Stellar physics
- A star emits electromagnetic radiation with a peak wavelength of 6.8 × 10–7 m.
(a) Use Wien’s law (λmaxT = 3 × 10–3) to calculate the surface temperature of the star.
(b) Calculate the power of the radiation emitted by each square metre of the star’s surface where the star is assumed to be a black body.
Stefan–Boltzmann constant = 5.67 × 10–8 J s–1 m–2 K–4.
2. The Sun has a radius of 7.0 × 108 m and a surface temperature of 5800 K.
(a) Calculate the power emitted per m2 from the Sun’s surface.
(b) Calculate the luminosity of the Sun.
(c) Calculate the apparent brightness of the Sun as seen from the Earth.
3. Three measurements of a distant star are possible from Earth. These measurements are:
peak emitted wavelength = 2.4 × 10–7 m
distance to star (parallax method) = 8.5 × 1017 m
apparent brightness = 4.3 × 10–9 Wm–2
(a) Use Wien’s law (λmaxT = 3 × 10–3) to calculate the surface temperature of the star.
(b) Calculate the energy emitted by each square metre of the star’s surface per second.
(c) Calculate the luminosity of the star.
(d) Calculate the radius of the star.
- A star is 86 ly from Earth and has a luminosity of 4.8 × 1028 W.
Calculate the apparent brightness of the star.
- The apparent brightness of a star is 6.2 × 10–8 Wm–2. The star is 16 ly from Earth.
Calculate the luminosity of the star.
- A star with luminosity 2.1 × 1030 W has an apparent brightness of 7.9 × 10–8 Wm–2 when viewed from Earth.
Calculate the distance of the star from Earth:
(a) in metres
(b) in light years.
- A star with radius 7.8 × 108 m and surface temperature 6300 K has an apparent brightness of 1.8 × 10–8 Wm–2.
Calculate its distance from the Earth.
- A star with radius 9.5 × 109 m and surface temperature 5900 K is 36 ly from Earth.
Calculate the apparent brightness of the star.
- Show mathematically that the luminosity of a star varies directly with the square of its radius and the fourth power of its surface temperature.
10. Show mathematically that the apparent brightness of a star varies directly with the square of its radius and the fourth power of its surface temperature and varies inversely with the square of its distance from the Earth.
- Two stars, A and B, are the same distance from the Earth.
The apparent brightness of star A is 8.0 × 10–12 Wm–2 and the apparent brightness of star B is 4.0 × 10–13 Wm–2.
Show that star A has 20 times the luminosity of star B.
- A star has half of our Sun’s surface temperature and 400 times our Sun’s luminosity.
How many times bigger is the radius of this star compared to the Sun?
- Information about two stars A and B is given below.
surface temperature of star A = 3 × surface temperature of star B
radius of star A = 2 × radius of star B
(a) How many times is the luminosity of star A greater than the luminosity of star B?
(b) Stars A and B have the same apparent brightness from Earth.
Which star is furthest from Earth and by how many times?
- The diagram shows one way of classifying stars. Each dot on the diagram represents a star.
(a) What name is usually given to this type of diagram?
(b) The stars are arranged into four main regions. Identify the region called:
(i) the main sequence
(ii) giants
(iii) super giants
(iv) white dwarfs.
(c) (i) In which of the regions on the diagram is the Sun?
(ii) The surface temperature of the Sun is approximately 5800 K. Explain why the scale on the temperature axis makes it difficult to identify which dot represents the Sun.
(d) In which region would you find the following:
(i) a hot bright star
(ii) a hot dim star
(iii) a cool bright star
(v) a cool dim star?
(e) A star is cooler than, but brighter than the Sun.
(i) What can be deduced about the size of this star compared to the size of the Sun?
(ii) What region would this star be in?
(f) A star is hotter than, but dimmer than, the Sun.
(i) What can be deduced about the size of this star compared to the size of the Sun?
(ii) What region would this star be in?
(g) The Sun’s nuclear fuel will be used up with time. What will then happen to the Sun’s position in the above diagram?
15. The Sun produces energy by a process known as the proton-proton chain reaction.
Describe the main steps of this process, giving details of the particles produced at each stage.
