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    The data for the star Eta Aquilae A are given in the table. | | Value |

    Question
    HLPaper 3

    The data for the star Eta Aquilae A are given in the table. | | Value | | --- | --- | | Mean luminosity | 2630 L_⊙ | | Mass | 5.70 M_⊙ | | Parallax angle | 2.36 × 10^-3 arcsec | | Apparent brightness | 7.20 × 10^-10 Wm^-2 | L_⊙ is the luminosity of the Sun and M_⊙ is the mass of the Sun.

    1.

    Show by calculation that Eta Aquilae A is not on the main sequence.

    [2]
    Verified
    Solution

    « LL⊙=M3.5M⊙3.5=5.703.5=»442✓\frac{L}{L_\odot}=\frac{M^{3.5}}{M_\odot^{3.5}}=5.70^{3.5}=» 442 \checkmarkL⊙​L​=M⊙3.5​M3.5​=5.703.5=»442✓ the luminosity of Eta (2630L⊙)(2630 L_\odot)(2630L⊙​) is very different «so it is not main sequence» \checkmark

    2.

    Estimate, in pc, the distance to Eta Aquilae A using the parallax angle in the table.

    [1]
    Verified
    Solution

    i) d«=12.36×10−3»=424d «=\frac{1}{2.36 \times 10^{-3}} »=424d«=2.36×10−31​»=424 «pc » \checkmark

    ii) Use of d=L4πb✓d=\sqrt{\frac{L}{4\pi b}} \checkmarkd=4πbL​​✓ =2630×3.83×10264π×7.20×10−10✓=\sqrt{\frac{2630 \times 3.83 \times 10^{26}}{4\pi \times 7.20 \times 10^{-10}}} \checkmark=4π×7.20×10−102630×3.83×1026​​✓ «=1.055×10193.26×9.46×1015»=342«pc»✓«=\frac{1.055 \times 10^{19}}{3.26 \times 9.46 \times 10^{15}} »=342 «pc» \checkmark«=3.26×9.46×10151.055×1019​»=342«pc»✓

    3.

    Estimate, in pc, the distance to Eta Aquilae A using the luminosity in the table, given that L_⊙ = 3.83 × 10^26 W.

    [2]
    Verified
    Solution

    i) d«=12.36×10−3»=424d «=\frac{1}{2.36 \times 10^{-3}} »=424d«=2.36×10−31​»=424 «pc » \checkmark

    ii) Use of d=L4πb✓d=\sqrt{\frac{L}{4\pi b}} \checkmarkd=4πbL​​✓ =2630×3.83×10264π×7.20×10−10✓=\sqrt{\frac{2630 \times 3.83 \times 10^{26}}{4\pi \times 7.20 \times 10^{-10}}} \checkmark=4π×7.20×10−102630×3.83×1026​​✓ «=1.055×10193.26×9.46×1015»=342«pc»✓«=\frac{1.055 \times 10^{19}}{3.26 \times 9.46 \times 10^{15}} »=342 «pc» \checkmark«=3.26×9.46×10151.055×1019​»=342«pc»✓

    4.

    Suggest why your answers to (i) and (b)(ii) are different.

    [2]
    Verified
    Solution

    parallax angle in milliarc seconds/very small/at the limits of measurement \checkmark uncertainties/error in measuring LLL or bbb or θ✓\theta \checkmarkθ✓ values same order of magnitude, so not significantly different \checkmark

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    5.

    Eta Aquilae A is a Cepheid variable. Explain why the brightness of Eta Aquilae A varies.

    [2]
    Verified
    Solution

    reference to change in size \checkmark reference to change in temperature \checkmark reference to periodicity of the process \checkmark reference to transparency / opaqueness \checkmark

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    6.

    Eta Aquilae A was on the main sequence before it became a variable star. Compare, without calculation, the time Eta Aquilae A spent on the main sequence to the total time the Sun is likely to spend on the main sequence.

    [2]
    Verified
    Solution

    shorter time \checkmark star more massive and mass related to luminosity OR star more massive and mass related to time in main sequence OR position on HR diagram to the left and above shows that will reach red giant region sooner \checkmark

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