Gravitation is the name given to the force of attraction between any two bodies of the universe. It was discovered by the Newton in the year 1665.
Evidence in support of Newton’s law of Gravitation
- The rotation of earth around the sun or moon around the earth is explained on the basis of this law.
- The prediction about solar and lunar eclipse, made on the basis of this law, always came out to be true.
- The formation of tides in the oceans in due to force of attraction between moon and ocean water.
- The predictions about the orbits and time period of the modern artificial satellites made on the basis of this law are found to be very accurate.
If the value of G becomes becomes 10 times its present value, then we would be crushed to the floor by earth’s attraction. If the value of G becomes 1/10th of its present value then the earth’s attraction becomes very weak and in that case we can take jump over a building.
Newton solved the apple-Earth problem by stating the shell theorem. According to which a uniform spherical shell of matter attracts a particle lying outside the shell as if the whole mass of shell be concentrated at the center of the shell.
No gravitation force acts on a particle due to a spherical shell if the particle is present inside the spherical shell.
Important characteristics of Gravitational force
- it is independent of nature of intervening medium
- It is independent of the presence or absence of other bodies.
- It is independent of nature and size of the bodies, till their masses remain the same and the distance between their centers is fixed.
- Form action and reaction pair i.e. the gravitation forces are equal in magnitude and opposite in direction and hence obey Newton’s third law of motion.
- The gravitational force is central force.
- It is a conservative force.
Gravity is the force of attraction exerted by earth towards its center on a body lying on or near the surface of earth. Gravity is merely a special case of gravitation and is also called earth’s gravitational pull.
g = GM/R^2 (R is the radius of earth)
Mass of earth = 6.08* 10^24 kg
G = 6.67 * 10^ -11 N-m^2/Kg^2
Density of earth: 5.5 * 10^3 kg/m^3
The value of acceleration due to gravity is lesser at mountains than in plains.
g’= g (1-2h/R)
The value of acceleration due to gravity decreases with depth.
g’ = g(1-d/R)
Acceleration due to gravity is zero at the center of earth. Therefore, the weight of the body of mass at the center of earth is zero but the mass of the body will not be zero.
The value of acceleration due to gravity increases as we go from equator to the pole. The value of acceleration due to gravity at poles will remain unchanged whether the earth is at rest or rotating. The effect of rotation of the earth on the value of acceleration due to gravity is maximum at the equator and is minimum at the poles.
Acceleration due to gravity is independent of mass, shape, size etc. of falling body i.e. there will be equal acceleration in a light and heavy falling body.
If a body is taken above the surface of earth, the value of acceleration due to gravity varies inversely as the square of the distance from the center of the earth. But if the body is taken inside the earth, acceleration due to gravity decreases linearly with distance from the center of the earth.
The value of acceleration due to gravity is minimum at mercury and maximum at Jupiter.
If the rate of rotation of earth increases, the value of acceleration due to gravity decreases at all places on the surface of the earth except at poles.
A satellite orbiting close to the surface of the earth has a time period of revolution about 84.6 minutes.
The escape velocity is independent of the mass and direction of projection of the body from the surface of earth/planet.
The body can easily attain the escape velocity if it is projected in the direction, the launch site is moving as the planet rotates about its axis.
Kepler’s law of planetary motion
- Kepler’s first law (law of orbit): Every planet revolves around the sun in an elliptical orbit. The sun is situated at one focus of the ellipse.
- Kepler’s second law (law of area): the radius vector drawn from the sun to a planet seeps out equal areas in equal internals of time i.e. the areal velocity of the planet around the sun is constant. Linear velocity of the planet when near to the sun is more than when its linear velocity when away from the sun.
- Kepler’s third law (law of period): the square of the time period of revolution of a planet around the sun is directly proportional to the cube of semi major axis of its elliptical orbit i.e. T^2=a R^2. (a is constant).