Unformatted text preview: λ3 = 4 −2/3
K ρc 4π G 1/ 2 = 6.7 × 1010 f (β )
πG 1/ 2 ρ−1/3
c
so M= −4πρc ρ−1
c 6.7 × 1010 f (β )
πG 3/ 2
2
ξ1 dD
dξ ξ1 = 1.4 × 10 = 70 32 1−β
β4 1−β
β4 1/ 2 kg × 1M
1.99 × 1030 kg 1/ 2 M
β M (Msun) 0.1 6640 0.5 200 0.9 82 These are really large masses! This mainly goes to show how unimportant radiation pressure is inside stars like the Sun. NOTE ON SOLUTION: You may not use Mathematica/Matlab “differential solve” (e.g., DSolve, NDSolve) functions to do this – you need to do the integration on your own (it’s good for the soul!). You can either write a simple code in any language, or it’s even possible to do this in an Excel/OpenOffice spreadsheet. In any case, you must show and describe your own work. HOW DO I DO THIS? Second
order differential equations can be integrated using the Euler method by solving two equations: one for the parameter and one for its derivative. In this case, the Lane
Emden equation can be written as: d2 D 2 dD
+
= −Dn
2
dξ
ξ dξ
which can be split into two first
ord...
View
Full Document
 Fall '08
 Norman,M
 Physics, Work, 2 m, 1m, 2 m, 3 K, 3 k, ξ dξ

Click to edit the document details