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VbvAstE-001

Book Boris V. Vasiliev Astrophysics

5.3.5 The comparison

5.3.5 The comparison with measuring data The mass spectrum (Fig.5.1) shows that the Sun consists basically from plasma with A/Z = 5. The radius of the Sun and its surface temperature are functions of Z too. This values calculated at A/Z=5 and differen Z are shown in Table (5.3.3) Table (5.3.3) R ⊙, cm T ⊙,K Z (calculated (calculated (5.37)) (5.38)) 1 2.0 · 10 11 1961 2 1.0 · 10 11 3923 3 6.65 · 10 10 5885 4 5.0 · 10 10 7845 One can see that these calculated data have a satisfactory agreement the measured radius of the Sun R ⊙ = 6.96 · 10 10 cm (5.39) and the measured surface temperature at Z = 3. The calculation shows that the mass of core of the Sun T ⊙ = 5850 K (5.40) M ⋆(Z = 3, A/Z = 5) ≈ 9.68 · 10 32 g (5.41) i.t. almost exactly equals to one half of full mass of the Sun in full agreement with Eq.(4.20). M ⋆(Z = 3, A/Z = 5) M ⊙ ≈ 0.486 (5.42) In addition to obtained determinations of the mass of a star Eq.(5.26), its temperature Eq.(5.38) and its radius Eq.(5.37) give possibility to check the calculation, if we compare these results with measuring data. Really, dependencies measured by astronomers can be described by functions: M = Const1 (A/Z) 2 , (5.43) R 0 = Const2 , (5.44) Z(A/Z) 1/2 T 0 = Const3Z (A/Z) 2 . (5.45) 37

2.10 log (TR/R o T o ) 1.55 1.00 measured TR~M 1.27 theory TR~M 5/4 0.45 -0.10 -0.2 0.1 0.4 0.7 1.0 1.3 1.6 logM/M o Figure 5.3: The relation between main parameters of stars (Eq.(5.46)) and corresponding data of astronomical measurements for close binary stars [11] are shown. If to combine they in the way, to exclude unknown parameter Z, one can obtain relation: T 0R 0 = Const M 5/4 , (5.46) Its accuracy can by checked. For this checking, let us use the measuring data of parameters of masses, temperatures and radii of close binary stars [11]. The results of these measurements are shown in Fig.(5.3), where the dependence according to Eq.(5.46). It is not difficult to see that these data are well described by the calculated dependence. It speaks about successfulness of our consideration. If main parameters of the star are expressed through corresponding solar values τ ≡ T 0 T ⊙ ,ρ ≡ R 0 R ⊙ and µ ≡ M M ⊙ , that Eq.(5.46) can be rewritten as τρ = 1. (5.47) µ 5/4 τρ Numerical values of relations for close binary stars [11] are shown in the last µ 5/4 column of the Table(6.2)(at the end Chapter (6)). 38

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