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.]