Question

A main sequence star has mass 2×1031 kg and radius 3×109
m. Obtain an estimate of
the average temperature throughout the star.

Answer 1

Answer on Question #61087, Physics / Astronomy | Astrophysics

A main sequence star has mass $2 \times 10^{31} \, \mathrm{kg}$ and radius $3 \times 10^{9} \, \mathrm{m}$ . Obtain an estimate of the average temperature throughout the star.

Find: $T_{\text{star}} - ?$

Given:

$\mathrm{m_{star}} = 2 \times 10^{31} \mathrm{~kg}$

$\mathrm{r_{star}} = 3 \times 10^{9} \mathrm{~m}$

$\mathrm{m_{sun} = 1,9891\times 10^{30}kg}$

$\mathrm{r_{sun} = 6,96\times 10^{8}m}$

$\mathrm{T}_{\mathrm{sun}} = 5778 \mathrm{~K}$

Solution:

The relationship between luminosity $L$ , temperature $T$ and radius $r$ :

$\mathrm{L_{star}} = \mathrm{L_{sun}}\quad \frac{\mathrm{r_{star}}}{\mathrm{r_{sun}}}^2\quad \frac{\mathrm{T_{star}}}{\mathrm{T_{sun}}}^4$ (1)

$\mathrm{m} = \frac{\mathrm{m_{star}}}{\mathrm{m_{sun}}} (2)$

Of (2) $\Rightarrow$ m=10.1

If $m = 10.1$ (2<m<20), then $l = \frac{L_{\text{star}}}{L_{\text{sun}}} = m^{3.5}$ (3)

(3) in (1): $(10.1)^{3.5} = \frac{3 \times 10^{9}}{6,96 \times 10^{9}}^2 \frac{T_{\text{star}}}{T_{\text{sun}}}^4$ (4)

Of (4) $\Rightarrow \frac{T_{\text{star}}}{T_{\text{sun}}} = 176.23$ (5)

Of (5) $\Rightarrow \frac{T_{\text{star}}}{T_{\text{sun}}} = 3.64$ (6)

Of (6) $\Rightarrow$ Tstar=21032 K

Answer:

21032 K

http://www.AssignmentExpert.com