Gravitational force is always attractive, conservative and independent of medium and acts on line foining the centres of the bodies.
Newton's law of gravitation:
Force acting between two bodies directly proportional to product of the masses and inversly proportional to square of distance between them.
Given by,
where G= Universal gas constant=
Gravity is the phenomenon of attraction of surrounding bodies to centre of particular body and is a vector quantity It holds the atmosphere around earth.
Given by:
so,
so,
Variation of acceleration due to gravity
1.with height
= for h< < R
2.With depth
At center of earth g'=0; x=R
3.With rotation of earth
At equator, ;
At poles, ; There is no effect of rotation at poles
Radius of earth= 6400 Km
Gravitational intensity: It is the force experienced by unit point mass placed at that point of consideration with gravitational field . It is scalar quantity.
Gravitational Potential (V): It is work done to take a unit mass from infinity to a certain point of consideration within gravitational field.field . It is scalar quantity.
Gravitational potential energy: It is work done to take a body of mass m from infinity to a point of consideration within gravitational field.
Gravitational potential energy on height h from the surface of earth
Its maximum value is 0 to infinity.
Change in gravitational PE when a body is raised from surface to height h is
=
Gravitational potential and intensity are related as
Gravitational field and potential
1.For point mass at distance r,
and
2.For hollow sphere of mass M having radius R
i. Outside point (r>R): and
ii. On the surface (r=R): and
iii. Inside point (r
3.For solid sphere of mass M and radius R
i. Outside point (r>R): and
ii. On the surface (r=R): and
iii. Inside point (r
4.For ring of radius R, mass M on its axis
#If two point masses and are kept at distance r then field intensity becomes zero at a distance
Motion of satellites
Time period
For nearer satellite, r=R so,
and = 84.6 min
Geostationary satellite appears stationary with respect to earth and launched on equateral plane (time period t = 24 hours) and height= 36,000 km
Energy of satellite
P.E. =
K.E.== binding energy
T.E. = P.E. + K.E.= = (PE=2TE=-2KE)
If a body is projected from earth then the maximum height attained by it is
or,
or,
so,
For escape velocity, h called escape velocity = 11.2 km/s for each
So, on increasing the orbital velocity of satellite by 41.4% the satellite escapes ( or KE by 100%)