Question

#1. How many times more luminous is an A main sequence star than the Sun? How many times more massive is it? (Hint: the data in the table below are your friend. Use them, and the HR diagram, to determine the A main sequence star's parameters.)

#2. Which would you expect to live on the main sequence longer? The Sun or the star in question #1? (Hint: Once you have determined the star's mass and luminosity in solar units, use the lifespan equation...)

O B A F G K M
35000K

20000K

9000K

7000K

5800K

4500K

3200K

60MSun

10MSun

2MSun

1.4MSun

1MSun

0.7MSun

0.3MSun

Answer 1

1. According to the table, an A main sequence star has a temperature of approximately 9000 K. Using the formula from the previous question:

Luminosity (in solar units) = (Temperature / 5777)^4 x Mass

Assuming a mass of 2 solar masses (which is a typical mass for an A main sequence star), we get:

Luminosity = (9000 / 5777)^4 x 2 = 30.27

Therefore, an A main sequence star is approximately 30 times more luminous than the Sun.

To find the star's mass, we can use the mass column in the table. An A main sequence star has a mass of approximately 2 solar masses.

2. The lifespan of a star on the main sequence depends on its mass and luminosity. The equation for main sequence lifespan is:

Lifespan (in years) = 10 billion / (Mass / Luminosity)

Using the values we found in Question 1 and assuming a mass of 2 solar masses, we get:

Lifespan = 10 billion / (2 / 30.27) = 456 million years

Using the same equation for the Sun (which has a mass of 1 solar mass and a luminosity of 1 solar unit), we get:

Lifespan = 10 billion / (1 / 1) = 10 billion years

Therefore, the Sun would live on the main sequence longer than an A main sequence star.