Stefan's law & Wien's displacement law

HIP 56948 is a star with a black-body temperature of 5800 K. The star is at a distance of 210 ly from the Sun.

Sketch, on Figure 1, the black-body curve for HIP 56948. Label the wavelength axis with a suitable scale and unit.

The diameter of HIP 56948 is the same as the diameter of the Sun.

Suggest a value for the absolute magnitude of HIP 56948.

Astronomers study HIP 56948 in their search for Earth-like exoplanets because HIP 56948 is similar to the Sun.

Suggest one difficulty in detecting an Earth-like planet around HIP 56948.

Mintaka Aa1 and Mintaka Aa2 are two stars in a binary system. This means that they orbit their common centre of mass with the same period.

Table 2 gives information about the two stars.

Show that the data in Table 2 are consistent with the two stars being in a binary system.

State the most prominent absorption lines in the spectrum of Mintaka Aa2.

Explain which star in Table 2 has the greater temperature.

Figure 2 shows how the apparent magnitude of the binary system varies with time.

Explain the variation in apparent magnitude shown in Figure 2.

In your answer you should explain:

the changes in observed brightness at P and Q, as shown in Figure 2

why the observed brightness at P is different from the observed brightness at Q.

Determine the angular velocity of the binary system.

Early observations of the star Betelgeuse indicated that:

radius r of Betelgeuse = 700 × radius of the Sun distance d of Betelgeuse from the Earth = 548 ly intensity received from Betelgeuse = I.

Recent data suggest that the intensity received from Betelgeuse is actually 1.15 I.

Based on these recent data, two groups of students reach different conclusions.

Group X suggest that:

• r is correct

• d is actually 530 ly.

Group Y suggest that:

• d is correct

• r is actually 750 × radius of the Sun.

Discuss for each group whether their conclusion could be correct. Assume that the measured temperature of Betelgeuse is constant.

Figure 3 shows the variation of intensity with wavelength for a star.

Show that Figure 3 is consistent with a black-body temperature of about 6.0 × 10³ K.

The radius of the star is 9.6 × 10⁶ m.

Calculate the power output of the star.

Which row gives the type and spectral class of the star?

The light from the star passes through an interstellar dust cloud before reaching Earth. The reduction in intensity when light passes through a dust cloud is assumed to be inversely proportional to the wavelength of the light.

An astronomer on the Earth estimates the black-body temperature of the star.

Discuss the effect that the dust cloud has on this estimate.

M40 A and M40 B are two stars that appear very close to each other when viewed from Earth. There are two possible reasons for this:

• they are an orbiting binary system

• they are distant from each other and only appear in the same line of sight.

In an orbiting binary system, the difference between the apparent magnitude and the absolute magnitude for each star is similar.

Table 3 shows data about these two stars.

Discuss the appearance of the two stars to an astronomer on the Earth. In your answer you should:

• compare the colour of the stars

• compare the brightness of the stars

• deduce, with a calculation, whether the stars form an orbiting binary system.

In the middle of the 20th century, there were two competing theories of the Universe. In 1964, electromagnetic radiation was observed coming from all directions in space. Figure 2 shows the distribution of this radiation as observed from Earth.

The graph provides evidence for one of these theories of the Universe.

Discuss the main features of this theory of the Universe.

In your answer, you should include:

• the main predictions and evidence for the theory, and

• a suitable calculation.

Figure 1 shows the evolution of a star similar to the Sun on a Hertzsprung-Russell (HR) diagram.

State the evolutionary stage of the star at each of the points W, X, Y and Z.

Theta Carinae is a star with a radius five times that of the Sun. It has a surface temperature of 31 000 K.

Annotate Figure 1 with a T to show the position of Theta Carinae.

An astronomer suggests that an Earth-sized planet orbits Theta Carinae.

Explain one difficulty with using the transit method to detect this planet.

The astronomer suggests that the Earth-sized planet receives a similar amount of power from Theta Carinae as the Earth does from the Sun.

The average power output of the Sun is 3.8 × 10²⁶ W.

Determine the orbital radius of the Earth-sized planet orbiting Theta Carinae.

Miaplacidus and Avior are two stars in the constellation Carina. Miaplacidus is a class A star. Avior is a class K star.

Figure 2 shows how the intensity of radiation arriving at the Earth varies with wavelength for one of these stars. Only the important features of the variation are shown.

Deduce, with reference to Figure 2, the identity of the star.

In your answer you should:

• explain the overall shape of the graph

• describe the processes in the star that lead to the decreases in intensity

• state the identity of the star.

Table 1 summarises some information about four stars in the constellation Cassiopeia.

Which star has the highest surface temperature? Tick () one box.

Figure 1 shows the intensity received at Earth from two of the stars, plotted against wavelength. The effect of absorption by the Earth’s atmosphere is not shown.

Discuss what information can be found from Figure 1 about the temperature and colour of these stars. Support your answer with suitable calculations.

State which star in Table 1 is dimmest on the absolute magnitude scale.

Calculate the absolute magnitude of Schedar.

Tsih has a mass over 15 times the mass of the Sun. Tsih may eventually collapse to form a black hole.

Calculate the radius of the event horizon for a black hole with a mass 15 times that of the Sun.

Table 2 gives data about the supergiant star Melnick 34 and the Sun.

Discuss why the evolution of a supergiant star in the local part of our galaxy could be dangerous for life on Earth.

Table 2 shows some properties of the four brightest stars in the constellation Canis Minor.

Discuss, with reference to the Hipparcos scale, why many star maps show only two stars in the constellation Canis Minor.

State and explain which star in Table 2 has the most prominent Hydrogen Balmer absorption lines.

Deduce which star, Gamma A or HD 66141, has the larger diameter.

Astronomers recently used the radial velocity method to discover an exoplanet orbiting HD 66141.

Describe the main features of the radial velocity method in the detection of planets.

Calculate the distance from the Earth to Procyon. Give an appropriate unit for your answer.

Sketch, on the axes in Figure 1, the black-body radiation curve for a typical star.

Explain, with reference to the SI units involved, how the curve you have drawn can be used to determine the black-body temperature of the star.

Two stars, 61 Cygnus A and 61 Cygnus B, can be seen very close together in the constellation Cygnus. Early astronomers were unsure whether the two stars form a binary system, or simply appear in the same line of sight. Table 1 shows some of the properties of the two stars.

Evaluate whether the data support the suggestion that the two stars form a binary system.

In your answer you should

• compare the two stars as seen by an observer on Earth

• support your evaluation with suitable calculations.

What is the spectral class of 61 Cygnus A? Tick (✓) the correct box.

Define the parsec. You may use a diagram as part of your answer.

Deduce which star is larger, Kornephoros or Rutilicus.

One of the four stars has the peak in its black-body radiation curve at a

Calculate the corresponding temperature for this curve.

Explain which star produced the black-body radiation curve described in question 03.3.

Which star has the brightest absolute magnitude? Tick () the correct box.

Determine the absolute magnitude of Sarin.