Periodic comets are lose aggregates of rock and ice on elliptical orbits around the sun as they approach perihelion, comets heat-up and lose gas and dust particles that, pushed by radiation pressure, form the comet's tails. if a periodic comet on a keplerian orbit with eccentricity e loses a dust particle at perihelion, the particle will be pushed on a new orbit with the same perihelion distance but a larger eccentricity: where β-frad/f,1 is the radiation pressure coefficient for the dust grain. i. find the expression for the semi-major axis a, of a dust particle lost at perihelion, as a function of β and of the original semi-major axis a and eccentricity e of the comet 2. find an expression for the minimum value of b so that the dust particle is ejected by the system (i. e. set on a parabolic orbit)