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Date November 2011 Marks available 6 Reference code 11N.3.SL.TZ0.11
Level Standard level Paper Paper 3 Time zone Time zone 0
Command term Show Question number 11 Adapted from N/A

Question

This question is about stellar distances and stellar properties.

On the grid of the Hertzsprung–Russell (HR) diagram shown, draw a line to represent the approximate position of the main sequence.

[2]
a.

Barnard’s star is a main sequence star that is 1.8 pc from Earth.

(i) Define the parsec.

(ii) Calculate the parallax angle of Barnard’s star as measured from Earth.

[2]
b.

Outline, using your answer to (b)(ii) and a labelled diagram, how the distance of Barnard’s star from Earth is measured.

[3]
c.

The apparent brightness of Barnard’s star is 3.6×10–12Wm–2 and its surface temperature is 3800 K.

Given that 1 pc=3.1×1016m, show for Barnard’s star

(i) that its luminosity is of the order of 1023W.

(ii) that its surface area is of the order of 1016m2.

[6]
d.

Markscheme

any suitable line from anywhere in top left-hand quadrant; (accept a straight line)
to bottom right-hand quadrant;
The shaded areas are the limits within which the line must be drawn.

a.

(i) distance at which 1 AU subtends an angle of 1 arcsec / distance at which the angle subtended by the radius of Earth’s orbit is 1 arcsec;

(ii) \(p = \left( {\frac{1}{d} = } \right)0.56{\mathop{\rm arcsec}\nolimits} \);

b.

 

Labelled diagram should relate to the following points:
measure against the fixed stars the angle Barnard’s star subtends at Earth in June and again in December;
difference between the two angles is twice the parallax angle;
orbital radius of Earth about Sun is 1 AU so distance to star is computed from \(d = \frac{1}{p}\);

c.

(i) L=4πbd2;
=4×3.14×3.6×10-12×[1.8×3.1]2×1032;
=1.4×1023W;
≈1023W

(ii) \(A = \frac{L}{{\sigma {T^4}}}\);
\( = \frac{{1.4 \times {{10}^{23}}}}{{5.67 \times {{10}^{ - 8}} \times {{3.8}^4} \times {{10}^{12}}}}\); (allow ECF from (d)(i))
=1.184×1016m\(^2\);
≈1016m2

d.

Examiners report

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

Syllabus sections

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