Apparent & absolute magnitude

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.

The apparent change in position of a nearby star relative to distant stars is due to an effect known as parallax.

Figure 2 shows how parallax arises. As the Earth moves from point P to point Q, an observer on the Earth sees the position of a nearby star S change in relation to distant stars.

Angle A is the parallax angle. This angle can be used to determine the distance to a nearby star, provided that the relative motion between the star and the Sun is negligible between observations.

The distance from the Sun to S is 79 ly. The Earth takes 6 months to move from point P to point Q.

Calculate, in degrees, angle A.

Parallax is used to determine the distance to a different star. Observations of the star produce the following data:

distance determined using parallax = 0.40 pc apparent magnitude = 13.5 absolute magnitude = 16.7

An astronomer suggests that the star moved significantly relative to the Sun between the two parallax observations.

Discuss whether this suggestion is valid.

Draw a labelled diagram to define the parsec (pc).

Table 1 shows data for two stars: Rigel and the Sun.

State the spectral class of Rigel.

The apparent magnitude of Rigel is 0.11

Calculate, in pc, the distance from Rigel to the Earth.

Figure 1 shows a Hertzsprung–Russell (HR) diagram.

Draw a line on Figure 1 to show the evolution of the Sun from formation to white dwarf.

One stage in the evolution of Rigel includes the emission of a gamma ray burst.

Outline the circumstances during which a gamma ray burst will be emitted by Rigel.

State what is meant by normal adjustment when applied to an astronomical refracting telescope.

Which combination of lenses gives the largest angular magnification when used as

V1031 and WASP-82 are two stars in the constellation Orion. V1031 appears 40 times brighter than WASP-82 when viewed from Earth. The apparent magnitude of V 1031 is 6.0

Calculate the apparent magnitude of WASP-82.

V1031 is just visible to the naked eye of an astronomer when her pupil diameter is 7 mm.

Suggest whether she can observe WASP-82 using a telescope with an objective diameter of 60 mm. Support your answer with a calculation.

CCDs are often connected to telescopes.

Explain two reasons why this improves the ability of astronomers to observe dim stars.

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.

U Cephei is an eclipsing binary system consisting of two stars that orbit their common centre of mass. The primary star is class B; the secondary star is class G.

Figure 1 shows the variation of apparent magnitude of U Cephei with time as observed from Earth.

Explain the shape of the graph in Figure 1.

A particular spectral line has a wavelength of 486.136 nm when measured from a source in the laboratory. This line is also present in the absorption spectrum of the primary star of U Cephei. When observed from Earth, the wavelength of the primary star’s absorption line varies as shown in Table 1.

State why the average of the values in Table 1 is different from the laboratory value.

Show that the orbital speed of the primary star is about 250 km s⁻¹.

Calculate the orbital radius of the primary star.

Which absorption lines would be most prominent in the spectrum of the primary star? Tick () one box.

A different eclipsing binary star system is thought to consist of a white dwarf star and a neutron star.

Discuss how astronomers could confirm this.

C 273 was the first quasar to be discovered. IC 1101 is one of the largest galaxies known. Table 2 shows some information about these objects.

State the property of the quasar that led to its discovery.

Show that the absolute magnitude X of quasar 3 C 273 is about −27

Assume that the quasar and the galaxy are both viewed from the same distance.

Explain which would be the brighter object.

The black hole at the centre of IC 1101 has a mass of 7.1 × 10¹¹ M_S

Calculate the average density within the event horizon of the black hole.

Which graph shows the light curve for a typical type 1 a supernova?

Tick () one box.

The Andromeda galaxy is approximately 7.7 × 10⁵ pc from Earth.

Deduce whether a type 1 a supernova which occurred in Andromeda can be observed from Earth with the naked eye.

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 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.