Grav

Kepler's laws of planetary motion, universal law
of gravitation. Acceleration due to gravity (g)
and its variation with altitude, latitude and
depth.
Gravitational potential and gravitational
potential energy, escape velocity, orbital
velocity of a satellite, Geo-stationary satellites.
(i) Newton's law of universal gravitation;
Statement; unit and dimensional formula of
universal gravitational constant, G
[Cavendish experiment not required];
gravitational acceleration on surface of the
earth (g), weight of a body W= mg from
F=ma.
(ii) Relation between g and G. Derive the
expression for variation of g above and
below the surface of the earth; graph;
mention variation of g with latitude and
rotation, (without derivation).
(iii) Gravitational field, intensity of gravitational
field and potential at a point
in earth’s gravitational field. Vp = Wαp/m.
Derive expression (by integration) for
the gravitational potential difference
∆V = VB-VA = G.M(1/rA-1/rB); here
Vp = V(r) = -GM/r; negative sign for attractive force field; define gravitational
potential energy of a mass m in the earth's
field; expression for gravitational potential
energy U(r) = Wαp = m.V(r) = -G M m/r;
show that ∆U = mgh, for h << R. Relation
between intensity and acceleration due to
gravity.
(iv) Derive expression for the escape velocity of
earth using energy consideration; ve depends
on mass of the earth; for moon ve is less as
mass of moon is less; consequence - no
atmosphere on the moon.
(v) Satellites (both natural (moon) and artificial)
in uniform circular motion around the earth;
Derive the expression for orbital velocity and
time period; note the centripetal acceleration
is caused (or centripetal force is provided) by
the force of gravity exerted by the earth on
the satellite; the acceleration of the satellite
is the acceleration due to gravity
[g’= g(R/R+h)2
; F’G = mg’].
Weightlessness; geostationary satellites;
conditions for satellite to be geostationary;
parking orbit, calculation of its radius and
height; basic concept of polar satellites and
their uses.
(vi) Kepler's laws of planetary motion: explain
the three laws using diagrams. Proof of third
law (for circular orbits only)