# Question 1 (_8 marks_) This question relates specifically to the following module learning outcomes: KU1, CS1–CS3, KS2 and PPS1. - a.As in Task 2 of [Exercise 1.3](https://learn2.open.ac.uk/mod/oucontent/olink.php?id=2158710&targetdoc=Topic+2+Part+1+The+spectral+continuum&targetptr=1.2.3)  (Section 1.2.3), select spectrum F0 from the drop-down list at the top of Figure 1.8, and estimate its temperature by fitting an appropriate Planck curve to it. Include the following in your TMA answer. - i.A screenshot, with a caption, showing the interactive plot with your best-fit Planck curve overlaid on the stellar spectrum. - ii.The temperature of the Planck curve you have shown in part i., with your estimate of the uncertainty in the temperature of the best fit. - iii.A brief discussion, in a couple of sentences, of any difference between the peak wavelength of the stellar spectrum and the peak wavelength of the Planck curve you have shown in part i., as measured by holding your cursor over the lines on the interactive plot. Comment also on how well the Planck curve fits the stellar spectrum. (**4 marks**) - b.As in [Exercise 2.1](https://learn2.open.ac.uk/mod/oucontent/olink.php?id=2158710&targetdoc=Topic+2+Part+2+Spectral+lines&targetptr=2.2.3) (Section 2.2.3), select the spectrum for Star 6 from the buttons above Figure 2.9, and attempt to classify it as B, A, G, K or M. Include the following in your TMA answer. - i.A screenshot, with a caption, showing the plot of the star’s Hα line with your estimate of its equivalent width. - ii.Your proposed classification of the star as B, A, G, K or M, with some justification (_one or two sentences_) based on its spectral features. (**4 marks**) # Question 2 (_24 marks_) This question relates specifically to the following module learning outcomes: KU1, CS1–CS3 and PPS1. In the activity for Topic 2 you estimated several properties of a binary system from observational data, and used these – along with other observational results – to determine further properties for the system. For this question you will attempt similar tasks for three other stars. Show all stages of your working when answering the below. Even if you cannot obtain a final answer, you should receive marks for correct intermediate steps or use of appropriate methods. You may need to draw on your knowledge of Topic 1 as well as Topic 2 for some parts of the question. - a.A double-lined spectroscopic binary system composed of stars A and B has a measured orbital period of 13.987 days, and radial velocity amplitudes of 175 km s−1 (star A) and 223 km s−1 (star B). Showing all your working, calculate the minimum masses of the two stars, in units of solar masses. Briefly explain why their true masses might be higher than the values you calculated. (**12 marks**) - b.A Cepheid variable star has a measured pulsation period of 12.3 days, and its continuum spectrum peaks at 511 nm (to 3 s.f.). Showing all your working, calculate its radius, in units of solar radii. You should assume that the Sun’s absolute magnitude is V, and K. Based on your findings, explain in a couple of sentences whether or not this is a main sequence star.