Gravitation

Submitted by:- Sanchay GumberClass :- 11

Summary

• Definition for Gravitation

• Acceleration Due to Gravity

• Variation Of “G” With Respect to Height And Depth

• Escape Velocity

• Orbital Velocity

• Gravitational Potential

• Time period of a Satellite

• Height of Satellite

• Binding Energy

• Various Types of Satellite

• Kepler’s Law of Planetary motion

GRAVITATION

1.Gravitation is a natural Phenomenon by which physical bodies attract each other.

2.Newton focused his attention on the motion of the moon about the earth.

3.He declared that the laws of nature that operating between earth and the apple is same as the laws of operating between earth and moon.

4.He calculated the acceleration due to gravitation(on earth) to be 9.8 m/s2

 

Evidence in Support of Law of Gravitation

• The rotation of the earth around the sun or that of the moon around earth is explained on the basis of this law.

• The tide are formed in ocean due to the gravitational force of attraction between earth and the moon.

• The value of g can be used to predict the orbits and timeperiod of an satellite.

Attraction Force between two bodies

Important Features of Law of Gravitation

• The Gravitation force between two masses is independent of the intervening medium.

• The mutual gravitational forces between two bodies are equal and opposite i.e. Gravitational Forces obey Newton’s third law of motion.

• The gravitational force is an conservative force.

• The law of gravitation holds only for point masses.

• The gravitational force between two point masses is a central force. Its magnitude depends only on r and has no angular dependence .

• The Gravitational force between two bodies is independent of the presence of other bodies.

Acceleration due to Gravity of the earth

•  

Variation in Acceleration due to Gravity

•  Variation of ‘g’ with respect to altitude

Variation in Acceleration due to Gravity

Variation of ‘g’ with respect to Depth

•  

The Variation of g with respect to Depth and Height (graph).

The Variation of g with respect to height will never be zero. It will increase after certain height.

The Variation of g with respect to depth will be zero when the body is placed at the center of earth.

 

Variation in Acceleration due to the shape of earth

• Gravitational field . Two bodies attract each other by the gravitational force even if they are not in direct contact. This interaction is called action at a distance. It can best explained in terms of concept of field. According to the field concept.

– Every mass modifies the space around it . This modified space is called gravitational field

– When any other mass is placed in this field , it feels a gravitational force of attraction due to its interaction with the gravitational field

• The space surrounding a material body within which its gravitational force of attraction can be experiences a force of attraction towards the centre of earth

Gravitational field

Gravitational Potential Energy

•  

A

P

R

O

r

x

B

dx

•  

Escape Velocity

• If we throw a ball into air , it rises to a certain height and falls back. If we throw it with a greater velocity , it will rise higher before falling down. If we throw with sufficient velocity , it will never come back . i.e. It will escape from the gravitational pull of the earth.

• The minimum velocity required to do so is called escape velocity.

• Consider the earth to be a sphere of mass M and radius R with centre O.

•  

Kepler’s law of planetary motion

• Law of orbits (first law) : Each planet revolves around the sun in an elliptical orbit with the sun situated at the one of the two foci.

Kepler’s law of planetary motion

• Law of areas (second law) : The radius vector drawn from the sun to a planet sweeps out equal areas in equal intervals of time i.e the areal velocity ( area covered per unit time) of a planet around the sun is constant.

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Kepler’s law of planetary motion

𝑣→

sun

𝑟→ 𝐹→

∆ 𝐴

𝑣→

planet

P’

Kepler’s law of planetary motion

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Kepler’s law of planetary motion

 

Kepler’s law of planetary motion