(i consider a self-gravitating ball of gas with density p(r) at radial distance r from its centre. let e(r) be the energy produced by unit mass of the gas at radial distance r from the centre. use the mass-density relation dm(r)/dr at radius r satisfies to show that the luminosity l(r) 4tr2p(r) = dl(r4t2p(r)e(r) (1) = dr this is the "energy production equation" 6 marks (ii) for the above system, derive the hydrostatic support equation for the pressure p(r) at radial distance r: dp(r)_mr)p{r) (2) = dr 6 marks 3 marks (iii) what are the conserved quantum numbers in every nuclear reaction? (iv) write down the three steps involved in the pp1-chain fusion reaction which fuses h nuclei into 4he in a main sequence star. 3 marks (v) give a qualitative sketch of the potential energy v of interaction between two h nuclei, as a function of their separation