Gravitation Notes and Formulas Class 9 / 11 / 12

                                                                                                                          QSTARNOTES                           

VISIT :qstarnotes.blogspot.com

                                          

                                                Gravitation 

In this notes whole chapter is divided into two parts : 1- Theoretical and 2- Formulas (All)

• Theoretical

Universal law of gravitation/ Newton’s law of gravitation: 

Newton’s law of gravitation or universal law of gravitation states that every object attracts another object with a force that is directly proportional to another object with a force that is directly proportional to the product of their masses and inversely proportional to the square of distance between their centres.

  F= Gmm/r^2 

Importance of universal law of gravitation ( useful for gain of 1-2 marks in exam )

1. the force that binds is to the earth 
2. The motion of the moon around the earth 
3. The motion of planet around the sun

• Centripetal force : centripetal force is a net force that acts on an object to keep it moving in a circular path 
• Centrifugal force : the centrifugal force is an internal force that appears to act on all object when viewed In a rotating frame of reference  or  centrifugal force is and internal force that acts on an object to make it flee from the centre.

 Kepler’s three law of planetary motion 

1. Law of orbits
2. Law of areas
3. Law of periods 

1. Law of orbits : In this universe, the orbit of a planet is elliptical with the sun at one of the foci.

 

This orbit is in elliptical shape and this is the Kepler first law or orbit.

1. Law of areas : the line joining the sun and planet sweeps equal areas in equal interval of time. This law is kepler’s second law of planetary motion  or  the areal velocity of planet around the sun is constant 

Areal velocity = area traced / time 

In this figure the sun is at a foci of an elliptical orbit. Now , according to this law,

                                              Area of OP₁P₂ = Area of OP₃P₄ 

Since arc P1 and P2 is smaller than that of arP3 and P4. Hence , it means speed of planet is greater when it is closer to the sun. This is the second law of planetary motion given by kepler

1. Law of period : In this law, the square of time is directly proportional to the cube of semi major axis of the elliptical orbit.

 

I.e T^2 x r^3 

This law is called 3rd law of kepler’s planetary motion,

Flow points : 

• If both masses doubled the force between object becomes 4 times 
• If both masses is doubled and distance is halved the force between object becomes 16 times 
• If both masses is doubled and distance also doubled then the force between object becomes unchanged 
• Dimensional formula of gravitational constant is [M^-1 L^3 T^-2]

• Formula 

DIFFERENCE BETWEEN  ACCELERATION DUE TO GRAVITY AND GRAVITATIONAL CONSTANT

RELATION BETWEEN ACCELERATION DUE TO GRAVITY AND GRAVITATIONAL CONSTANT F=Gmm/R^2      - eq.1     F=mg      -eq.2
From eq. 1 and 2 we get mg=Gmm/R^2 g=Gm/R₂