1. Planning: Well before your scheduled observing run, you must discuss with me or Paul Kerry (D16): which objects to observe, what time of night to observe, what filters you require, what sequence of exposures you require, etc. You will need to include a section on your planning in the final report.
   
   
2. Observing: Your observing sessions will be supervised by Paul Kerry and must be completed in a specified period: Monday, 14 October - Friday, 13 December 2013 (weeks 3-11), although please note that observing is not usually possible over weekends and there may be short periods when Paul Kerry is unavailable.
   
   Sign-up sheets will be posted on the Astronomy Noticeboard outside the Astronomy Lab (E36), along with full instructions on how to contact Paul Kerry on the night. Although you should be able to complete all your observations in a single session, to allow for the vagaries of British weather we expect you to sign up for at least two evenings per week until you have successfully completed your observing. If you cannot do this, you must discuss the problem with me or Paul Kerry before the start of the designated observing period, or as soon as the problem (e.g. illness) becomes apparent.
   
   Attendance at the observing is compulsory - you will not receive any marks for the project if you fail to show up or, if the weather is bad for part of the specified observing period, you have not made every effort to sign up for other time slots. Note that, unless previously agreed with me or Paul Kerry, if you are unable to attend a successful observing session with the other members of your group, it will not be possible for you to observe at a later date on your own. Note also that no resit of the observing project is possible, so missing it will make it much more difficult to pass the module.
   
   We strongly advise signing up for observing as soon as possible: students who fail this module tend to be those who leave signing up until the last minute and then suffer from poor weather at the end of the observing period. This is no excuse, as there are usually clear periods at the start of the observing period which no students sign up for. Only if the entire period is unusable, or if you have genuinely serious reasons as to why you could not do the observations (which in most cases must be supported by documentary evidence), will this component not count towards the final mark.
   
   
3. Data reduction and report: After you have obtained your observations, you will need to contact Paul Kerry to help you reduce and analyse your data using the computers and software available in the Astronomy Lab. Note that this element of the project, and the subsequent write-up, must be your own work - do not work in your observing groups.
   
   Your write-up must follow the same style as for a formal laboratory report. There must be sections describing the planning stage, the observations (a description of the equipment used, the observing conditions and the data that was taken), the data reduction and the data analysis. You will be penalised if you omit an analysis of the errors, and if you fail to compare your results with literature values. Please submit your reports to the departmental office by the deadline: Thursday, 19 December 2013. Note that this is the final week of term, and has been set to make the observing window as long as possible. However, you will undoubtedly have other pieces of work to hand in around this time, so it is in your interests to complete your observing and hand in your report as early as possible in the semester.

You are free to observe any object you wish. However, it is important to note the following limitations.

• You will only be able to use the imager, not the spectrograph. Hence, you will only be able to measure the brightness and colours of objects, and how they vary with time. The CCD camera on the 16-inch telescope has UBVRI filters and a field of view of approximately 18' x 12'.
  
  
• You will not be able to observe for more than a single session of about 4 hours. Hence, you will not be able to monitor the variability of an object with a period substantially longer than this, unless you are attempting to observe a specific event (e.g. the transit of an extrasolar planet).
  
  
• It is only a 16-inch telescope, mounted in the centre of a large city. Hence, you will not be able to observe particularly faint objects - it is recommended that you do not attempt to observe objects much fainter than about 15th magnitude.
  
  
• It is important that you can, in principle, make some kind of simple measurement from your data, i.e. taking pretty pictures of a galaxy just for the sake of it is not acceptable, but measuring the H-R diagram of an open cluster to determine the turn-off position is acceptable.
  
  

Some examples of the data obtained for previous projects are given here. Before you email me with your final choice of project, it is imperative that you come to see me to discuss your ideas so that I can confirm with you that the project is feasible. Past experience suggests that the best projects tend to be one of the following, although we are always keen for students to show initiative and come up with their own ideas for projects:

• Hertzsprung-Russell (HR) diagram of an open cluster. The aim here is to measure the distance and age of an open cluster. A list of open clusters is available here.
  
  Make sure that you pick a cluster that is visible from Sheffield at the start of the night. You can do this using The Sky in the astro lab, Stellarium on your own PC, or the on-line ING Object Visibility page (where you must enter the longitude and latitude of Sheffield in the following format: 358 30 51 53 22 50 185).
  
  The cluster you select must also be small enough so that the majority of the cluster fits within the 18' x 12' field of view of the CCD, i.e. don't select one much larger than 20' in diameter. However, don't pick one that is too compact either, as the individual stars in the cluster will be difficult to resolve. The cluster should also have a reasonably large number of stars (definitely greater than 50; greater than 100 would be best). Finally, the cluster should not be too distant or reddened and hence faint, and must be of sufficient age to show a relatively clear main-sequence turn off. The latter two items can be checked by inspecting existing HR diagrams of the cluster using WEBDA (simply enter the name of your chosen cluster in the Display the Page of the Cluster box).
  
  You can download isochrones computed by the University of Padova from here. To give you a good first guess at which isochrone is likely to fit best, go to the WEBDA page for your cluster and click on "General menu for Isochrone plots (basic)" - it is recommended you choose Padova isochrones with Solar metallicity (Z=0.019). You can plot an HR diagram for your cluster on this page, and then overplot the best-fit isochrone.
  
  When you construct an observed HR diagram, you must correct for both atmospheric extinction and interstellar extinction. The atmospheric extinction correction can be made by assuming standard values for the extinction coefficient, as given in table 2, and then transforming all of your measured magnitudes to above-atmosphere values. Be careful, however, as it is possible that you will have already corrected for atmospheric extinction if you used a photometric zero point determined from one of the cluster stars. To correct for interstellar extinction, you must use the formula (B-V)₀ = (B-V) - E(B-V), where (B-V)₀ is the intrinsic colour index of the cluster (i.e. corrected for interstellar extinction), (B-V) is your observed (i.e. uncorrected) colour index, and E(B-V) is the colour excess (or reddening) in magnitudes. Hence you will find that you will have to shift your data in the x-direction on the HR diagram in order to align it with the isochrone, and the value you shift it by is equal to the reddening, E(B-V). Once you have determined E(B-V) in this way (and checked it against the value given by WEBDA), you will then have to correct your V-band apparent magnitudes using the equation: V₀ = V - A_V, where V₀ is the intrinsic V-band apparent magnitude of the cluster (i.e. corrected for interstellar extinction), V is your observed (i.e. uncorrected) V-band apparent magnitude, and A_V is the visual extinction in magnitudes. The ratio A_V / E(B-V) is usually denoted by the symbol R_V and a generic value for our galaxy covering a large wavelength range is R_V = 3.2±0.2. Hence the formula to correct your V-band apparent magnitudes becomes: V₀ = V - [R_V x E(B-V)] = V - [(3.2±0.2) x E(B-V)]. Once you have corrected the y-axis of your data in this way, the difference between the isochrone and your data in the y-direction on the HR diagram will give you the distance modulus of the cluster.
  
  To determine the age of your cluster, you will have to download a series of isochrones of different ages, using the WEBDA value for the age as a guide. The isochrone which best matches the main-sequence turn-off point gives the age of the cluster. It is likely you will find that the determination of the interstellar extinction, distance and age of the cluster will be an iterative process.
  
  
• Light curve of a delta Scuti star. The aim here is to measure the period and hence distance of a delta Scuti star. A list of delta Scuti variables is available here.
  
  Make sure that you pick a delta Scuti star that is visible for at least one orbital period around the start of the night - see the description of how to do this in the HR-diagram project above.
  
  The delta Scuti star you select must have a magnitude of less than V~15, and the brighter the better. The orbital period must be less than ~4 hours, i.e. ~0.17 days. The amplitude of the pulsation must be as great as possible. The lower limit is dependent on the brightness of the target you select, but I would avoid objects with pulsation amplitudes of less than, say, 20%, i.e. ~0.2 magnitudes.
  
  Once you have obtained your light curve, you must attempt to estimate the period of the pulsation in days. The simplest way of doing this would be, of course, to measure the separation between two repeated features in your light curve, such as two consecutive peaks or troughs. However, this would effectively ignore the rest of the data you have obtained, and so it is hoped that you will employ a more sophisticated approach in the period determination. You should then use your measured period to estimate the absolute V-band magnitude using the period-luminosity relations for delta Scuti stars given by Petersen and Hog (1998) and/or McNamara, Clementini and Marconi (2007). You can then use this absolute V-band magnitude in conjunction with your measured (mean) apparent V-band magnitude (so make sure that you observe with the V filter!) to derive the distance to the star in parsecs via the distance modulus equation.
  
  
• Light curve of an eclipsing cataclysmic variable star. The aim here is to use the eclipse width to measure the radius of the accretion disc. A list of cataclysmic variables (CVs) is available here.
  
  Make sure that you pick a CV that is visible for at least one orbital period around the start of the night - see the description of how to do this in the HR project above.
  
  The CV you select must be eclipsing, i.e. it must have an EB entry in the table of 1 or 2. The quiescent, out-of-eclipse brightness, indicated by the Mag1 entry, must be less than V~15, and the brighter the better. The orbital period must be less than ~4 hours, i.e. an Orb. Per. value of less than ~0.17 days.
  
  Once you have obtained your light curve, you should measure the width of the eclipse in units of days. Dividing this by the orbital period in days will convert the eclipse width to phase units, i.e. the fraction of the orbit spent in eclipse, and dividing this by two will give the half-width of the eclipse. You should then use your eclipse half-width in phase units in conjunction with "Method 1" outlined by Harrop-Allin and Warner (1996) to plot the disc radius as a function of inclination and mass ratio. You can then use this plot to select the most likely range of values of the disc radius.
  
  
• Light curve of an asteroid. The aim here is to measure the rotation period of an asteroid and determine if the asteroid is likely to be a rubble pile or a solid body. A list of minor planet light curve parameters is given here, and a version of this list ordered by period is given here.
  
  Using the above list, you should select asteroids which have rotation periods of less than ~4 hours. The amplitude of the variability, given by the Variation column, must be as great as possible. The lower limit is dependent on the brightness of the target you select, but I would avoid objects with amplitudes of less than, say, 20%, i.e. ~0.2 magnitudes.
  
  To determine the magnitude, right ascension and declination of the targets, which are all time dependent, you need to enter the names of the asteroids you have selected in the large box at the centre of the Minor Planet and Comet Ephemeris Service, and then click on the Get ephemerides/HTML page button. The asteroid you select must have a magnitude of less than V~15, and the brighter the better. Make sure that you pick an asteroid that is visible for at least one orbital period around the start of the night - see the description of how to do this in the HR project above.
  
  Once you have obtained your light curve, you should attempt to measure its rotation rate. There are various ways in which this can be done: visual inspection of your light curve; folding your data on trial periods; Fourier analysis, etc. Once you have determined the rotation rate, you should compare this to the maximum rate assuming it is a rubble pile. A basic discussion of this topic and links to the literature can be found here. Note that the correct physical description of the situation is that gravity supplies the centripetal force required to keep the rubble in circular motion. As the rotation rate increases, the required centripetal force increases until a point comes when gravity is no longer able to provide it, and the object flies apart. You should not have to mention the term "centrifugal force" in your explanation, which is an imaginary force.