Solution to Suggested Comprehension Ex. For Part 1 (Construction of a Star)

From the next to last U,V values given in the model table (i.e. at r/R = 0.262), confirm the values for: M_r/M, log P and log (rho) ,  i.e.   log   r .  Note the pressure at given M_r  is given by :

P   =      G  r M_r/ V r


We have: U = 2.006 and V = 2.829

M_r/M = 0.395 =  1.568  x 10³³  g

density:  log (rho) =  log   r 


 r   =     UM_r/4p r³

=  [(2.006) (1.568  x 10³³  g)]/ 4p (2.567  x 10¹⁰  cm) ³

r  =   14.80  g/ cm ³        log   r  = 1. 1703

Pressure:

P   =      G  r M_r/ V r

=  [(6.67 x  10^-8 dyne-cm ²/ g^.2)  (14.80  g/ cm ³ )(1.568  x 10³³  g)/   (2.829)(2.567  x 10¹⁰  cm)

P   =  2.131  x 10¹⁶    dyne/ cm ²

log P   =   16.3286