than the gravitational force between Mahendra and Virat
• When Mahendra is falling down due to the gravitational force of the earth, his velocity after one second will be 9.77 m/s
• Gravitational force due to the earth acts on the moon and artificial satellites, causing them to revolve around the earth
• Moon and artificial satellites orbit the earth due to the earth attracting them towards itself
• Moon and artificial satellites do not fall on the earth due to their velocity along their orbits
• Acceleration due to gravity at a given point on earth is the same for all objects and does not depend on the properties of the object
• Value of g on the surface of the earth is 9.77 m/s^2
• Value of g decreases with height above the earth's surface
• Value of g varies along the surface of the earth, being highest at the poles (9.832 m/s^2) and lowest at the equator (9.78 m/s^2)
• Value of g changes if we go inside the earth, decreasing as we go deeper inside
• Weight is the force with which the earth attracts an object, measured in Newtons
• Weight of an object changes from place to place due to the varying value of g, while mass remains constant everywhere
• Gravitational waves are waves on the fabric of space-time, predicted by Einstein in 1916