Please tell how is OM=r sin alpha? — results. You may need to know that the areal velocity is given :
dA (it — %
appllcafion of the above discussion can be made to the motion or a planet
under the gravitational force of the sun. For convenience the sun may be taken io be so
that it is at rest. me gravitational foree of the gun on ihé is directed towards the
This force also satisfies the requirement F = FM"). sinec F = G where rrh and are
respectively the masses of thc planet and lhe sun and G is the unlyersal constant of gravltatlon.
"The two results (l) and (2) described above, therefore, apply to the motion of the planet. In fact,
the result (2) is the well-known second law of Kepler.
p'
is the treJectory of the particle under the force. At a position p, the force is directed
along OP, O is the centre of the force taken as the origin In time the particle moves faun P P,
PP' As = v AL The tangent PQ at P to the trqjectory gives the direction Qi the trebcity at me
swept In At is the area of sector POP' (r sin a) PP'/2 = (r v sin a) At/2.)
