Friday, May 26, 2017

Public Service Announcement

I am sad to say that it's been many a day since I have written a post here.  But now that my semester is over, I have finally gotten back to writing.  Some day, I'll have better time management skills and be able to write in this blog as often as I want.  But until that day comes, most of my writing will be done during seasons when class is not in session.

On another note, I have an important announcement.

From now on, I will continue writing my blog on my own website: http://mwilson1.github.io
So, to all of my fans across the world, you'll have to go there from now on to keep up with all of my astronomy thoughts.  See ya there!

Sunday, October 16, 2016

NSF: A proposition for you.

Just like the personal statement, I am sharing my research proposal for the sake of the many undergrads that have been asking me for advice and essays as they prepare to apply for the NSF Graduate Research Fellowship.

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For exoplanets with a radius 1 to 5 times the radius of Earth, the physical properties evaluated for most of these planets either have high uncertainties or cannot be ascertained at all.  This problem is exacerbated by the faintness of the host star, which makes detailed follow up analysis difficult and expensive.  However, the rate at which Earth-like exoplanets around bright stars are detected and characterized with satisfactory precision can be substantially increased with an observatory that specializes in searching for such exoplanets.  This is why I propose to observe and analyze bright stars via an observatory recently constructed specifically for finding and characterizing rocky planets around the nearest stars.
Background
Within the past two decades, the search for exoplanets and the characterization of their physical properties have given planetary astronomers a vast amount of new knowledge.  The Kepler Mission is responsible for finding more than 900 of these exoplanets [1].  This is confirmed by radial velocity (RV) surveys, where the stellar spectra revealed Doppler shifts that are induced by a star’s companion exoplanet(s). These discoveries revealed that there are many exoplanets within the Galaxy and that they have a large range of masses and radii [2].  There are more planets with a radius less than 4 times the radius of Earth than there are planets larger than this size within the Galaxy [3].  For most of these small-radius exoplanets found by Kepler, their physical properties currently cannot be found because of their excessively faint host stars.  However, this information can be determined for small-radius exoplanets that orbit bright stars. 
Among the planets we find around bright stars via RVs, we expect that only a few of them will transit their host star, as a result of the random orientations that an exoplanet’s orbit can have on the sky.  These few transiting exoplanets are extraordinarily valuable because they offer numerous advantages to study the host star, such as revealing the mean density of the star and the orbital inclination of the exoplanet.  However, finding these valuable transiting exoplanets requires precise photometry of very bright stars.  The orbital inclination along with many other parameters derived from the photometry can be coupled with spectroscopic measurements of the star to ascertain the physical properties (such as the mass and radius) of the exoplanet [4].  For most transiting exoplanets with a radius similar to the Earth’s radius, such physical properties of the exoplanet cannot be determined with satisfactory precision.  This is usually due to the RV signals being dominated by noise from stellar jitter, which is an effect from convective cells of gas rising to the photosphere and thus jostling the surface enough for such jostling to be detected in the RV measurements.  Consequently, there is a need for an observatory that is capable of resolving this stellar jitter in order to obtain high precision RV measurements.  Fortunately, the MINiature Exoplanet Radial Velocity Array (MINERVA) can do this as well as achieve high precision photometry for Earth-like exoplanets transiting bright stars. 
Research Plan
During my graduate career, I propose to conduct a survey of bright stars with MINERVA while using the defocusing technique to obtain high precision photometry in order to characterize Earth-like exoplanets.  By observing bright stars, high precision for the RV becomes feasible to obtain from the spectra.  However, achieving high precision for the photometry of bright stars is difficult for two reasons:
1) Relative photometry must be done to achieve the required precision.  This method entails the observation of satisfactory comparison stars, i.e. stars that are not variable and are similar in brightness and color to the nearby primary target.  Unfortunately, it is typically difficult to find such comparison stars within one telescope’s field of view when the primary star is bright. 
2) Bright stars saturate quickly. 
Resolving these two issues has captivated me much more than the complexities of the RVs.  Therefore, the photometry will be the primary focus of this proposed research.  I can achieve high photometric precision by using MINERVA’s four telescopes and the defocusing technique.  I will conduct this research at Harvard University, which has access to the MINERVA telescopes located on Mt. Hopkins in Arizona.  Each telescope is a PlaneWave CDK-700 with a diameter of 0.7m, a 20.8’ x 20.8’ field of view and an Andor iKON-L camera.
The issues regarding bright star photometry will be resolved by the following methods:
1. To find bright comparison stars, I will use one MINERVA telescope to observe the primary star with the transiting exoplanet while the other three telescopes observe nearby bright comparison stars.  2. The defocusing technique will be used to avoid saturating the CCD quickly.  This method entails the dispersion of stellar photons across more CCD pixels, in comparison to a star in focus.  This allows for a significantly longer exposure time than otherwise capable with a bright star in focus.  Such an increase in the exposure time substantially reduces flat fielding errors, decreases the fractional overheads, and thus results in high precision photometry [5].
Research Outcomes
MINERVA was built to consistently achieve a photometric precision of less than 1 millimagnitude.  While observing with only one telescope, this feat has already been demonstrated [6].  I expect to achieve this precision also, while one telescope observes the primary star and the other three measure the flux of comparison stars.  Due to the volume of data—at two light curves per telescope per week, we estimate 1,248 light curves over the 3-year lifetime of the project—we require the photometry to be highly automated.
My second internship at the Harvard-Smithsonian Center for Astrophysics (CfA) has equipped me with the knowledge to perform this exoplanet research.  I have already written Python code that can perform a variety of tasks including, create schedules which can be read by the MINERVA telescopes and query SIMBAD for a list of potential comparison stars most closely matching the target stars in magnitude, color and proximity. After observations, my code performs relative photometry and produces a light curve of the primary star.
Broader Impacts
After my first REU at the CfA, I gave talks at the Adler Planetarium about my research and continued to update astronomers there via our “Astro-Hangout” YouTube videos (linked to on my blog).  During the proposed research, I will continue to give talks and teach Adler visitors how bright stars enlighten those who seek to learn more about Earth-like exoplanets.  I will also mentor younger students of underrepresented groups so that they may benefit from my resources as a Harvard graduate student, NSF GRFP Fellow and Adler volunteer astronomer.  The excellent guidance I received from the Banneker Institute (BI) at the CfA is my inspiration for becoming a graduate student mentor for the BI.  I will lead my mentees toward opportunities that can jumpstart their careers early, just as the BI mentors have been doing for minority students like myself.  This institute has proven that minority students can be just as brilliant as the stars I am proposing to observe, and I look forward to mentoring and inspiring future BI undergraduates by first earning this NSF GRFP Fellowship and enrolling in Harvard University. 
References
[1] Han, E. et al., 2014, PASP, 126, 827                   [4] Winn, J., 2010, ArXiv:1001.2010 
[2] Johnson, J. A. et al., 2010, PASP, 122, 905         [5] Southworth, J. et al., 2009, MNRAS, 396, 1023 
[3] Fressin, F. et al., 2013, ApJ, 766, 81                   [6] Swift et al., 2015, JATIS, 1, 2

Saturday, October 15, 2016

NSF: It just got personal.

  Over the past few months, many undergraduates have been asking me for my advice and essays regarding the NSF Graduate Research Fellowship that I earned as a senior undergrad.  I decided that it would be easier to simply post my essay on here so that I can direct the students here, rather than me constantly sending out emails to each student, whenever someone asks.

  I am proud of this essay primarily because the words flowed from the heart.  That is a big deal to me since I do not consider myself a great writer, and because I do not practice writing as much as I want to I often have a blank screen for the first 30 minutes when writing essays.  The flow takes time to begin.  I am also proud of this essay because I was blessed with the opportunity to actually do exactly the things I promised to do.  (As all applicants know, the NSF wants you to predict certain things about your future but will not hold you to such promises if you are award the fellowship.)  For example, I was a tutor for the Banneker Institute classes throughout the entire summer right before I started graduate classes.

  I can provide a lot of tips as to why specifically this was a winning essay but I won't go into such extensive detail on this post.  However, I will say that this essay intertwines nicely with my NSF research proposal and that is part of the reason why I won.  So read that as well (in the next post).

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    My research advisor at Harvard University once told to me, “The most important skill for an astronomer to have is computer programming.”  Now that I have two years of astronomy research experience that has obliged me to learn four programming languages, I see why my advisor, Dr. John Johnson, came to this conclusion.  My astronomy research career began during my second year of college.  My love for astronomy drew me into this career, but as I began to work on research projects I found that I have a passion for computer programming as well.  Astronomy research became even more fun once I dove into the world of computers and code.  As I completed academic and research projects using MATLAB, IDL, Python and Sherpa, I fell in love with creating anything I could imagine.  When programming, I feel like a god.  I become the Creator of my own virtual Universe.  My code obeys me.  Seeing the execution of my code and the beautiful plots that come about are what satisfy my desire for creativity and independence.  My skills with writing code does for me on a computer what my skills with a paintbrush cannot do for me on a canvas.  This virtual world has given me something that reality cannot; and that is the chance to feel omnipotent and limitless.
    
    The limits of my success in graduate school will be virtually non-existent with the help of this NSF GRFP Fellowship.  With this fellowship, I will conduct research in the Astronomy PhD program at Harvard University and utilize my newfound resources to bring astronomy closer to the masses outside of the science community.  I have already taken action to increase scientific literacy in the general public via my work at Chicago’s Adler Planetarium.  During my graduate career, I will teach the Adler visitors about the exoplanet research stated in my proposal, in which the precise spectroscopy and photometry of very bright stars with transiting exoplanets will help me find the mass and radius of the potential Earth-like exoplanets around those stars.  It will be cool to tell visitors that I am responsible for the detection and characterization of distant exoplanets that resemble Earth.  With this fellowship’s annual $12,000 allowance for tuition, I can spend less time working as a Harvard teaching fellow and more time striving to increase participation of minority students in the science community.  My ambition for increasing diversity in STEM fields is primarily inspired by my amazing experience with the Banneker Institute at the Harvard-Smithsonian Center for Astrophysics (CfA).  I am excited to explain how I have already made progress with these goals.  Seeing these goals come to fruition requires support from this fellowship and diligence towards my blog, website, elocution and activism.

    My blog uses simple terms to discuss complex topics in astrophysics research.  The purpose of this blog is to teach the intimate details that usually get overlooked when people describe the job of an astronomer.  These details include an astronomer’s knowledge of mathematics and writing code.  In my blog (http://bi-mwilson.blogspot.com), I demonstrate how my many Python scripts fit models to astrophysical data.  I even allow my readers to run my code for themselves!  I also give a simple explanation of the statistics employed by my code.  As my blog shows, I have fun explaining the variety of statistical methods that astronomers can use in their research.  This blog is currently my primary way of increasing scientific literacy across the globe.

    My website gives the world a chance to learn about the research projects I have worked on in the past.  My website (http://mwilson1.github.io) shows that one of these projects is my search for stars that have magnetic activity cycles in their coronae.  When I was an NSF REU intern at the CfA during the summer after my sophomore year, I used X-ray data gathered by the Chandra and XMM-Newton Observatories to examine flux variation over a period of ~11 years among the 10 brightest stars within the Chandra Deep Field South.  To study these stars, I learned Python and wrote scripts that performed a variety of tasks, including fit satisfactory models to the stellar spectra, calculate the flux of the star for each epoch of observations, and produce pretty light curves.  It was a challenging but rewarding experience to write all of the scripts from scratch.  Furthermore, I wrote a 16-page document reporting the background information, methodologies and results of my research.  I also presented this research as a poster talk at the winter AAS conference in 2015.  Near the end of that summer, the uncertainties in my light curves suggested that I did not have enough data—i.e. X-ray photons—to conclude whether or not I found the 5th star in our Universe that has a confirmed X-ray coronal cycle, but we did conclude that none of my stars exhibited flux variability about a factor of 10 like the Sun does over ~11 years.  Fortunately, my advisors and I will have plenty of Chandra data in 2016 to further analyze the same stars.  I am eager to see them again at the upcoming AAS conference in January of 2016 when I utilize my skills in elocution to present another engaging poster talk.

    Elocution is too powerful of an art form to neglect when seeking to capture the attention and support of a large body of people.  I first discerned the power of public speaking during my candidacy campaign and office of Student Government President at my high school.  I later found that this skill transitions nicely to my astronomy research.  I have given talks to scientists at Chicago’s Adler Planetarium, my university—Embry-Riddle Aeronautical University (ERAU)—, the CfA, the FIU McNair Research Conference and the AAS Meeting.  Throughout my experiences at conferences and colloquia, I have discerned that most scientists need to take the art of public speaking more seriously.  Seeing, in person, a younger audience’s dissatisfaction and disdain for science after listening to someone deliver a dry and excessively complex scientific presentation is the primary reason for why I am consistently earnest when I prepare a talk or give a speech.  This reason is also why I enjoy the frequent practice of describing my research to friends and colleagues.  Such practice allows me to go to the Adler Planetarium whenever I am on winter or summer break from college and, with simplicity, teach youth about astronomy and inspire their growing imaginations.  Fortunately, this GRFP Fellowship’s annual stipend will help with my costs of travel as I journey back and forth between Cambridge and Chicago every summer and winter as I currently do between Daytona Beach and Chicago.  Furthermore, with the additional time I will have to focus on increasing diversity in the astronomy community—as opposed to working more as a teaching fellow to cover tuition—I will be a graduate student mentor for future Banneker Institute (BI) undergraduates at the CfA.

    My activism will be focused on supporting the BI and mentoring its interns.  This institute seeks to increase the participation of minority groups and awareness of social justice issues in the astronomy community.   Interns will benefit from my breadth of research experiences that have given me the skills to see a variety of perspectives when approaching research questions and issues.  During my second year at ERAU, I used MATLAB and IDL to analyze Doppler shifts in the spectra of the Moon’s diffuse sodium and potassium atmosphere.  The velocity of these atoms insinuated the mechanisms (such as meteoric impact ablation) that may be the primary cause for why atoms—even from the lunar regolith—reach speeds sufficient for escaping the lunar atmosphere.   During my third year, I studied terrestrial, high-altitude Hydrogen-Alpha emission in order to ameliorate the MSIS-90 model that is used for specifying geocoronal atomic hydrogen column densities.  The summer after my third year, I used Python to analyze data and produce light curves of defocused bright stars—as described near the end of my research proposal.  My background with lunar, terrestrial, stellar and exoplanet research will help interns see various techniques astronomers can use to approach different problems.  I will also expose the interns to the work I do at the Adler Planetarium, with hopes that the impact I have made at the planetarium will inspire the BI interns to participate in public outreach as well.  This is important because as more minority students project their excellence and teach their science to the public, the social constructs that have, for so long, discouraged minorities from pursuing careers in STEM fields will be mitigated.

    Throughout my research career, I have found that my activism couples well with my elocution.  During my first research project, I tutored 5th grade students, who were predominantly African-American, at an elementary school in Daytona Beach. The 5th grade teacher frequently asked me to give the class an update on my research and show them how cool it was that organizations provided funding for me to travel across the US to give talks or observe on a telescope.  At ERAU, I am the student mentor for two freshmen and one sophomore.  Two of my mentees are women of color.  However, even if I had mentees that did not belong to an underrepresented group, I have found that merely discussing my research or giving a talk causes people to ponder the notion that people of a race or ethnicity unlike their own can be just as intelligent and beneficial to society as they are.  With this NSF Fellowship, I can reinforce this truth.  Moreover, with the support of this fellowship and my friends at ERAU, the BI, the CfA and the Adler Planetarium, my current efforts towards increasing scientific literacy, diversity in STEM fields and awareness of social justice issues will receive a great reinforcement that I will then use to inspire my mentees and young science enthusiasts around the world.   

Friday, August 5, 2016

Space Physics: Gradient-B Drift

Now that you understand why a proton or electron from the Sun that bombards the Earth's magnetic field lines undergoes cyclotron motion, let's make things slightly more complicated.  Now, the magnetic fields that we'll deal with have a gradient.  Simply put, this means that the magnetic field line is stronger on one end than on the other sections of the magnetic field line.  In mathematical terms, the magnetic field vector \( \textbf{B} \) is no longer constant with respect to position; thanks to the gradient, changes in \( \textbf{B} \) only depend on location.  (For now, this vector is only a function of position--it remains constant over time.)   Just to clarify, I'll add that the Lorentz force--discussed in the previous post--applied by the \( \textbf{B} \) field onto the particle is dependent on the direction, or angle with respect to the \( \textbf{B} \) field, of the particle's velocity, but this force is not dependent on the location of the particle while it is inside of that magnetic field as long as that magnetic field has no gradient.
Pheww!! ... tough explanation ... it can be hard sometimes to explain the concept of vectors in contrast to vectors that are functions of position to people that might not utilize vector mathematics in their everyday lives.


The simulation I am about to show has a proton traveling in the presence of a magnetic field with a gradient.  For the sake of laziness, I'll just call this magnetic field a Gradient-B field ( \( \nabla B \) ) from hereon.  It is important to note that because we are now dealing with \( \nabla B \) field--a magnetic field where its strength changes depending on your location within the field--the Lorentz force applied to the proton will change as the proton travels from one location to another within this field.  When the proton enters a \( \nabla B \) field, it drifts in a direction other than the direction of the magnetic field vector \( \textbf{B} \).  In my previous post, the particle only drifted parallel to \( \textbf{B} \) but as it drifted in that direction it also traveled in a circle--hence cyclotron motion.

The average velocity due to the \( \nabla B \) drift is described as
\[ v_a  =  \frac{\mu}{q} \frac{ \textbf{B}\times \nabla_{\perp}B }{B^2}  \]
where mu \(\mu\) is
\[ \mu = \frac{m v_{\perp}^2}{2B} \]
and \( \nabla_{\perp}B \) is the strength of the \( \nabla B \)  field in the direction perpendicular to the \( \textbf{B} \) field.


  
Top View
Star is the beginning and circle is end of simulation.
 For this simulation, I used the following equation to describe the motion of a proton:
\begin{equation} \textbf{r}(t)-\textbf{r}(0) = \frac{v_{\perp}}{\Omega_c}[1 - cos(\Omega_c t)]\hat{\textbf{e}}_x + \frac{v_{\perp}}{\Omega_c}sin(\Omega_c t)\hat{\textbf{e}}_y + v_{\|}t\hat{\textbf{e}}_z + \frac{\mu}{q} \frac{ \textbf{B}\times \nabla_{\perp}B }{B^2}t
\end{equation}
however!! it is important to know that the initial velocity I set for my proton was \( v_{\perp} = \textbf{v}(0) = 4000\) \( \hat{\textbf{e}}_y \) m/s which means that the velocity of the proton when \(0\) seconds has gone by is 4,000 meters per second only in the +y-direction.  I will also note that I set the \( \textbf{B} \) field to point in the +z-direction but the \( \nabla B \) vector is pointed in the +x-direction.  These details are important for understanding why the particle traveled the path that is shown in the video.

Because of the mathematics, I knew how the proton should have behaved but I needed to confirm my hypothesis with the video.
Here are some questions I asked myself when I first saw the video my code created:

Did the proton really undergo cyclotron motion?
Yes.  That's why it travels in that loopty-loop fashion, as seen in the "Top View" image.

Why did the proton drift in the +y-direction?
This is because the velocity drift due to \( \nabla B \) is in that direction.  This is shown in the \( v_a \) equation because of the cross product \( \textbf{B}\times \nabla_{\perp}B \).  In terms of the directions, this cross product adheres to the right hand rule: \( \hat{\textbf{e}}_z \times \hat{\textbf{e}}_x = \hat{\textbf{e}}_y \) , which is the +y-direction.

Why didn't the proton ever move in the \( \pm \)z-direction?
This is because my initial condition for velocity \( \textbf{v}(0) = 4000\) \(\hat{ \textbf{e}}_y \) m/s is not in the \(\pm \)z-direction nor does the Lorentz force \( \textbf{F} = q(\textbf{v} \times \textbf{B}) \) ever at any point in time push the proton in the \(\pm\)z-direction.

Why does the proton maneuver in both x and y directions if the initial condition of the proton started it off going in only the +y-direction?
This is because the Lorentz force accelerates the proton into +x-direction at the beginning ( \(\textbf{v} \times \textbf{B} == \hat{y} \times \hat{z} = \hat{x} \) ) and as time goes on the Lorentz force continues to accelerate the particle in different directions until eventually the particle has gone a circular path.


Hopefully, I answered all of the questions that may or may not have already popped into your head when watching my code run.  I think that this is enough fun for today.  Next time, we'll see what flabbergasting events transpire in the simulation when the initial velocity changes.

Friday, July 8, 2016

Space Physics: Cyclotron Motion

I'll discuss a basic topic in Space Physics today that is certainly not a basic idea for the average person outside of science to understand.  However! that should not matter nor should it intimidate you!  Any person (such as myself) that attempts to teach ANY scientific concept should be capable of explaining their science in such a way that even children with little scientific background can understand the concept.

(Credit: spaceweather.com)
The basic topic is the behavior of a proton as it approaches the Earth's magnetic field.  Remember, an atom--those boxes you see on a periodic table--can consist of a positively charged proton and a negatively charged electron.  Because I am discussing a topic in the field of space physics, I will also remind you that the Earth's magnetic field is always being hit by protons and electrons from the Sun.

Today, I will describe one of the ways a proton behaves when encountering an unchanging magnetic field line. 

When a proton approaches a magnetic field line, the proton spirals around a magnetic field line and continues in the direction of that line.  This is known as cyclotron motion.

Top View
The video illustrates a simulation in which a magnetic field line is aligned with the z-axis and is pointing upward in the +z direction (also denoted as the \( +\hat{\textbf{e}}_z \) direction).  This is why the proton travels in the +z direction over time while moving in a circle.  Mathematically, the +z direction of the particle's motion is shown via the \( v_{\|}t\hat{\textbf{e}}_z \) term at the end of my cyclotron motion derivation.

The image to the right provides a top view of the simulation.  This perspective allowed me to verify if the proton truly has a circular trajectory in 2D space.  It is easy to see (thanks to the numbers on the axes) that the proton traveled 0.23 meters in the +y direction as well as the -y direction.  The trajectory looks visually like an ellipse (ugghhhh, thanks MATLAB...) but after looking at the numbers, I found that the proton truly did travel 0.23 meters from the center of the circle in all directions.  The radius of this circular cyclotron motion is known as the Larmor orbital radius:
\[r_L = \Big| \frac{v_{\perp}}{\Omega} \Big| = \Big| \frac{mv_{\perp}}{qB} \Big| \]
where \(\Omega\) is the frequency of the orbit, m is the mass of the particle (in this case a proton), \(v_{\perp}\) is the component of velocity of the particle that goes in a direction that is perpendicular to the magnetic field B, and q is the charge of that particle (in this case +1.602\(\times \)10\(^{-19}\) Coulombs).

Now, let's see how the electron behaves in the presence of a magnetic field line.  Notice anything different?
Top View
Hmmmm... Interesante.  At first glance, it seems to have done the same thing as the proton.  One difference seen is that the electron's cyclotron motion is counterclockwise while the proton's motion is clockwise.  Another distinction is noticed when looking at the simulation from the top view.  The Larmor radius is now 1.26\(\times \) 10\(^{-4}\) meters.


Mathematically speaking, the reason why the electron's Larmor radius is shorter than the proton's Larmor radius is because the mass of an electron is about 1800 times less than the mass of a proton, and because the \(r_L\) is directly proportional to the m, the super tiny electron mass makes its Larmor radius super tiny as well.

The difference in clockwise vs counterclockwise motion between proton and electron is due to the Lorentz force:
\[ \vec{F} = q(\vec{E} + \vec{v} \times \vec{B} ) \]
where \(\vec{E}\) is the electric field.  Basically, this equation means that whenever a charged particle is in the presence of an electric or magnetic field, a force will be applied to that particle which will cause it to either to accelerate or change directions.  The arrows on top of the variables indicate that they are vectors, which means that the electric field strength, the particle's velocity, and the magnetic field strength are all pointed in some direction.  In my simulation, I have not included an electric field.  Therefore, in this case, \(\vec{E}=0\) and \( \vec{F} = q ( \vec{v} \times \vec{B} ) \).  Between the proton and electron simulations I did not change the velocity nor the magnetic field.  The only thing that was different is the charge q.  Since protons and electrons have opposite charge, the magnetic field's force \(\vec{F}\) was pushing them in opposite directions!  Before clicking on my previous videos, you could have predicted if the motion was going to be clockwise or counterclockwise as long as you would have used the right hand rule for the cross product \( \vec{v} \times \vec{B} \).

Later, I will discuss other behaviors that particles from the Sun exhibit when they encounter the Earth's magnetic field.


Deriving Position from Velocity of Pure Cyclotron Motion
\begin{equation} \textbf{v}(t) = v_{\perp}sin(\Omega_c t)\hat{\textbf{e}}_x + v_{\perp}cos(\Omega_c t)\hat{\textbf{e}}_y + v_{\|}\hat{\textbf{e}}_z
\end{equation}
\[ \int_{t=0}^{t} \textbf{v}(t) dt = \int_{t=0}^{t} \big( v_{\perp}sin(\Omega_c t)\hat{\textbf{e}}_x + v_{\perp}cos(\Omega_c t)\hat{\textbf{e}}_y + v_{\|}\hat{\textbf{e}}_z \big)dt  \]
\[ \textbf{r}(t)-\textbf{r}(0) = -\frac{v_{\perp}}{\Omega_c}[cos(\Omega_c t) - 1]\hat{\textbf{e}}_x + \frac{v_{\perp}}{\Omega_c}[sin(\Omega_c t)- 0]\hat{\textbf{e}}_y + v_{\|}[t - 0]\hat{\textbf{e}}_z \]
\begin{equation}\label{Eq2: Analy path} \textbf{r}(t)-\textbf{r}(0) = \frac{v_{\perp}}{\Omega_c}[1 - cos(\Omega_c t)]\hat{\textbf{e}}_x + \frac{v_{\perp}}{\Omega_c}sin(\Omega_c t)\hat{\textbf{e}}_y + v_{\|}t\hat{\textbf{e}}_z
  \end{equation}

Monday, January 4, 2016

Wilson Inspired... by the Banneker Institute

Thoughts pondered and experiences gained during my 10 weeks a part of the Banneker Institute summer graduate school preparatory program at the Harvard-Smithsonian Center for Astrophysics. As the days pass by, I am moving exponentially up the learning curve in regards to my skills in Coding and my knowledge of the Universe. This fact may or may not be discerned in my posts over time. Peruse my posts, Share with others, and Enjoy the read!  "

...was how the previous heading description of my blog went.
I made this blog with the purpose of enhancing my writing skills, discussing the details of my summer research project, and expressing my thoughts about anything my heart desired.  Seeing how it has turned out thus far, I am happy that Harvard professor, Dr. John Johnson, recommended that all of us interns create this blog and write in it as often as possible.

"You might have to follow the advice given in [one] post, which gives you a link to a previously written post that you should read first."

 

I decided to write about the lessons we learned during the Astro-Statistics class we took that summer.  Occasionally, I discussed my research project as well.  For both of these topics, it was necessary to have them be a continuous series of blog posts.  So, to get the full understanding of some of my posts, you might have to follow the advice given in that post, which gives you a link to a previously written post that you should read first.

This blog has become a hobby that I plan on continuing for years to come.  Most of my future content will be me teaching a scientific concept or talking about an event or person in the scientific community.  As time goes on, I will be writing more material that people outside of the scientific community can understand.  Working for the Adler Planetarium consistently reminds me of how vital it is for astronomers to teach and inform the lay[wo]men about astronomy.  Thus, I will be doing this through my blog as well. 
People who are not as scientifically inclined as the PhD astrophysicists I work with will enjoy these 3 blog posts among others:
( 06-12-15 ) Harvard Colleagues and Friends
Part VII : High Precision Photometry of Transiting Exoplanets as I currently know it
Someone You Should Know: Lauren Woolsey

When I have spare time and an intriguing topic, I will keep writing in this blog because I have already seen how beneficial this has been to my research and personal life.  Considering the intricate code, physics, and mathematics that entail astronomy research, writing the details down in an organized fashion has been a life-saver when I must re-do a procedure or re-calculate something months after doing it the first time.  I have been in this circumstance several times during my 2 years of undergraduate research.  On those days, I always remember to give myself a pat on the back as a way of motivating myself to keep being diligent in my writing.

"With an inspiring leader like Dr. Johnson, it is impossible for interns to walk out of the Banneker Institute the same as they came in."

 

In regards to my personal life, articulating my thoughts through writing is an empowering experience.  I now understand why many astronomers use this powerful form of communication to organize their thoughts as well as to inform, inspire, and influence the world.  Although people may use their blogs for writing poetry, telling stories, marketing themselves or informing others about scientific results, I am happy that one of the first blogs I have read in my entire life is used for activism towards social justice issues.  The blog I am referring to is Dr. Johnson's.
This guy is a great role model for the newest members of the astronomy community as well as the oldest.  This is true in regards to the diligence and intelligence necessary for scientists to conduct excellent research as well as the patience and open-mindedness necessary to form healthy collaborations amongst scientists of various nationalities, ethnicities, and ... well ... genders too (because according to current statistics, white men are appallingly over-represented in the astronomy community and thus often lack the experience of working with others of a different background than theirs).  I am sure that if you visit Dr. Johnson's blog, you will see why he is such a well-respected and powerful figure in the astronomy community.  Moreover, you will get a glimpse of why his internship, the Banneker Institute, is one of the most unique experiences a summer intern can have. 

With an inspiring leader like Dr. Johnson, it is impossible for interns to walk out of the Banneker Institute the same as they came in.  Because of the Banneker institute, I am sure that NO hardships of graduate school will halt my relentless pursuit for the PhD.  Thanks to the Astro-Statistics class, my computer programming skills have drastically improved.  Furthermore, my public speaking skills have skyrocketed after being taught the art of elocution by Professor Johnson and his colleagues while also delivering a talk to my peers every 2 weeks.  And last but not least, my mind has been enlightened to the intrinsic, yet subtle, injustices and prejudices that currently plague the science community.

My time as a Banneker Institute Fellow may have ended, but I will certainly remain an affiliate of the program and support other interns as more arrive summer after summer.