CBSE Class 11 Physics Gravitation Notes Set 02

GRAVITATION

CONCEPTS

• Kepler's law of planetry motion

(a) Kepler's first law (law of orbit): Every planet revolves around the sun in an elliptical orbit with the sun is situated at one focus of the ellipse.

(b) Kepler's second law (law of area): The radius vector drawn from the sun to a planet sweeps out equal areas in equal intervals of time , i.e., the areal velocity of the planet around the sun is constant.

(c) 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 semimajor axis of the elliptical orbit of the planet around the sun.

• Gravitation is the name given to the force of attraction acting between any two bodies of the universe.

• Newton's law of gravitation: It states that gravitational force of attraction acting between two point mass bodies of the universe is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them, i.e., F=Gm1m2/r2, where G is the universal gravitational constant.

• Gravitational constant (G): It is equal to the force of attraction acting between two bodies each of unit mass, whose centres are placed unit distance apart. Value of G is constant throughout the universe. It is a scalar quantity. The dimensional formula G =[M^-1L³T^-2]. In SI unit, the value of G =6.67X10^- 11Nm²kg^-2.

• Gravity: It is the force of attraction exerted by earth towards its centre on a body lying on or near the surface of earth. Gravity is the measure of weight of he body. The weight of a body of mass m=mass X acceleration due to gravity=mg. The unit of weight of a body will be the same as those of force.

• Acceleration due to gravity (g): It is defined as the acceleration set up in a body while falling freely under the effect of gravity alone. It is vector quantity. The value of g changes with height, depth, rotation of earth the value of g is zero at the centre of the earth. The value of g on the surface of earth is 9.8 ms^-2. The acceleration due to gravity (g) is related with gravitational constant

(G) by the relaion, g=GM/R² where M and R are the mass and radius of the earth.

• Variation of acceleration due to gravity:

(a) Effect of altitude, g’=Gr²/(R+h)² and g’=g(1-2h/R)

The first is valid when h is comparable with R and the second relation is valid when h<<R.

The value of g decreases with increase in h.

(b) Effect of depth g’=g(1-d/R)

The acceleration due to gravity decreases with increase in depth d and

becomes zero at the center of earth.

(c) Effect of rotation of earth: g’=g-R ω²cos²λ

The acceleration due to gravity on equator decreases on account of rotation of earth and increase with the increase in latitude of a place.

• Gravitational field: It is the space around a material body in which its gravitational pull can be experienced by other bodies. The strength of gravitational field at a point is the measure of gravitational intensity at that point. The intensity of gravitational field of a body at a point in the field is defined as the force experienced by a body of unit mass placed at that point provided the presence of unit mass does not disturb the original gravitational field. The intensity of gravitational field at a point distance r from the center of the body of mass M is given by

E=GM/r²=acceleration due to gravity.

• Gravitational potential: The gravitational potential at a point in a gravitational field is defined as the amount of work done in bringing a body of unit mass from infinity to that point without acceleration. Gravitational potential at a point, V=work

done(W)/test mass(m0)= -GM/r.   V= W/m_{o - GM /r}

Gravitational intensity (I) is related to gravitational potential (V) at a point by the relation, E= -dV/dr

•  Gravitational potential energy of a body, at a point in the gravitational field of another body is defined as the amount of work done in bringing the given body from infinity to that point without acceleration.

Gravitational potential energy U=gravitational potential X

mass of body =-GM X m.

• Inertial mass of a body is defined as the force required to produce unit acceleration in the body.

Gravitational mass of a body is defined as the gravitational pull experienced by the body in a gravitational field of unit intensity. Inertial mass of a body is identical to the gravitational mass of that body. The main difference is that the gravitational mass of a body is affected by the presence of other bodies near it. Whereas the inertial mass of a body remains unaffected by the presence of other bodies near it.

• Satellite: A satellite is a body which is revolving continuously in an orbit around a comparatively much larger body.

(a) Orbital speed of satellite is the speed required to put the satellite into given orbit around earth.

Blinding energy of satellite = -E = GM m/(R+h)

• Geostationary satellite: A satellite which revolves around the earth with the same angular speed in the same direction as is done by the earth around its axis is called geostationary or geosynchronous satellite. The height of geostationary satellite is = 36000 km and its orbital velocity = 3.1 km s^-1.

• Polar satellite: It is that satellite which revolves in polar orbit around earth ,i.e. , polar satellite passes through geographical north and south poles of earth once per orbit.

• Escape speed: The escape speed on earth is defined as the minimum speed with which a body has to be projected vertically upwards from the surface of earth( or any other planet ) so that it just crosses the gravitational field of earth (or of that planet) and never returns on its own. Escape velocity ve is

• For a point close to the earth’s surface , the escape speed and orbital speed are related as ve =√2 ν_o

• Weightlessness: It is a situation in which the effective weight of the body becomes zero.

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