Mechanics & Properties of Matter - Part 3

MECHANICS & PROPERTIES OF MATTER - PART 3

GRAVITATION :

·  Planetary motion is one of the important periodic motions. According to Ptolemy’s (2^nd century A.D.) geocentric theory, the earth was assumed to be at the centre of the universe and the sun, the moon, the planets and even the stars were thought to move around in complicated paths.

   Later Copernicus proposed a new theory called heliocentric theory (15 century A.D.) In this theory the sun was considered to be at the centre and the earth and other planets revolve around the sun in circular orbits of different radii.

    Copernicus also believed that the earth rotates on its axis once every day. The famous Indian mathematician and astronomer Aryabhatta who lived in the fifth century A.D. perceived the earth’s rotation on its axis.

·  Later in 16th century Tycho Brahe made very careful and accurate measurements of the motion of the planets and the sun. Based on the study of Tycho Brahe, another astronomer Kepler laid the foundation of modern astronomy.

Kepler deduced three laws which accurately described the motions of planets about the sun.

These laws formed the basis of the famous Newton’s law of universal gravitation.

1.    Kepler’s laws First law (Law of orbits)

·        Each planet moves around the sun in an elliptical orbit with the sun at one of its foci.

2.     Second law (Law of areas)

   As the planet moves in its orbit, a line drawn from the sun to the planet sweeps out equal areas in equal intervals of time.

3.     Third law (Law of periods)
     The squares of the periods of revolution of the planets are        proportional to the cubes of their mean distances from the sun.

           The planets with the mean distances from the sun, their orbital periods and velocities are listed in the table.

LAWS OF PERIODS 

Name of the Planet	Time Period (Yrs)	Mean Distance from the Sun R (x 109m)	Mean Velocity ( x 103 m/s-1)	( x10-25)
Mercury	0.241	57.91	47.875	2.991
Venus	0.615	108.21	35.056	2.985
Earth	1	149.6	29.806	2.987
Mars	1.881	227.94	24.144	2.988
Jupiter	11.862	778.3	13.072	2.988
Saturn	29.458	1427	9.651	2.986
Uranus	84.015	2869	6.804	2.99
Neptune	164.788	4498	5.438	2.984

About 100 years later, Newton demonstrated that Kepler’s laws were the consequence of a simple force that exists between any two masses.

Newton’s law of gravitation and laws of motion, provide the basis for the motion of planets and satellites.

NEWTON’S UNIVERSAL LAW OF GRAVITATION

Everybody in the universe attracts every other body with a force which is directly proportional to the product of the masses of the two bodies and inversely proportional to the square of the distance between them.

SURFACE TENSION 

• Have you seen insects like ants, water-spider walking on the surface of water ? You have seen mosquitoes sit and move freely on the surface of stagnant water.
• When we sprinkle water at the roots of trees and shrubs, the sprinkled water gradually rises to their branches upwards.
• Surface tension of a liquid is defined as the tangential force per unit length acting at right angles on an imaginary line drawn on the surface of the liquid.
• It’s unit is N m^-1.