Summary:

The primary goal of my project is to create a 3d model of the shape and strength of the Earth’s magnetic field and define the locations of the Van Allen Belts within that model. According to the research I have done so far, a planetary magnetic field resembles the field of cylinder. Applying relevant Earth properties, I would then be able to create an initial model of the field.  Furthermore, due to the proximity of these belts to the Earth, I will not have to take interactions with the solar wind into account when modeling the field. The modeling will be done with the Mathematica program. With the model complete, I would hope to compare it to other, more exact models of the Earth’s magnetic field to confirm the theoretical location of the Van Allen Belts. I would also be interested in noting if there is any relationship between core size of the planet and development of a magnetic field. My current research hasn’t turned up any leads for a mathematical way to approach this problem however.

Timeline:

•Week  1: (week of 4/6) Research the Van Allen Belts and Define Project Parameters -During this first week I plan to research the different possible facets of my project in order to determine the particular parameters I will be creating the 3d model with. This also includes looking for previously made 3d vector fields that can teach me how to plot the vector field in Mathematica. Furthermore I will be looking into some of the secondary objectives of my project to see if the ideas can be executed in a reasonable amount of time.

•Week 2: (week of 4/13) Creating the Initial 3D Model – During the second week of the project, we proceed onto the next step of creating our basic 3D magnetic field model. This 3D vector field model will be created using Mathematica and will create a visual representation of the Earth’s magnetic field. The initial model will be based off of the magnetic field of a cylinder, a design which has been suggested by multiple sources.

•Week 3: (week of 4/20) Finishing the Initial 3D Model and Model Comparisons – This week will be used to put any necessary finishing touches on the initial model and determine the location of the Van Allen belts within the model. I will also be comparing the model to observed data and other proposed models of the field. From these findings, I will be able to determine the accuracy of the field modeled in Mathematica. If the simple cylindrical model is not as accurate as predicted, this week will also be taken to edit the model and improve its accuracy.

•Week 4: (week of 4/27) Extended Modeling – During this week I will finish all alterations on a final edited model. If there is extra time, the current plan is to systematically alter the model to see how certain changes effect the magnetic field. Specifically my goal is to see if there exists some sort of correlation between the planet’s core size and the development of its magnetic field and subsequently its Van Allen Belts. If a correlation like this can be seen, the magnetic fields of other planets will be modeled and compared to actual data. This will allow us to confirm if the created model can be applied to other planets with only minor alterations to its coding.

•Week 5: (week of 5/4) Finishing Touches – During this week, any extra modeling will be quickly finished up and the rest of the week will be dedicated to organizing the collected data into a final presentation.

Sources:

Currently the sources I have browsed are:

http://www.phy6.org/Education/Iradbelt.html

http://vanallenprobes.jhuapl.edu/science/overview.php

https://www.spenvis.oma.be/help/background/traprad/traprad.html#APAE

http://www.nasa.gov/mission_pages/rbsp/main/index.html#.U0O-7fmIDlx