Gravitational Motion Physics : : Geostationary Satellites
Kepler’s Laws of Planetary Motion :
- Every planet revolves round the sun in an elliptical orbit with sun at one of the foci.
- The line joining the sun to the planet sweeps out equal area in equal interval of time i.e., the area velocity is constant.
|dA / dT = constant|
- The consequence of this theory is that the linear velocity is different at different places.
- It is maximum at a place where the distance between the planet and the sun is minimum.
- The orbital velocity is minimum when the distance between the planet and the sun is maximum.
- The square of time period of revolution is directly proportional to the cube of average distance between the planet and sun T2 ∞ R3 or the square of time period of revolution is proportional to the cube of semi – major axis of ellipse.
|T2 ∞ a3|
Newton’s Universal Law of Gravitation :
- Every two objects in the universe attract each other.
- “The force of attraction is directly proportional to the product of masses and inversely proportional to the square of the distance between the two masses”
|F ∞ m1 m 2 / r²
(or) F = G . m 1 m 2 / r²
Acceleration Due to Gravity :
- When a body falls freely, then the increase in velocity per second is called acceleration due to gravity.
- It is represented by g.
|g = GMe / R²e|
- where, Me = mass of the earth,
- Re = radius of the earth.
- Value of g depends upon the radius of the earth as g ∞ 1 / R.
- So, value of g is maximum at poles and minimum at equator.
- Value of g at poles is greater than its value at equator by 1.80 cms-2
Variation in the Value of G With Height :
- Value of g at the surface of the earth is 9.8 m / s²
- Value of g at the centre of earth is zero.
- Value of g at infinity becomes zero.
If the body is taken inside the earth, acceleration due to gravity decreases linearly with the distance from centre of the earth.
If the body is taken above the surface of the earth, acceleration due to gravity varies inversely as the square of the distance from the centre of earth.
- If we go up to height of equal radius of earth then value of g becomes one fourth of the value of g at the earth.
g is a vector quantity. Its direction is towards the centre of the earth. Its value is independent of the shape, size, mass, etc of the body but depends upon mass and radius of the earth or planet due to which there is a gravity pull.
- The rate of decrease of the acceleration due to gravity with height is twice as compared to that with depth.
- The value of acceleration due to gravity is minimum at planet mercury and maximum at planet Jupiter.
If gravity suddenly disappears :
- All bodies will lose their weights.
- We shall be thrown away from the surface of earth due to centrifugal force.
- The motion of the planets around the sun will cease because centripetal force will not be provided.
- Motion of the satellite around earth will also be not possible as no centripetal fore will be provided.
- If the rate of rotation of earth increases, then the value of g decreases at all places except at the poles.
If the earth starts rotating with an angular speed 17 times the present speed of rotation the object will fly off the equator ( i.e., g will be zero at the equator )
- If the observed value of g becomes zero at equator, then the length of the day will be 1.4 h.
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