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Date May 2015 Marks available 8 Reference code 15M.3.SL.TZ1.15
Level Standard level Paper Paper 3 Time zone Time zone 1
Command term Calculate, Determine, and Outline Question number 15 Adapted from N/A

Question

This question is about a particular star called Barnard’s star.

The peak wavelength in the spectrum of Barnard’s star is 940 nm. The following data are available.

\[\frac{{{\text{apparent brightness of Barnard's star}}}}{{{\text{apparent brightness of the Sun}}}} = 2.5 \times {10^{ - 14}}\]

\[\frac{{{\text{luminosity of Barnard's star}}}}{{{\text{luminosity of the Sun}}}} = 3.8 \times {10^{ - 3}}\]

(i) Show that the surface temperature of Barnard’s star is about 3000 K.

(ii) Suggest why Barnard’s star is not likely to be either a white dwarf or a red giant.

[4]
a.

(i) Determine, in astronomical units (AU), the distance between Earth and Barnard’s star.

(ii) Calculate the parallax angle for Barnard’s star as observed from Earth.

(iii) Outline how the parallax angle is measured.

[8]
b.

Markscheme

(i) \(T = \frac{{0.0029}}{\lambda }\);
3080/3090 (K); (more than 1 SD must be shown)

(ii) temperature too low for white dwarf;
not luminous enough for red giant;

a.

(i) \(L = 4\pi {d^2}b\);
\(\frac{{{d_B}}}{{{d_S}}}\left( { = \sqrt {\frac{{{L_B}}}{{{L_S}}}\frac{{{b_S}}}{{{b_B}}}} } \right) = \sqrt {\frac{{3.8 \times {{10}^{ - 3}}}}{{2.5 \times {{10}^{ - 14}}}}} \);
3.9×105 AU;

(ii) conversion of AU to 1.89 pc;
0.53 (arc-seconds);

(iii) measure position of star;
with respect to fixed background;
with six months between readings;
parallax angle is half the total angle / OWTTE;
May be shown in a diagram. 
b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Option D: Astrophysics » Option D: Astrophysics (Core topics) » D.1 – Stellar quantities
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