Aldebaran is a red giant star in the constellation of Taurus.

(i) Describe the differences between a constellation and a stellar cluster.

(ii) Define the luminosity of a star.

(iii) The apparent brightness of Aldebaran is 3.3 ×10^–8 W m^–2 and the luminosity of the Sun is 3.9 ×10²⁶ W. The luminosity of Aldebaran is 370 times that of the Sun. Show that Aldebaran is at a distance of 19 pc from Earth. (1 pc=3.1 × 10¹⁶ m)

Distances to galaxies may be determined by using Cepheid variable stars.

By considering the nature and properties of Cepheid variable stars, explain how such stars are used to determine galactic distances.

(i) a constellation is a collection of stars that form a (recognizable) pattern (as viewed from Earth);
the distances between the stars may be very large;
a stellar cluster is a group of stars held together by (mutual) gravitational attraction/gravity/are physically relatively close;
there can be many thousands of stars in the cluster;
all stars in the cluster were created about the same time;

(ii) the (total) power radiated/emitted/produced (by the star);

(iii) luminosity of Aldebaran = 370×3.9×10²⁶=1.44×10²⁹ W;
\( = \sqrt {\frac{{1.44 \times {{10}^{29}}}}{{4\pi  \times 3.3 \times {{10}^{ - 8}}}}}  = 5.9 \times {10^{17}}\);
\( = \frac{{5.9 \times {{10}^{17}}}}{{3.1 \times {{10}^{16}}}} = 19{\rm{pc}}\);

the (outer layers of the star) undergo a (periodic) expansion and contraction;
which produces a (periodic) variation in its luminosity/apparent brightness;
the (average) luminosity depends on the period of variation;
by measuring the period, the luminosity can be found;
by then measuring its apparent brightness, its distance from Earth can be found;