96
Gaseous Stars
[ch. Ill
Inserting the numerical values R/m = 8’26 x 10 7 and 7 = 6’66 x 10~ 8 , and
further measuring M and r in terms of the mass ( 2’00 x 10 33 ) and radius
( 6*95 x 10 10 ) of the sun, this assumes the form
in which M and r are measured in terms of the mass and radius of the sun.
From equation (82'6) we obtain at once
This completes the analysis necessary for the evaluation of internal tem
perature, density, etc. Starting from any values of n, we calculate the value
of \ c from relation (85‘2) ; equation (88'7) next gives the mass of the corre
sponding star, and equation ( 88 ‘ 6 ) then gives the central temperature for a
star of this mass.
weight is constant throughout the star. In this casey = 0, so that from
equations (88‘7) and ( 88 ' 8 ),
The value of B now depends only on n, and is readily determined from
Emden’s numerical solutions.
Emden gives solutions only for the values n = 2*5, 3, 4, 4*5, 4*9 and 5, so
that solutions for intermediate values of n must be obtained by interpolation.
The interpolation becomes easy on noticing that the values of l/r 1( and of
from Emden’s solutions, those corresponding to the values n = 325 and 35
being obtained by interpolation.
The table refers to the case in which g is constant throughout the star so
that j — 0, and the relation (85*2) between n and X c reduces to
so that, on substituting for T c ' from ( 88 ‘ 2 )
x/ + lj (pf = B( 1 + x.)«
(88-7),
where
( 88 - 8 ).
Stars with uniform effective molecular weight.
89. The problem assumes its simplest form when the effective molecular
X c > 4 if 2 = 5(1+ \ c ) 3
(891),
where
Table X (p. 97) gives values calculated
4 + \ c
1 + 4\ c + 2 1
n = 3 + (l-2Z)
(89-3).