2) Do the

*first two radiative envelope computations*for temperature, density and pressure, i.e. at radial fractions r/R = 0.183 and r/R = 0.200.

Soln. (A) At r/ R = 0.183 And we have: U = 2.562 and V = 1.389

r = 9.800 x 10

^{10}cm (0.183) = 1.793 x 10

^{10}cm

M

**/M = 0.172 so**

_{r}M

**= 3.970 x 10**

_{r }^{33}g (0.172) = 6.83 x 10

^{32}g

*density*:

r = UM

**/4p r**_{r}^{3}
= [(2.562) (6.83 x 10

^{32}g)]/ 4p (1.793 x 10^{10}cm)^{ 3}^{}

r = 24.16 g/ cm

^{ 3 }log r = 1. 3831*Pressure*:

P = G r M

**/ V r**_{r}
= [(6.67 x 10

^{-8}dyne-cm^{2}/ g^{.2}) (24.16 g/ cm^{ 3 })(6.83 x 10^{32}g)/ (1.389)(1.793 x 10^{10}cm)
P = 4.417 x 10

^{16}dyne/ cm^{ 2}
log P = 16.645

*Temperature*:

T = t m (H/R) (GM/r)

log t = - 0.15695 so t (dimensionless T) = 0.6969

T = (0.6969) [m (H/R) (GM/r) ] (for m = = 0.64, H = 1.672 x 10

^{-24})
So:

T = 1.417 x 10

^{7}K and log T = 7.1516
Soln: (B)

At r/ R = 0.200 And we have: U = 2.450 and V = 1.684

r = 9.800 x 10

M

M

r = 9.800 x 10

^{10}cm (0.200) = 1.960 x 10^{10}cmM

**/M = 0.217 so**_{r}M

**= 3.970 x 10**_{r }^{33}g (0.217) = 8.61 x 10^{32}g*density*:

r = UM

**/4p r**_{r}^{3}
=

[(2.450) (8.61 x 10

^{32}g)]/ 4p (1.960 x 10^{10}cm)^{ 3}^{}

r = 22.31 g/ cm

^{ 3 }log r = 1. 3485*Pressure*:

P = G r M

**/ V r**_{r}
= [(6.67 x 10

^{-8}dyne-cm^{2}/ g^{.2}) (22.31 g/ cm^{ 3 })(6.83 x 10^{32}g)/ (1.684)(1.96 x 10^{10}cm)
P = 3.884 x 10

^{16}dyne/ cm^{ 2}
log P = 16.5893

*Temperature*:

T = t m (H/R) (GM/r)

log t = - 0.19200 so t (dimensionless T) = 0.6426

T = (0.6426) [m (H/R) (GM/r) ] (for m = = 0.64, H = 1.672 x 10

^{-24})
So:

T = 1.346 x 10

^{7}K and log T = 7.1291
3) Estimate the uncertainty in the core radius as a consequence of the 'fuzziness' of the interface parameters.

The percentage uncertainty can be computed as:

D ( r

_{c}_{ }) = 100%(0.172 - 0.148) / 0.172 = 0.024(100%)= 2.4 %_{}

^{}

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