Chapter 8, Problem 10P

To determine

• Which star is brightest?
• Which star is most luminous in absolute magnitude?
• Which star is largest?
• Which star is farthest away?

Answer to Problem 10P

• The brightest star is a.
• The most luminous star in absolute magnitude is c.
• The largest star is c.
• The farthest away star is d.

Explanation of Solution

Given:

Table

Star	Spectral type	$m_v$
a	G2 V	5
b	B1 V	8
c	G2 Ib	10
d	M5 III	19
e	White dwarf	15

Formula used:

Absolute magnitude of the star is given as

Calculation:

Consider the H-R diagram

Figure.1

(a)

The classification of the star is G2 V, here G suggests that class of the star, and V suggest that it is a main sequence star. By the help of this we can estimate the absolute magnitude of the star using H-R diagram

It is clear from the figure that the absolute magnitude of the star is 5

Apparent magnitude of the star is give as

$m_v-M_v=-5+5{\log }_{10}\left(d\right)$

Plugging the values in the above equation

$\begin{array}{c}5-5=-5+5{\log }_{10}\left(d\right)\\ 5=5{\log }_{10}\left(d\right)\\ d=1\text{parsec}\end{array}$

(b)

The classification of the star is B1 V, here B suggests that class of the star, and V suggest that it is a main sequence star. By the help of this we can estimate the absolute magnitude of the star using H-R diagram

It is clear from the figure that the absolute magnitude of the star is -1

Apparent magnitude of the star is give as

$m_v-M_v=-5+5{\log }_{10}\left(d\right)$

Plugging the values in the above equation

$\begin{array}{c}8-\left(-1\right)=-5+5{\log }_{10}\left(d\right)\\ 14=5{\log }_{10}\left(d\right)\\ d=631\text{parsec}\end{array}$

(c)

The classification of the star is G2 Ib, here G suggests that class of the star, and Ib suggest that it is supergiant star. By the help of this we can estimate the absolute magnitude of the star using H-R diagram

It is clear from the figure that the absolute magnitude of the star is -7

Apparent magnitude of the star is give as

$m_v-M_v=-5+5{\log }_{10}\left(d\right)$

Plugging the values in the above equation

$\begin{array}{c}10-\left(-7\right)=-5+5{\log }_{10}\left(d\right)\\ 22=5{\log }_{10}\left(d\right)\\ d=25,118\text{parsec}\end{array}$

(d)

The classification of the star is M5 III, here G suggests that class of the star, and III suggest that it is giant star. By the help of this we can estimate the absolute magnitude of the star using H-R diagram

It is clear from the figure that the absolute magnitude of the star is 0

Apparent magnitude of the star is give as

$m_v-M_v=-5+5{\log }_{10}\left(d\right)$

Plugging the values in the above equation

$\begin{array}{c}19-0=-5+5{\log }_{10}\left(d\right)\\ 24=5{\log }_{10}\left(d\right)\\ d=63,095\text{parsec}\end{array}$

(e)

The absolute magnitude of the white dwarf is always greater or equal to 10.

Apparent magnitude of the star is give as

$m_v-M_v=-5+5{\log }_{10}\left(d\right)$

Plugging the values in the above equation

$\begin{array}{c}19-10=-5+5{\log }_{10}\left(d\right)\\ 14=5{\log }_{10}\left(d\right)\\ d=630.95\text{parsec}\end{array}$

Thus, it is clear that, brightest star in apparent magnitude is a, most luminous absolute magnitude star is c, largest star is c because it is a supergiant star, and farthest away star is d.

Conclusion:

• The brightest star is a.
• The most luminous star in absolute magnitude is c.
• The largest star is c.
• The farthest away star is d.