Practical exercise 2: HOW BIG ARE THE STARS?

This exercise is an adaptation of those one suggested from the educational portal of NASA:

https://imagine.gsfc.nasa.gov/educators/lessons/star_size/

Aim

During this exercise the students will have an idea about the sizes of stars and will understand the relation between mass and radius of stars.

Necessary materials

• the table with data, 

• calculator.

Instructions for the teacher

This exercise will give opportunity of the students by using data for specific stars to understand how different are stars according their sizes, masses, radii, density and how these parameters are connected between each other. You can create some preliminary idea by using this picture illustrating the size differences in star:


For the purpose of the exercise the teacher should give the students the text table containing stars of different types from the Hertzsprung-Russell diagram with data about their radii, masses and densities comparing the Sun.

  Star Radius
(Solar radii)

Density
(Solar density)

Mass
(Solar mass)

Supergiants Antares 776 0,00000004 20
Beta Lirae 19,2 0,0014 9,7
Betelgeuse 1 000 0,0000005 10
Deneb 96 0,00002 20
Gamma Cygni
67 0,00007 20
Rigel 78 0,00004 20
Giants Aldebaran
Arcturus 35 0,00018 8
Beta Pegasi 40 0,00014 9
Capella 13 0,00096 2,1
Main sequence stars
Our Sun 1,0 1,0 1,0
Altair 1,6 0,415 1,7
Barnard’s star 0,15 53,3 0,18
61 А Cygni 0,7 1,69 0,58
Hadar 22 0,0023 25
Kruger 60 0,35 6,30 0,27
MU-1 Scorpii 5,2 0,1000 14
Procyon A 2,6 0,102 1,8
Sirius A 1,9 0,335 2,3
White dwarfs 40 B Eridani 0,018 71,000 0,41
Sirius B 0,022 90,000 0,99
Van Maanen star 0,007 47,000 0,14

Detailed instructions for the students

Arrange the stars from the list according their radius starting from the smallest to the largest one.

Answer

1. Van Maanen star 12. Capella
2. 40 B Eridani 13. Beta Lyrae
3. Sirius B 14. Hadar
4. Barnard’s star 15. Arcturus
5. Kruger 60 16. Beta Pegasi
6. 61 A Cygni 17. Gamma Cygni
7. Our Sun 18. Rigel
8. Altair 19. Aldebaran
9. Sirius A 20. Deneb
10. Procyon A 21. Antares
11. MU-1 Scorpii 22. Betelgeuse

Next to every star in your list above write the ratio stellar radius to stellar mass (in relative units to solar units rounding the result to the second decimal place.

Answer

1. Van Maanen star 0,05 12. Capella 6,19
2. 40 B Eridani 0,04 13. Beta Lyrae        1,98
3. Sirius B 0,02 14. Hadar                      0,88
4. Barnadr’s stars 0,83 15. Arcturus     4,38
5. Kruger 60 1,30 16. Beta Pegasi       0,44
6. 61 A Cygni 1,21 17. Gamma Cygni 3,35
7. Our sun 1,0 18. Rigel   3,9
8. Altair 0,94 19. Aldebaran 21,75
9. Sirius A  0,83 20. Deneb  4,8
10. Procyon A 1,44 21. Antares 38,8
11. MU-1 Scorpii 0,37 22. Betelgeuse    100

Explain the relation between radius and mass according the type of the star – supergiants, giants, Main sequence stars, white dwarfs.

[Answer: As a whole the white dwarfs have the smallest radii, then the Main sequence stars coming. The giants have larger radii and supergiants have the largest radii. Surprisingly this arrangement is not valid if it is seen the radius/mass ratio. The reason is that the density also plays a role. |For example the white dwarfs have the smallest radius and a modest mass amongst the stars but they have also the highest density while the supergiants have a huge radius but much lower density.]