“Use and Applicationsof the Astronomical Telescope”

Guidelines for Writing theReport

Report

In this report you will summarize the results from “The Astronomical Telescope I” and “The Astronomical Telescope II” experiments. You will synthesize what you learn regarding the two main properties of a telescope. You will apply what you learned to elaborate and answer some questions regarding the use and applications of telescopes.

In “The Astronomical Telescope I” experiment you had the chance to learnthe concept of angular resolution, how it is calculated and how the aperture(diameter) of the telescope is related to the resolution. You learned how this property allows you to distinguish fine details in an astronomical object or to resolve binary stars. During the experiment you were able to learn how small the size of an arcsecond is. All of this helps you to appreciate the technical challenges of resolving fine details of celestial bodies that we observe.

In “The Astronomical Telescope II”, you learned about the light gathering power of a telescope and how that is related to the aperture of a telescope. You also familiarize yourself with the magnitude system, which is how astronomers quantify the brightness of stars and other celestial objects. You also learned how the aperture (diameter) of a telescope relates to the brightness of the stars that can be seen and how that determines the faintest stars you can see with it.

Your report should be understandable to a reader unfamiliar with the details of the experiments. The report should cover the purpose of the experiment, the methods used to gather your data, the physical principles your data is meant to demonstrate, the results derived from your data, and conclusions drawn from your results, including reading errors and personal effect when taking readings. Finally it will include applications of the two main properties of telescopes. Be thorough but concise – explain everything that is required straightforwardly and without embellishments or irrelevant details.

Regarding errors, do not include mistakes or vague statements. What it is relevant in an experiment are reading errors and how those will influence the final values. Errors may be caused by the instruments used to take the measurements (rulers, meter stick), or introduced by the observer deciding when the“canals”(lines) or “stars” merge or when the each of the six artificial stars are no longer visible to the observer. Be specific and mention numbers. How you can trust in the final values that you give? Do not be vague and include statement such as” I was careful and I trust my values” or “my values are precise” or “I estimate that my errors are small”. These statements have no value regarding errors and may lower your grade.

Another important aspect of the report is that some questions and topicsincluded in the text of the write up or being suggested mustbe integrated in the text of the report. Do not simply list the answers to these questions or the topics. “Yes” or “no” answers are not valid unless you include an explanation of your reasoning.

You are asked to solve several problems at the end of the write up of the experiment Telescopes II, on pages 4.8 (problems 4 to 8). Answer those in a separate section. And make sure you include the formulas, all the steps followed and intermediate calculations. If you cannot show how you got your final values, you may not receive much credit.

The report should contain all of the following sections:

  • Introduction
  • Purpose of the experiment
  • Discussion of the physical principles and any equations used
  • Short description of how the data were obtained (i.e. the procedure)
  • Data tables, graphs, and calculations
  • Discussion, including comparison of results with excepted values, sources of error, and any other required analysis
  • Conclusions
  • Original (signed) data sheets attached at the end

Guidelines for Each Section

Introduction

The telescope is the main tool used by astronomers. Specify that this report summarizethe twomain properties of the telescope.Also specify what you learned about the measurement system used by astronomers to measure the brightness, the magnitude and angular size of an object. Astronomers seek ever-larger telescopes because a telescope’s diameter is the main parameter that determine its ability to separate closely-space celestial bodies or details and make extremely faint objects visible. To explorehow these relationships work, you used a telescope with an adjustable aperture to look at artificial stars, simulating the detrimental effects of smaller aperturesin the resolution and light-collecting power.

Purpose of the Experiment

For this part, explain that through the two experimentsyou exploredthe two basic properties of the telescope as a tool for collecting light from celestial bodies. Explainhow the aperture size of the telescope relates toits abilities to resolve objects of small angular size and detect objects much fainter than the human eye can see. Specify that you used anempirical model given by the Dawes’Limit equation to predict the minimum aperture necessary to resolve the two objects in the target. Specify that you used experimental values of the resolving power for those targetsto test the validity of values predicted by the Dawes formula. State how you used of the magnitude system to quantify brightness, and the Dawes’ Limit to quantify a telescope’s resolving power.

Discussion of Physical Principles and Equations

Explain the concept of angular size of an object. Include the equation to calculate the angular size of an object usingits physical size and the distance to the object. Also describe the Dawes’Limit equation and how it empirically relates angular resolution to the size of the telescope needed to reach that resolution.

Discuss the magnitude system, especially how brightness ratios and magnitude differences are related. Describe how a telescope’s light collecting area relates the range of magnitudes of stars it can detect.

Methods

Very briefly describe how you carried out your experiment here. In particular, explain how you manipulated the aperture size of your telescope with an iris diaphragm to find the apertures at which the simulated stars and “canals” became unresolved and how you measured the aperture sizes. How did you use an empiricalmodel that predicted the minimum aperture and how did you compare your experimental results with the values given by the Dawes’ Limit equation?

Describe how you adjusted and measured the aperture of your telescope to find and to plot the relationship between the telescope’s aperture size and faintest magnitude (faintest) star visible through it. Briefly include how the simulated target stars were calibrated on the magnitude scale.

Data Tables and Graphs

In this section, type all data tables neatly, with all values reported in the correct units to the correct number of significant figures. To figure out the number of significant figures, pay attention to the significant figures of your values of the aperture read using the ruler. Should you consider the values (and the reading uncertainties) of the distance measured with the meter stick? Which one of the uncertainties is more relevant and why?

If you do the calculations with a calculator, you may get a lot of figures. Some of those figures are not valid. It is you who must determine how many of those figures are significant and omit the rest.

Include 2 tables of your trials measuring the diameter of the telescope aperture for “canal” and the “double star”. One table for the canals and another for the double star, with the averages of your data at the bottom.

Your calculations of the results for the angular size of your observing targets and the aperture required to resolve them according to Dawes’ Limit must be included in the table next to the average of the two experimental values for an easy comparison.

Also include a third table with the magnitudes and the aperture sizes at which stars of each magnitude disappear. The aperture sizes must be listed with the correct units (your choice of centimeters or millimeters).

Plot the above values here in this section. Be neat. You can do the plot by hand, but use a ruler to draweach axis. Include a regularly-spaced scale for both axes,with enough divisions so it is easy to plot and read the values plotted.

Remember that you will be asked to compare your plot from the Astronomical Telescope II to the figure on page 4.2 of that experiment’s introduction – make sure that magnitude and aperture size are on the appropriate axes (but do not report aperture size in inches – use either centimeters or millimeters).

Important: at the end of the report, attach all original, signed data sheets and include all plots!

Discussion

Here you will discuss your results. For the Astronomical Telescope I data, include percent error calculations comparing the averages of your measurements of the aperture of the telescope necessary to resolve the separation of the two lines and the two dots to the values calculated with the Dawes’ Limit formula. Comment on the size of your percent errors and possible sources of uncertainty. Do not speculate on possible mistakes you might have made, and remember that rounding to the correct number of significant figures is not a source of error.

How well do your results agree with the empirical Dawes’formula? Include here the answers to any short-answer questions directly related to your experimental results in the “your report” sections of the lab manual or on your data worksheets, unless otherwise instructed. Include the answers to questions as integral parts of the text, not as isolated or numbered answers to prompts. Also paraphrase the questions in the text as context for your answers—do not force a reader to search for the question in the lab manual!

Conclusions

Briefly summarize your results. Include here how you should address the practical applications of your methods.

Applications of the properties of telescopes

Include in thissection detailed solutions to the 3 problems included in separate pages at the end of these instructions. These problems are an application of some of the concepts learned in these two experiments, and allow you to answer some interesting questions.