Gravitation
ISC SYLLABUS
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.
Elaboration of ISC Syllabus – Gravitation
(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. 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)
VIDEOS
Newton’s Law of Gravitation
Acceleration Due to Gravity
Acceleration due to gravity below surface of earth
Variation of g at different places on earth surface
Graph of g with distance
Gravitational Field
Gravitational Potential Energy
Escape Speed
Motion of Satellite
Gravitational Potential
Kepler’s Laws of Planetary Motion
