p2_paralax.tex

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\documentclass
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{tufte-handout}

\usepackage{amsmath}

\usepackage{booktabs}
\usepackage{graphicx}
\usepackage{kmath,kerkis} % The order of the packages matters; kmath changes the default text font
\usepackage[T1]{fontenc}

\usepackage{enumitem}


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\begin{document}
\begin{fullwidth}
    \mbox{\LARGE PreCalculus BC: Project Two - \today }\hfill
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\section*{Introduction}

In the project, we will be investigating the parallax effect. Parallax is a
displacement or difference in the apparent position of an object viewed along
two different lines of sight, and is measured by the angle or semi-angle of
inclination between those two lines. (src: wikipedia)

Parallax can be used to approximate the distance to objects that are far away,
such as stars. Alpha Centauri, which is the nearest star to Earth has a parallax
of 0.000211 degrees.

\section*{Places to start}

Your first task will be to research the concept of parallax. What is it? How
can it be used to find distances of far away objects? What information is needed
in the calculation? In the process of this investigation, you will learn that
most astronomical angle measurements use degrees, minutes of arc, and seconds
of arc. A portion of your report should be dedicated to explaining how these
angle measurements are used in astronomy and some historical background into
why they are used. We will often talk in class about how radians provide a better
way to measure angles. If that's the case, then why do astronomers continue
to use degrees? There are many clues as to why this is the case in history. While
I am not asking you to write a history report, I do think that addressing
the historical background of the practice of astronomy will provide your report
with a great deal of depth and meaning.

Second, you will need to describe the process of finding the distance to Alpha
Centauri using parallax. Your report will need to present the calculation and
interpret the results. You can also compare your results to the measurement
found on the Alpha Centauri wikipedia page which is 4.37 light years or 1.34
pc.

Last, your report will need to address how robust this method of finding distances
is. For example, can parallax be used to find the distance to objects that are
not far away? Is there some minimum distance that can be used? In other words,
where does this process breakdown?

\section*{Your report}

As always, your report should include an abstract, procedure, and conclusion
section. This report will be somewhat different in that there is not a specific
mathematical problem to solve. This report will read more like a research paper
whose goal is to explain the concept of parallax to the reader. Your report will
accomplish this by providing some historical background and examples related
to using parallax. Your report should also investigate advantages and disadvantages
to this method of measuring distances.

To help you with the abstract and conclusion, please consider the following.
The abstract should be a short introduction to the problem of approximating distances
we cannot directly measure such as the distance to nearby stars. The conclusion
will contain a summary of the method of parallax and will highlight the advantages
and disadvantages of the method.

You have two main areas of focus. The first is developing your ability to explain
concepts in a clear and meanginful way. The second is to use SageMathCloud to
draw illustrations.

During the next few weeks, we will talk about how to draw illustrations
using SageMathCloud. Your report will need to make use of these illustrations
to explain how parallax works to measure distances.

\end{document}