{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# How long would it take to fall through the Earth?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**A computational essay by Karl Henrik Fredly, undergraduate at the University of Oslo (karlhf@student.uv.uio.no)**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Introduction"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The year is 2094, and a man named Bruce is on his way to the North Pole Tropical Resort. He believes that he will arrive there one hour early to a meeting with his polish friend Antoni. But Bruce has made a huge mistake: Antoni is on the South Pole, while his other polish friend is the one that is on the North Pole. He got his poles mixed up! Luckily, the Resort has dug a tunnel through the Earth, which Bruce can fall through to get to Antoni. However, the question remains: Will Bruce make it in time to his meeting? How long does it take to fall through the Earth?\n",
"\n",
"In this computational narrative, I am going to look at the movement during a fall under the influence of the Earth's gravity, without being hindered by the ground or the air. Solving this kind of problem might be relevant when exploring space, where moving through a big object might occur, in contrast to the Earth which is practically impossible to move through.\n",
"\n",
"I will look at how position, velocity and acceleration changes during the fall, and use these findings to better understand the movement. To achieve this, I will first describe gravity in and around spherical objects, then find how the Earth's mass changes with radius, and finally combine these two models to describe the fall through the Earth."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*The Kola Borehole (From absolute-knowledge.com)*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Gravity in and around the Earth"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For the purpose of this essay I am going to assume that the Earth is a perfect sphere with a varying density given by the [Preliminary Reference Earth Model (PREM)](https://en.wikipedia.org/wiki/Preliminary_reference_Earth_model). This model gives the density of the Earth at different distances from the center.\n",
"\n",
"\n",
"I will also assume that there is no air resistance. With air resistance, Bruce would quickly reach terminal velocity and slowly lose all of his speed, getting trapped in the center of the Earth. Furhermore, I will assume that the fall is from pole to pole, as the Earth's rotation would interfere if that was not the case."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The Shell Theorem"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The main difference between being affected by gravity while outside the Earth, and being affected while inside it, is how much of it is below you to \"pull you down\". As you venture further down, less of the Earth will be below you to pull you down, and more of it will be above you to pull you up. In addition to this, as you get closer to different parts of the Earth, they will have a greater pull on you due to being closer to you."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The aforementioned factors lead to some calculations beyond the scope of this narrative, which will not be addressed. I will instead use a result called the [Shell Theorem](http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/sphshell2.html) which makes this problem much more manageable. The Shell Theorem has the following implications for this problem:\n",
"\n",
"- A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its centre\n",
"- When at a distance r from the center, all mass at a greater distance than r can be ignored"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This means that I don't have to calculate the gravitational pull from all throughout the Earth, since I can act as if all of the Earth's mass is located in its center. I also only need to worry about the what is further in than the point Bruce is currently at."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The gravitational force between two objects is given by $F = \\frac{GMm}{r^2}$\n",
"\n",
"where G is the gravitational constant $6.68\\times10^-11\\frac{Nm^2}{kg^2}$, M is the mass of one of the objects, m is the mass of the other object and r is the distance between the objects. The force acts on both of the objects, and is pointed from one object to the other.\n",
"\n",
"M will be the mass of the Earth that needs to be considered. M will vary however, so I will need to use the PREM to find the total mass of the Earth at different distances from the center."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The variable density of the Earth"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For plotting and calculations I import numpy, pyplot and polynomial."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np #Used for mathematical functions and constants\n",
"import matplotlib.pyplot as plt #Used for plotting\n",
"import numpy.polynomial.polynomial as poly #Used later for finding a polynomial that approximates the data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Preliminary Reference Earth Model gives the density of the Earth at different distances from the center. \n",
"\n",
"The data can be found here: http://ds.iris.edu/ds/products/emc-prem/ at \"Model Download\". I use the file \"PREM_ANISOTROPIC\".\n",
"\n",
"First I read the data and store them in arrays."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"radius = []\n",
"density = []\n",
"\n",
"#The file has 199 lines starting with \"[Radius] [Density]\" that we read like this\n",
"infile = open(\"FallingThroughTheEarthResources/PREM_ANISOTROPIC.txt\",\"r\")\n",
"lines = infile.readlines()\n",
"for line in lines[3:]: #The data starts at line 3.\n",
" numbers = line.split()\n",
" radius.append(float(numbers[0]))\n",
" density.append(float(numbers[1]))\n",
"infile.close()\n",
"radius = np.array(radius) #I store the radius and density to numpy arrays in order to easily divide them by 1000 for plotting\n",
"density = np.array(density)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using pylot I plot the data:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(radius/1000,density/1000) #Dividing by 1000 to get more plot-friendly units\n",
"plt.xlabel(\"Radius [km]\")\n",
"plt.ylabel(\"Density [kg/m^3 * 10^(-3)]\")\n",
"plt.title(\"The density of the Earth at different radiuses\")\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*This image (taken from en.wikipedia.org/wiki/Structure_of_the_Earth) shows how the different layers and densities of the earth fit together.*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Mass at different heights"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next ! need to find out how the total mass further in changes with a varying radius. By working my way from the center I can add one and one \"shell\" to find the total mass at different distances from the center. I have to find the total mass by adding these shells due to the relatively rough resolution of our density data."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that I use the same density for the inner and outer distance to calculate the mass of the shell. The density I use for the spheres is the average of the Earth's density at the outer and inner radius of the shell. So that:\n",
"\n",
"$$ M_{shell} = M_{outer} - M_{inner} = \\frac{4}{3}\\pi r_{outer}^3 Density - \\frac{4}{3}\\pi r_{inner}^3 Density $$\n",
"\n",
"By doing this calculation for every shell and adding them up, I find the total mass of the Earth up to any distance from the center. This process is known as numerical integration using the midpoint rule, and in code it looks like this:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pi = np.pi\n",
"masses = []\n",
"shellMass = 4/3*np.pi*radius[0]**3*density[0] #The innermost shell. In our case this has a mass of 0.\n",
"masses.append(shellMass)\n",
"\n",
"for i in range(1,len(radius)):\n",
" shellDensity = (density[i-1]+density[i])/2 #The average of the density at the outer and inner radius\n",
" #We find the mass of the shells corresponding to every data point\n",
" shellMass = 4/3*pi*radius[i]**3*shellDensity - 4/3*pi*radius[i-1]**3*shellDensity\n",
" #We add the next total mass to the list, adding the mass of the current shell with the previous total mass\n",
" masses.append(shellMass + masses[i-1])\n",
" \n",
"plt.plot(radius/1000,masses)\n",
"plt.xlabel(\"Radius [km]\")\n",
"plt.ylabel(\"Mass [kg]\")\n",
"plt.title(\"Mass of the Earth at different radiuses\")\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The total mass increases very slowly near the center, and faster near the surface. While the density is higher near the center, the volume is much smaller. Meaning that the total mass does not change much when the radius increases at first, as the volume of the inner shells are so small.\n",
"\n",
"I can compare the total mass at the outermost radius, with the actual mass of the Earth, which is about $5.972*10^{24}kg$, to get an idea of the accuracy of our calculations."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The total mass we find using this model is 5.973E+24 kg\n"
]
}
],
"source": [
"print(\"The total mass we find using this model is {:.3E} kg\".format(masses[-1]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This accuracy is encouraging. Note that the total mass is not the only useful result here, as I will use the mass at different radiuses to find the acceleration."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Acceleration at different heights"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The gravitational force between two objects is given by $F = \\frac{GMm}{r^2}$. The Shell Theorem states that at a distance $r$ from the center, one only needs to consider the mass further in than $r$. Additionally, Newton's second law states that force is equal to mass times acceleration, so that:\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"F = ma \\Rightarrow a = \\frac{F}{m} = \\frac{GMm}{r^2m} = \\frac{GM}{r^2}\n",
"\\end{align*}\n",
"$$\n",
"\n",
"This means that Bruce's mass won't mean anything, just like in real life. From here I find the acceleration at the different radiuses in the dataset:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"G = 6.674 * 10**(-11) #The gravitational constant\n",
"acceleration = []\n",
"acceleration.append(0) #I need to handle the initial acceleration here to not have to divide by zero in the loop\n",
"\n",
"for i in range(1,len(radius)):\n",
" acceleration.append(G*masses[i]/(radius[i]**2))\n",
"acceleration = np.array(acceleration)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I can plot these findings as well. I am eventually going to need a general function for gravity since this dataset does not give the acceleration at the distances between the data points. To better show this I will plot only the data as points next to the smooth graph."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(19, 4))\n",
"plt.subplot(131)\n",
"plt.plot(radius/1000,acceleration) #The smooth graph\n",
"plt.xlabel(\"Radius [km]\")\n",
"plt.ylabel(\"Acceleration [m/s^2]\")\n",
"plt.title(\"The gravitational acceleration from the Earth at different radiuses\")\n",
"\n",
"plt.subplot(132)\n",
"plt.plot(radius/1000, acceleration, linestyle=\"\", marker=\"o\", markersize=2) #The data plotted as points\n",
"plt.xlabel(\"Radius [km]\")\n",
"plt.ylabel(\"Acceleration [m/s^2]\")\n",
"plt.title(\"What the data points actually look like\")\n",
"\n",
"plt.subplot(133)\n",
"#We also plot how gravity changes moving from the surface and down by turning the plot around.\n",
"plt.plot(abs(radius-radius[-1])/1000,acceleration, color=\"red\")\n",
"plt.xlabel(\"Distance from surface [km]\")\n",
"plt.ylabel(\"Acceleration [m/s^2]\")\n",
"plt.title(\"Gravity as Bruce falls from the surface\")\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The red graph shows that as Bruce starts falling, the acceleration will first stay nearly constant before increasing slightly until about 3000km. This is because, as he gets closer to the more dense inner parts of the Earth, the gravitational pull from them will increase. Since the outer layers are so much less dense than the mantle or core, he does not \"lose\" much gravitational pull compared to the pull he gains from being closer to the denser parts. When he is at around 3000 km, gravity starts weakening. This happens because the amount of mass pulling him down is starting to reduce fast."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Creating a function to describe the acceleration"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So far I have worked out the acceleration at all the points that the dataset contains, but if I am to calculate what a fall through the Earth would look like I will need a general formula, or a function that finds the acceleration at any height.\n",
"\n",
"I can achieve this by using the method polyfit. Polyfit uses linear algebra to find the polynomial that best fits the data points given. I have found that a polynomial of degree 3 works well here, and that using a separate polynomial before and after the maximum spike of the acceleration offers greater accuracy."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"turn = np.argmax(acceleration) #The spike in the acceleration graph\n",
"deg = 3\n",
"#The following two lines use linear algebra to find polynomials that I can use to find gravity at any height\n",
"coefs1 = poly.polyfit(radius[:turn], acceleration[:turn], deg) #Polynomial for the points further in than the \"spike\"\n",
"coefs2 = poly.polyfit(radius[turn:], acceleration[turn:], deg) #Polynomial for the points further out than the \"spike\"\n",
"\n",
"earthRadius = radius[-1]\n",
"earthMass = masses[-1]\n",
"def grav(r): #This function returns the gravitational acceleration at any radius\n",
" dist = abs(r) #The absolute value of the distance\n",
" direc = -np.sign(r) #The direction of gravity. It is opposite of our position, since gravity pulls us towards the center\n",
"\n",
" if dist > earthRadius: #If we are outside the Earth\n",
" return(direc*G*earthMass/r**2) #Normal formula for acceleration using the mass of the entire Earth\n",
"\n",
" elif dist < radius[turn]: #If we are further in than the \"spike\"\n",
" sum = 0\n",
" for i in range(deg+1): #a0 + a1*r + a2*r**2 + a3*r**3\n",
" sum += coefs1[i]*dist**(i) #Adding up all of the coefficients times the radius\n",
" return(direc*sum)\n",
" \n",
" else: #Function 2 for distances further out than the \"spike\"\n",
" sum = 0\n",
" for i in range(deg+1):\n",
" sum += coefs2[i]*dist**(i)\n",
" return(direc*sum)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I will not go into detail on how these polynomials that I will use as a general function for gravity are found. However, it is important to understand that what I did was find polynomials that have graphs that are similar to the one I just plotted. If I write out the coefficients of the first polynomial, the one that approximates gravity between the surface and the \"spike\" in gravity, they look like this:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[-2.93375495e-02 3.87773093e-06 -2.39818116e-13 3.84955504e-21]\n"
]
}
],
"source": [
"print(coefs1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\begin{align*}\n",
"f_1(r) &= a_0 + a_1r^1 + a_2r^2 + a_3r^3 \\\\\n",
"f_1(r) &= -2.93*10^{-2} + 3.88*10^{-6}r - 2.40*10^{-13}r^2 + 3.85*10^{-21}r^3\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To show this new general function in relation to the values for gravitational acceleration I found from the data, I will plot them together and summarize the errors for every point:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Total error = 1.0836096370862585\n"
]
},
{
"data": {
"image/png": 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IkSN67NgxVVVdt26dpu272bNn67XXXnvi9ZnNF6pycr7kit1r9cCz5+rBJ8/SCePey3ie1FTVDbN14RNNVZ8qrnFPVtEJzw9QPbQzT0M1oQdYqBnk1LC64p80fwspqkyav+WMl5VZS5G08gYNGtC7d28+/vhjoqIyvofepUsXIiIiqFu3Lrt27QJg3rx59OjRg4iICM466yzatWt3yusOHjzIgQMHaNvWeeb1LbfccmJaUlISd9xxB/Xr16dHjx6sWrUqw3X7O585A9sXw9hrSEw8zg2JTzB8TZWM5xOBGpcy48IP6Xn8CZak1qR3wqfw6gUsee0Guj32Gk9MX56noZvQFlaJv1eLqkSK0KtF1TNeVpkyZdi/f/9JZfv27aNs2bIAfP3119x1110sWrSIJk2akJycfMoyChQocGJY3QfipP3Piqpm+sHz6quvUqFCBZYuXcrChQtJTEw8o/lMDsXOg3HXQXQRPq77Huuonu15N6JrfQ6Ub8btSQ/Tv9g70LQ/5+2bzecxT3LL4hvgtzfgcFwebYAJZWHVnHNEl3qM6JJ16xd/FS1alIoVKzJr1iwuv/xy9u3bx3fffcd9991HamoqW7dupV27drRu3ZpJkyZx+PBhv5bbunVrxo8fT9++fYmLi2POnDn06tXrpHlKlixJiRIlmDdvHq1bt2bixIknph08eJAqVaoQERHB+PHjSUlJAaBYsWLEx8dnO5/JBWu/hc/6Qqnq0GcGDxSvxAM3+PfSHx5o6zN2E68e68bRvz5jYInf4Ydh8NNwVhW7iLf2NKZC44482a1ZILbAhLiwSvy5bcKECdx111089NBDADz11FPUrFmTpKQkbr75Zg4ePIiq8sADD1CyZEm/ltmtWzdmzZpFvXr1qFWrFi1atKBEiRKnzDd27Fj69+9P4cKFufrqq0+UDxo0iG7dujFlyhTatWtHkSJFAKfqKSoqioYNG9KvX79M5zNnaNkUUqbdyYrU6nxz1v94tHilM1rcsG4toFsLZ2T3alj8MeV/m8Bb0b9wbNnbkHwNXNAFzrsaChTNhQ0w4SAonrnbtGlTTf8gltWrV1OnTh2PIgqsw4cPU7RoUfbu3Uvz5s359ddfOeuss7wOK6jlyfmycCx89QB/pNbhtsSHSJDCbHihQ66v5snpS1n/54/cW2klLRN+hcO7OK7RbC3WkHNbdYZzL4fydZ17ByasicgiVW2avtyu+POhjh07cuDAARITE3niiScs6QeDX1+HH5+A867m+0JDSPhzV67cS8rIM10bQteGzkhqCjcMe40rIv6k7aFlTgw/PsGh6LLMSqhDRLVWdO50PZStDRFhdUvPZCFgiV9EPgQ6ArtVtZ5bVhr4FKgOxAI9VXV/ZssIV3PmzPE6BOMvVZj9PPwyEi7oCl1H81RUDE9dn0frj4ikVvOreHH++WxpWpUR7UrBhv9j7vSPaR2xlHLb5sLbI6FgCdbG1OXbfZUod14zenfqACWr2reCMBWwqh4RuQQ4DEzwSfwjgX2q+qKIDAVKqeqQ7JYVblU9JvcF5HxR5be3B3BR3GcsLN2RpndPgIjI3F1HDj0xYwWT5m/m7kaRPFB7H2z5g78X/kRN2U6EuO/5AiXYFHUOvx8qQ6mz69D+kouhzLnOTemoGE/jN7kjz6t6VPUXEamerrgzcKk7PB6YA2Sb+I3Jd1JT4esHuCjuM8Ykt+f5Hb3YkE+SPmTQgq1RLyakrmD6/HXcUy+RO2sfhZ3L2b9gLu0j1lNq+yz45E0AUlU4HF2a4uWrQfFK/L6nIL/sjKbWOdXoenEDKFzG+StYEmKKQHShwH9zUIXk45B8zOna4qT/6f5OTHP+flm1lfXb93JBhYK0qFoEUpJYsSWOf/bGU61UDOeXLwypySzevJeExGSiIiElVYmMiCAxBSIiI0hMjSA1IpojKZEQGcPhlGiqVihDUmQh5v+TSKGiJdkYH0lidDG2Hy9EsbIVmXB3B4gpmi+/VeV1HX8FVd0BoKo7RKR8ZjOKyABgAEDVqoGpKzUmR1KS4YtBsOxT5lToy/NbrqZXi2peR5WtjJozT09ewaT5W7itSUkeaxnDg+98TlXZSaXUffQsFAF711MvbjOtoo7BVuCTDBYskRBTlIOpBdh3PILChQtRoVRxiCzApv1J7Iw/TvnihalZvijr446w/eBxKhePoWbZQqCpbN4Tz774o1QoEkGlopGQmsT++CMkHT9GsagUCkmSk8RzqIVGcWFkNIl7oiCxGERGU3BfElUlkuQDkVC0NEREkpyUQIREkJoKAqSmphAjqUSkKoVJITo1hWhJpkBqIgUikigUl0hhEmgblQoJQNoD3goA8cALkBhRkPioMvydUJwjBcqz9lgpKp1Tmy7tLoLSNaF4ZU/uveTbm7uqOhoYDU5Vj8fhGONIToTPb4PVM+GyYVx6ycNs8DqmM5D+w6BIs4K8MX8LvVpUpadbPnLGCmbMX0ffC4szuHUZOLqXB8fOoihHKCrHeaRdZTh+mB9/X0MMicQcSeGas0tBynF2x+8kEmX/oXgoGcGhgwcohnLgUAKUjoGISP6JTyFZC7H3cDSVqleByBhm795FgkaTmBJDv7a1Iaogr8yK5ajGkEgMz/Zoxl1T1nBUo0mkABP/cylEF+Ly1+dzJDWaJCnAoqc7QlRBnp25mknuNqVt6/gZK06U1XPLHn/1Z9btOkyJQlEcTkihaMFIDh5LznS8V4uqoMrnCzZQryzs27uHs2KOEZ14kNLEU0YOUkEOUj5pP+VlP7WOr6Jt5F6itqbCBGd/H9MYNmpF1mkV1qWezSqtRp0LWzO0xyUBPe55nfh3iUhF92q/IrA7j9efa2JjY+nYsSMrVqw4UTZ8+HCKFi3K4MGDM3zNzJkzWbVqlWc9dAbKRRddlCudvM2ZM4eYmBguuugiAN59910KFy5Mnz59znjZueHpaYtos/ghLotcDFc/D63u8jqkXJfRt4KMyoo0O4uJbuLkcmfa0sR/k+k17vxf+STYpl3qMd1nvIk7z7c+ZVe4ZYuj/i3jSqfs4EGfskb1KB27gu/Sxs925rmoOf/OE1PktLbp5B/PncY+61r/lLInZqxgjBtHLE5MNcsXIXb3IcrpXqpF7KK67KKGbOdc2U7ziDV0jfzVefHKl9i+ojTLUmvyV+q5TEu5hIUv9jplHWcioO343Tr+r3xu7r4M7PW5uVtaVR/Jbjn58eZuThJ/fneiAyePmv0Fcv+d8fmSeJR5z15J64gVDEvqz7PPvZp7wZmwcpX7zSK94hyhjmyhXsRGGkRsopGsp1rEblofH8W8F27N0boyu7kbsHe4iEwGfgdqi8g2EbkNeBG4UkT+Bq50x0NSoLtlfv/992nWrBkNGzakW7duHD169MRyBw4cSJs2bahVqxZfffXViXV37tyZa665htq1a/P0008DzgdYnTp1GDRoEI0bN2br1q1MnjyZ+vXrU69ePYYMce69b968mfPOO489e/aQmppKmzZt+OGHHwCn+wpwrtjbtm1Lz549qVWrFkOHDmXixIk0b96c+vXrs2GDUyny5Zdf0qJFCy688EKuuOIKdu3aRWxsLO+++y6vvvoqjRo1Yu7cuSc92GbJkiW0bNmSBg0a0LVr1xP9JF166aUMGTKE5s2bU6tWLebOnZvLRxI4fhgm9eSiiJU8kjQQaXZb7q/DhI0fHmhL7IvXnvK37MWe7C/fjDEp13Jf0t20TRxFk4R3+EfL5XoMgWzVc1Mmky7P9ZV9OxR25nLvhWfVh/Y5/1x68cUX2bRpEwUKFODAgQMZzrNjxw7mzZvHmjVr6NSpE927d2fatGnExsayfPlydu/eTZ06dejfv/8pr73++uu54447ABg2bBhjxozhnnvuAZxk/vPPP7NhwwbatWvH+vXrAViwYAErVqygcOHCNGvWjGuvvZayZcuydu1axo4dy9tvv8327dsZMmQIixYtolSpUlx11VXMmDGDLl26MGTIEAYOHEiLFi2oW7cuV1111SlxLV26lNWrV1O6dGlq1KjB7bffzoIFC3jttdd44403GDVqFK1bt+aPP/5ARPjggw8YOXIk//3vfxk4cOBJV/yzZs06sdw+ffrwxhtv0LZtW5588kmefvppRo0aBUBycjILFizgm2++4emnn+ann37K8XE7RcIhmNgDti0g4vr3GdmgR+4t25h0clrddLrsp3w55GW3zAArVqygTZs21K9fn4kTJ7Jy5coT03r27ElERATnnXceNWrUYM2aNQBceeWVlClThkKFCnH99dczb948AKpVq0bLli0B+PPPP7n00kspV64cUVFR9O7dm19++QWA22+/nfj4eN59991MHzHZrFkzKlasSIECBahZs+aJD4f69esTGxsLwLZt27j66qupX78+L7/88kmxZyR9N9R9+/Y9ERM4H4IATZo0ObGOXHHsAHzUFbb9Cd0/BEv6JkTk21Y9p+UMrsxzKrNumc855xzA6Zb5l19+YebMmYwYMSLD5JbTbpnBqdKZMWMGDRs2ZNy4cSf92jf9h1LaeGblvh20ZbX+o0ePsm3bNsDpT6hYsWKnzOO7TRERESfGIyIiTnRNfc899/Dggw/SqVMn5syZw/Dhw7Pb3CylrSMyMjLD7q9z4vmpv3HdskHUidxKVM8JUKdjrizXmPzArvhzyLdbZuBEt8ytW7c+qVvmkSNHcuDAgdPqlvnzzz8nNTWVXbt2Zdp9Q3x8PBUrViQpKemkbpkBpkyZQmpqKhs2bGDjxo3Url0bgB9//JF9+/Zx7NgxZsyYwcUXX3zKclu0aMHPP//Mnj17SElJYfLkySeutIcMGULv3r155plnTlQz5cTBgwepXLkyAOPHjz9Rnr7r6DQlSpSgVKlSJ+rvP/rooxMxBcTRfXReNpBaspU7Ex+wpG9CTmhc8XvEy26ZR4wYQYsWLahWrRr169c/KWHWrl2btm3bsmvXLt59910KFiwIOB8qt9xyC+vXr6dXr140bdr0lKqRihUr8sILL9CuXTtUlQ4dOtC5c2d+/vln/vzzT3799VciIyP5/PPPGTt2LLfeevqtDYYPH06PHj2oXLkyLVu2ZNOmTQBcd911dO/enS+++II33njjpNeMHz+egQMHcvToUWrUqMHYsWNPe71+ObIXJnSmVuQOBhx/iCrNOwVmPcZ4yLplzofOpFvmfv360bFjR7p3735S+bhx41i4cCFvvvlmIELO9/w6X47shQmdYO96uHGS072xMUHMumUOItYtsweO7IHxnWDfBrhpMtS8zOuIjAkYu+I3YSHL8+VwHLvevIoSx7Yy+dyXufWWnP1Yxpj8Js9/wJUXguFDy3gvy/PkyB6Y0Inix7bRP+lhnl1VIe8CM8YjQZv4CxYsyN69ey35myypKnv37j1xg/sk7o1c9m3kk3NfZr7WD9hTs4zJT4K2jr9KlSps27aNuLg4r0Mx+VzBggWpUqXKyYVH9zlJf+96uOkTbq3ZDqvgMeEiaBN/dHT0iR9LGXNaju5zWu/sWefeyM3419HGhKqgreoxJkeO7eefN67h+I7VjK/2vDXZNGHJEr8JHwkH4aPrKXt0A3cmPcAzqyt5HZExnrDEb8LD8Xinl82dy5ha41nmamO7kWvCVtDW8Rvjt8QjMOkG2LYQeoyld93O9PY6JmM8ZInfhLakYzD5RtjyO1z/PtTt7HVExnjOqnpM6Eo+zt+vdyZ141ymnv041O+e/WuMCQOW+E1oSkmCKbdyXvx8hibfzpC/63odkTH5hiV+E3pSU2DaAFj7NV9VfoDPUy+zG7nG+LA6fhNaUlNh5j2wchpc+QwdL74Pe4yKMSezK34TOlThm8GwZCJc+ihcfJ/XERmTL1niN6FBlXlv/wcWjmFu+d7QdojXERmTb1niN6Hhl5dpHTeZ8clX0m/rtZDuwfLGmH9Z4jfB7/e3YfZz/FWqPSNS+tGrRTWvIzImX7Obuya4LRoP3z8KdTrRuPtY1kfaKW1MduyK3wSvFZ/Dl/fBuVdAtw/Akr4xfrHEb4LSR+NHkzTlDjYVaQg9P4KoAl6HZEzQsMRvgk/sPHpsfIzVWpUu++6BmMJeR2RMUPEk8YvIAyKyUn7kxfsAABzsSURBVERWiMhkEcnggajGZGD7Eph0I/EFK9E/aSidWpzvdUTGBJ0sK0VF5HU/lnFIVYf5u0IRqQzcC9RV1WMi8hlwIzDO32WYMBW3Dj6+HgqVolz/b1lYorLXERkTlLK7G9YZeDKbeYYCfid+n/UWEpEkoDCw/TRfb8LNgS3wUReQCOgzAyzpG5Nj2SX+V1V1fFYziEip01mhqv4jIq8AW4BjwA+q+kMGyx0ADACoWtU62Aprh+PY804HYhL289H5b3NXmZpeR2RMUMuyjl9VR2W3AH/m8eV+UHQGzgEqAUVE5OYMljtaVZuqatNy5cqdzipMKEk4BBO7USRhF7cmPsz/llnrHWPOVLY3d0XkahG5TUSqpyvvn8N1XgFsUtU4VU0CpgEX5XBZJpQlJcAnvWDXSqbUfI4lnG/dKxuTC7K7ufsCcDHwF/CYiIxS1TfcyXcDH+ZgnVuAliJSGKeq53JgYQ6WY0JZagpMux1i58L179OnQU/6eB2TMSEiuyv+jsBlqno/0ARoLyKvutNy1AuWqs4HpuJ8mCx3Yxidk2WZEKUKX90Pq7+Ea16EBj29jsiYkJJd4o9S1WQAVT0AXAcUF5EpQExOV6qqT6nq+apaT1VvUdXjOV2WCT0/v3MP/DWBORX6Qsv/eB2OMSEnu8S/QUTapo2oaoqq3gasBeoENDITnv54h7a7P2JS8mXctuVqr6MxJiRll/h7AAvSF7o/2Do7IBGZ8LV8Knw3lFUlLuGplNuse2VjAiTLm7uqeiyLaf/kfjgmbG2YDdMHQtWLqHvLFP6Otl48jAkUf5pzRolITlrvGOOf7Uvg05uhbC24aTJY0jcmoLJM/CJSFPgS+DNvwjFhZ99GmNgdCpWCmz+HQiW9jsiYkJfdFf8c4BtVfScPYjHh5nAce9/tyL7Dx3it4ktQvKLXERkTFrJL/CWArXkRiAkzxw/DpB4UPh7HbYkP8/pSezi6MXklu07aLgGmi4iq6hd5EZAJAylJMKUf7FjKtBrPs2xNNeuKwZg8lF2rnh0iciUwCbDEb85c2q9y1/8IHUfRu+mt9PY6JmPCTLatelQ1HuiaB7GYcDDnBVj8MbQdAk1v9ToaY8KSX49eTOu2AZxulUWkQeBCMqFqxpjn4eeXWFS6I1z6qNfhGBO2/Er8IjJHRIqLSGlgKTBWRP4X2NBMSFn3Ax23vMzslIb02nEDiN3MNcYr/j5svYSqHgKuB8aqahOcfvWNyd72xTClH7sKn8e9yffTs0UNryMyJqxl16rnxHwiUhHoCTwewHhMqNm/GSb2hMJlqHz7TJYXO8vriIwJe/5e8T8DfA+sV9U/RaQG8HfgwjIh4eg+51e5Kcfh5qlgSd+YfCG7J3DdhPMw9CnAlLRyVd0IdAtwbCaYJSXAJ71hfyzcMgPK1fY6ImOMK7uqnmrAFBGJBmYB3wILVFUDHpkJXqmp8MVdsOU37ku6h+JLSjCiutdBGWPSZFnVo6ovquplQAec1jz9gb9EZJKI9BGRCnkRpAkys5+DFVMZmXwjX6S0YtL8LV5HZIzx4dfNXfdHXNPdP0SkLtAemADYY5LMv/76COa+Ao37EJ8ygMgFW607BmPyGfG31sb90VZ1fD4sVHVaYMI6WdOmTXXhwoV5sSpzJjb8H0zsAedcAr0+g8horyMyJqyJyCJVbZq+3K8rfvdBLA2AlUCqW6xAniR+EwR2rYLP+kLZ2tBjvCV9Y/Ixf9vxt1TVugGNxASv+F0c+KALxxMjmFBzBA8XLO51RMaYLPjbjv93t17fmJMlHoXJNxKTeID+iQ/z7uLjXkdkjMmGv1f843GS/07gOCCAqqp11hbOUlNh+gDYvpjpNV5gjfWrb0xQ8DfxfwjcAizn3zp+E+5mPQ2rv4Srn6d3q/9Yv/rGBAl/E/8WVZ0Z0EhMcFk0Hn4dBU37Q8tBXkdjjDkN/ib+NSIyCfgSp6oHyLvmnCaf2TgHvn4Qal4G7UdaF8vGBBl/E38hnIR/lU+ZNecMR3v+5tjEm9maXIHPCg9hmDXbNCbo+PvL3Vx9Rp6IlAQ+AOrhfID0V9Xfc3MdJgCO7oNJPTmaLPRPepgdC/cxzLrqMyboZNmcU0QGZLcAf+bJwGvAd6p6PtAQWJ2DZZi8lJwIn/WBg9uYdt5L7KCCteAxJkhld8U/VET2ZDFdgPuA0f6uUESKA5cA/QBUNRFI9Pf1xgOq8M1DEDsXuo7mjoY3cIfXMRljciy7xP8zcF028/x4muusAcThPLe3IbAIuE9Vj/jO5H6TGABQtapdWXrq97fgrwnQZjA0vMHraIwxZ8jvTtpybYUiTYE/gItVdb6IvAYcUtUnMnuNddLmnY/Gj6b3xkdYVfJS6t03DSL8/bG3McZrmXXS5sW7eBuwTVXnu+NTgcYexGGys3s1XTY+yUqtxg27+1rSNyZE5Pk7WVV3AltFJO1ZfJcDq/I6DpONI3th0g1odGHuTHqY61uc53VExphc4m87/tx2DzBRRGKAjUCuNhc1ZyitBU/8Torf+i2/VWnidUTGmFzkb3/8BXAerl6dkx/E8kxOVqqqS4BT6p1MPqAK3wyGzfPg+g/Akr4xIcffK/4vgIM4LXCs391QtmA0/DUe2jwEDXp4HY0xJgD8TfxVVPWagEZiPDfuow+5Zf0Q1pVoQ512w7wOxxgTIP7e3P1NROoHNBLjrb0b6LJ+GOu0Cj3j+lsLHmNCmL9X/K2BfiKyCXsQS+hJOASTbyI6KoqBRwfTpUUtryMyxgSQv4m/fUCjMN5JTYFpd8De9RTpM4Ofz7nE64iMMQHm1/d5Vd0MlMTpvuE6oKRbZoLd/z0L676D9i+BJX1jwoJfiV9E7gMmAuXdv49F5J5ABmbywPKpMO9/0KQfNLvd62iMMXnE36qe24AWaR2pichLwO/AG4EKzATYjqUkThvEktTz+SapH8PtKVrGhA1/m24IkOIznuKWmWB0ZA980pu9qUUYlHgfH/25w+uIjDF5yN8r/rHAfBGZ7o53AcYEJiQTUClJ8FlfOBLHjNpvsX95YXugijFhxt9HL/5PRObgNOsU4FZVXRzIwEyAfP+40x1D19H8p2F3/uN1PMaYPJdl4heR4qp6SERKA7HuX9q00qq6L7DhmVy1+GNY8B60utseqGJMGMvuin8S0BGnjx7fJ7aIO14jQHGZXPbexE/pt+4+thVrSs0rnvY6HGOMh7JM/Kra0f1/Tt6EYwIifhed1w1ht5ai594BLIr0qjduY0x+4G87/ln+lJl8KDkRpvSldMRRBiY/RIcWF3gdkTHGY9nV8RcECgNlRaQU/zbhLA5UCnBsJjf88Dhs+Z2YbmP4un53r6MxxuQD2X3nvxO4HyfJL+LfxH8IeCuAcZncsGSS079+q7vBkr4xxpVdHf9rwGsico+q2q90g8n2xfDl/VC9DdjNXGOMD3/b8b8hIvWAukBBn/IJgQrM5NwLU+fSZ3k/isSUpGSPcWA3c40xPvy9ufsUTr88bwDtgJFApwDGZXIqJZlLlg2lLAfpd+QeKFLW64iMMfmMv331dAcuB3aq6q1AQ6BAwKIyOfd/I7g4YgVPJPenfvN2XkdjjMmH/K0DOKaqqSKSLCLFgd3Yj7fyn1Uz4ddR0ORWRl430utojDH5lL+Jf6GIlATex2ndcxhYELCozGm56tWfSdm9li8LPEnhyk2dh6oYY0wmsk38IiLAC6p6AHhXRL4DiqvqsoBHZ/zyz644ZsSM4qhGU7jnBIiyWjhjTOayreNXVQVm+IzHWtLPP56YvpyR0e9RQ7bzUtFHoERlr0MyxuRz/t7c/UNEmgU0EpMjBRe9y7WRC3g55SZeftiehmmMyZ6/dfztgIEiEgscwe2dU1UbBCow44fNvzE0ajLfpzTjSJNBXkdjjAkS/ib+9gGNwpy++F0wpR+Rpatz9YDPubpgCa8jMsYECb+qelR1M3A2cJk7fNTf12ZGRCJFZLGIfHUmywlLKckwtT8kHIIbPgJL+saY03A6v9wdAjzqFkUDH5/huu8DVp/hMsLT/z3jPD7xuteggnWzbIw5Pf5etXfF6aLhCICqbgeK5XSlIlIFuBb4IKfLCFeTxr0Fv77G/DJd7fGJxpgc8TfxJ7rNOhVARIqc4XpHAY8AqZnNICIDRGShiCyMi4s7w9WFiL0buG7TCJak1qDf9q5eR2OMCVL+Jv7PROQ9oKSI3AH8hPMr3tMmIh2B3aq6KKv5VHW0qjZV1ablypXLyapCS9Ix+KwvkVHR3JN0P91b1PQ6ImNMkPK3W+ZXRORKnAew1AaeVNUfc7jOi4FOItIBp4vn4iLysarenMPlhYdvH4Fdyynceypzz7vS62iMMUHM747a3USf02Tvu5xHcW8Si8ilwGBL+tlYMgn+mgBtBoMlfWPMGcrumbvxuPX66Sfh/ICreECiMv/atRK+etB5kla7x7yOxhgTArJ79GKOW+74Q1XnAHMCuY6gdjwePusDBYtDtzEQEel1RMaYEOD3j7BEpLWI3OoOlxWRcwIXlkGV5e/0JWXPBsac9QQUq+B1RMaYEJHTH3DFcOY/4DJZ+fMD6h+YxSvJN/D8yjJeR2OMCSGe/IDLZGP7Yvj+MdYWb8X7qdfRq0VVryMyxoQQf1v1JKqqikhu/YDLZCbhIEzpB0XKUfvOiawvYlf7xpjclec/4DJZUIUv7oYDW6H7WLCkb4wJAC9+wGUys2A0rJ4JVz4DVVt4HY0xJkT5lfjdFjxz05K9iBQSkeqqGhvI4MLKP3/B949DrWuglT1JyxgTOP5W9Uzh5A7VUtwykxuOHWDf+N5sTynO8zH3QsQZPerAGGOy5G+GiVLVxLQRdzgmMCGFGVX48l6KH9/J3Yn3MGbRQa8jMsaEOH8Tf5yIdEobEZHOwJ7AhBRmFo6BVV8wq9JAllLbmm4aYwLO3+acA4GJIvKmO74N6BOYkMLIjmXw3WNw7hVc3es5NlgVjzEmD/jbqmcD0FJEigKiqvGBDSsMHI+HqbdC4dLQ9T2r1zfG5Bl/u2x4XkRKquphVY0XkVIi8myggwtZqk6Pm/s2QrcPoEhZryMyxoQRfy8z26vqgbQRVd0PdAhMSKFv2ocjYflnzKrQH6q39jocY0yY8TfxR4pIgbQRESkEFMhifpOZuLVcs+W//JZSl4Gb23kdjTEmDPl7c/djYJaIjMV5MEt/YELAogpVSQkwtT8aVYiHjt7FjS2qex2RMSYM+Xtzd6SILAOuwHn61ghV/T6gkYWiH4bBrhUU6TWF32td5XU0xpgwdTrP3P0O+A5ARC4WkbdU9a6ARRZqVn8Jf74Pre4GS/rGGA/5nfhFpBFwE3ADsAmYFqigQs6BrU6vm5UuhMuf8joaY0yYy+5h67WAG3ES/l7gU5x2/HZX0l8pyfD57ZCa4jw3N8p6ujDGeCu7Vj1rgMuB61S1taq+gdNBm/HT7NEPwdY/mFLxQShT0+twjDEm28TfDdgJzBaR90Xkcpybu8Yfsb9yyc7xTE25hKHrzvc6GmOMAbJJ/Ko6XVVvAM4H5gAPABVE5B0RsTuUWTm6D6bdwf6CVXgmuZ91vmaMyTf8bc55BJiI01FbaaAHMBT4IYCxBS+3q2UO76bs7T+yrNKFXkdkjDEnnHbPYKq6T1XfU9XLAhFQSFg01mm+efmTTkseY4zJR6xLyNy2e43T1XLNy5w2+8YYk89Y4s9NSQns/LA3e5Oieang/dbVsjEmX7LMlJt+Gs5ZCet5KOlORv91xOtojDEmQ3me+EXkbBGZLSKrRWSliNyX1zEExN8/wfx3+L1sd+ZqY2vFY4zJt/zusiEXJQMPqepfIlIMWCQiP6rqKg9iyR2H42DGf6B8XVrd8RYbogt6HZExxmQqz6/4VXWHqv7lDscDq4HKeR1HrlGFLwZBwkGnSwZL+saYfM7TOn4RqQ5cCMzPYNoAEVkoIgvj4uLyOjT/LXgf/v4BrhoBFep6HY0xxmTLs8TvPrj9c+B+VT2UfrqqjlbVpqratFy5cnkfoD92rXL62D/3Smg+wOtojDHGL54kfhGJxkn6E1U1OLt3Tkpg59ib2ZNcgBcL3AtiXRgZY4KDF616BBgDrFbV/+X1+nPN/43grIQNPJx0J+//ddjraIwxxm9eXPFfDNwCXCYiS9y/Dh7EkXMbZsPvbzK/7PX8Yk03jTFBJs+bc6rqPIK5a+ej+5ymm2Vr0WLAW2yIKex1RMYYc1q8aMcfvFThq/vhyB646ROwpG+MCULWZcPpWDoZVn0Blz0OlRp5HY0xxuSIJX5/7dsE3zwM1S6Gi+71OhpjjMkxS/z+SE1h85g+HDqeyitFHoSISK8jMsaYHLPE749fR1HtyDKGJd3KO4sTvY7GGGPOiCX+7OxYCrOfZ3nJy/laL7amm8aYoGeterKSdAymDYAi5ag/4AM2FC7tdUTGGHPGLPFn5aenIW4N3DIdLOkbY0KEVfVkZsNsmP8ONL/TeX6uMcaECEv8GTm2H2YMgrK14IrhXkdjjDG5yhJ/BpaOvoOkQ7t4p/Qj9utcY0zIscSf3oppNNz/I68nd+WV5UW8jsYYY3KdJX5f8Tvh6wfZWrgu76V2saabxpiQZK160qjCzHsg6RhnD5zAurLneR2RMcYEhCX+NH9NcJ6de81LYEnfGBPCrKoHnA7Yvn8MzrnEnp1rjAl5lvhTU4gd05f44ym8Uug+iLBdYowJbZbl/nib6keWMjypr3XAZowJC+Gd+HevgVkjWF28DTP0EmvFY4wJC+F7czclGWYMhJgi1BnwIRuKlvc6ImOMyRPhm/jnvQrbF0OP8WBJ3xgTRsKzqmfHMvj5RajXHS7o4nU0xhiTp8Iv8Scfh+kDoXAZ6PCy19EYY0yeC7vE//Poh2D3Sj4qN9j62DfGhKXwSvyxv9J618d8knwpw9dU8ToaY4zxRPgk/qP7YNod7C9YhedS+lrTTWNM2AqPVj1pHbAd3k3Z239keaULvY7IGGM8Ex6Jf+GHsOYruOo5sKRvjAlznlT1iMg1IrJWRNaLyNCArmzXKqcDtpqXQ8tBAV2VMcYEgzxP/CISCbwFtAfqAjeJSN2ArCzpGEztDwWKQdd3rQM2Y4zBmyv+5sB6Vd2oqonAJ0DnQKxo/nuDIG414ys8ar/ONcYYlxeJvzKw1Wd8m1t2EhEZICILRWRhXFzc6a9FlZ92Fubt5E48s7pijoM1xphQ40XilwzK9JQC1dGq2lRVm5YrVy4HaxESmv6H/6bcZE03jTHGhxeterYBZ/uMVwG2B2JFI7rUY0SXeoFYtDHGBC0vrvj/BM4TkXNEJAa4EZjpQRzGGBOW8vyKX1WTReRu4HsgEvhQVVfmdRzGGBOuPPkBl6p+A3zjxbqNMSbcWcN2Y4wJM5b4jTEmzFjiN8aYMGOJ3xhjwoyonvLbqXxHROKAzTl8eVlgTy6Gk9csfu8Ec+xg8XstP8RfTVVP+QVsUCT+MyEiC1W1qddx5JTF751gjh0sfq/l5/itqscYY8KMJX5jjAkz4ZD4R3sdwBmy+L0TzLGDxe+1fBt/yNfxG2OMOVk4XPEbY4zxYYnfGGPCTEgn/jx9qLufRORDEdktIit8ykqLyI8i8rf7v5RbLiLyuhv/MhFp7POavu78f4tI3zyM/2wRmS0iq0VkpYjcF0zbICIFRWSBiCx143/aLT9HROa7sXzqdhmOiBRwx9e706v7LOtRt3ytiFydF/G7640UkcUi8lUQxh4rIstFZImILHTLguLccddbUkSmisga9z3QKpjiP0FVQ/IPp8vnDUANIAZYCtTNB3FdAjQGVviUjQSGusNDgZfc4Q7AtzhPLWsJzHfLSwMb3f+l3OFSeRR/RaCxO1wMWAfUDZZtcOMo6g5HA/PduD4DbnTL3wX+4w4PAt51h28EPnWH67rnVAHgHPdci8yjY/AgMAn4yh0PpthjgbLpyoLi3HHXPR643R2OAUoGU/wntiMvV5anGwatgO99xh8FHvU6LjeW6pyc+NcCFd3hisBad/g94Kb08wE3Ae/5lJ80Xx5vyxfAlcG4DUBh4C+gBc4vLKPSnzs4z41o5Q5HufNJ+vPJd74Ax1wFmAVcBnzlxhIUsbvriuXUxB8U5w5QHNiE2ygm2OL3/Qvlqh6/HuqeT1RQ1R0A7v/ybnlm25Avts2tOrgQ56o5aLbBrSpZAuwGfsS54j2gqskZxHIiTnf6QaAM3sU/CngESHXHyxA8sYPzfO0fRGSRiAxwy4Ll3KkBxAFj3aq2D0SkCMET/wmhnPj9eqh7PpfZNni+bSJSFPgcuF9VD2U1awZlnm6DqqaoaiOcq+fmQJ0sYsk38YtIR2C3qi7yLc4ijnwTu4+LVbUx0B64S0QuyWLe/BZ/FE417TuqeiFwBKdqJzP5Lf4TQjnx59lD3XPBLhGpCOD+3+2WZ7YNnm6biETjJP2JqjrNLQ6qbQBQ1QPAHJz615IikvZEOt9YTsTpTi8B7MOb+C8GOolILPAJTnXPqCCJHQBV3e7+3w1Mx/ngDZZzZxuwTVXnu+NTcT4IgiX+E0I58QfTQ91nAml39vvi1JunlfdxWwe0BA66XyW/B64SkVJuC4Kr3LKAExEBxgCrVfV/wbYNIlJOREq6w4WAK4DVwGygeybxp21Xd+D/1KmYnQnc6LacOQc4D1gQyNhV9VFVraKq1XHO5/9T1d7BEDuAiBQRkWJpwzjHfAVBcu6o6k5gq4jUdosuB1YFS/wnycsbCnn9h3NXfR1OHe7jXsfjxjQZ2AEk4Xzy34ZT7zoL+Nv9X9qdV4C33PiXA019ltMfWO/+3ZqH8bfG+Vq6DFji/nUIlm0AGgCL3fhXAE+65TVwkt96YApQwC0v6I6vd6fX8FnW4+52rQXa5/F5dCn/tuoJitjdOJe6fyvT3pPBcu64620ELHTPnxk4rXKCJv60P+uywRhjwkwoV/UYY4zJgCV+Y4wJM5b4jTEmzFjiN8aYMGOJ3xhjwowlfmOMCTOW+E3IEJEUt7vfFSLyZdoPtU7j9cNFZLA7/IyIXHGG8VQXkWNuv0Bp4yuye10Wy3tZRHamxWhMTkVlP4sxQeOYOn3wICLjgbuA53KyIFV9Mpdi2pAW05lS1YdF5EhuLMuEN7viN6Hqd9weD0WkqIjMEpG/xHkISOe0mUTkcXEeRvITUNunfJyIdHeHY0WkrDvcVETmuMNt3W8YS9zeGov5G5yI1HBf00xE+onIDPdbyiYRuVtEHnSn/yEipXNljxjjssRvQo6IROL0o5LWN1MC0FWdXiHbAf91+09pgtPnzYXA9UCz01zVYOAu94q+DXDMz/hq43Ryd6uq/ukW1wN64XRa9hxwVJ0eIH8H+pxmXMZkyRK/CSWF3Pr0vThPN/rRLRfgeRFZBvyE802gAk6ynq6qR9XpWvp0O/H7FfifiNwLlNR/+8TPSjmcTrxuVtUlPuWzVTVeVeNw+s3/0i1fjvPgHmNyjSV+E0rS6vir4TwW7y63vDdOwm3iTt+F04EZ+NcPejL/vlfSXoeqvgjcDhQC/hCR8/1Y1kGch3BcnK78uM9wqs94KnYvzuQyS/wm5KjqQeBeYLD77IASOA8wSRKRdjgfDAC/AF1FpJBbP39dJouMBZq4w93SCkWkpqouV9WXcHps9CfxJwJdcLrr7XWam2ZMrrArCROSVHWxiCzFqcOfCHwpIgtxupFe487zl4h86pZtBuZmsringTEi8hjOYybT3O9+kKTg9Mv+rZ+xHRHnaVo/Wisd4wXrltmYABHnmcRfqWq9XFzmcOCwqr6SW8s04ceqeowJnBSgRNoPuM6UiLwM3IzzrFdjcsyu+I0xJszYFb8xxoQZS/zGGBNmLPEbY0yYscRvjDFh5v8BUm6vsWFoLWUAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"accelApprox = [abs(grav(r)) for r in radius] #Note that we are only interested in the size of the acceleration here\n",
"error = 0\n",
"for i in range(len(radius)):\n",
" error += abs(accelApprox[i] - acceleration[i]) #How much the line misses by at every point\n",
"print(\"Total error = {}\".format(error))\n",
"\n",
"plt.plot(radius/1000,acceleration, label=\"Using data\", linestyle=\"\", marker=\"o\", markersize=2)\n",
"plt.plot(radius/1000,accelApprox, label=\"Using approximation\")\n",
"plt.xlabel(\"Radius [km]\")\n",
"plt.ylabel(\"Acceleration [m/s^2]\")\n",
"plt.title(\"Acceleration using the data and the approximation\")\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is very little difference, which is the goal. This function for gravitational acceleration works for the distances in between the points in our dataset, *and* the ones outside. If Bruce was further out than the radius of the Earth (above the ground), the function would give the acceleration using the formula $\\frac{GM}{r^2}$ with the total mass of the Earth as M. This means that I can find the acceleration outside the Earth and all over the insides of the Earth.\n",
"\n",
"So far I have looked at positive distances and positve accelerations for the sake of seing how their sizes relate. From now on I will include the direction of gravity in the calculations. When Bruce is above the center, gravity will point down, and when he is below the center, gravity will point up. The sign of gravity will be the opposite of the sign of his height."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rads = np.linspace(-radius[-1]*1.5,radius[-1]*1.5,10000)\n",
"accs = np.array([grav(i) for i in rads])\n",
"\n",
"plt.plot(rads/1000,accs)\n",
"plt.xlabel(\"Height above center [km]\")\n",
"plt.ylabel(\"Acceleration [m/s^2]\")\n",
"plt.title(\"The gravitational acceleration with changing direction\")\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With the function for gravitational acceleration, I am ready to start calculating the movement."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Calculating movement under the effect of a variable gravity"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I will first need to define some parameters. I found that 10000 steps of 1 second gives good accuracy and speed for the purpose of this narrative."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"n = 10000 #number of steps in our calculation\n",
"dt = 1 #number of seconds each step takes"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Bruce's position will be starting at the surface of the Earth (at a heigh equal to the Earth's radius), and will then decrease as he gets closer to the center, reaching negative values when he is below the center.\n",
"\n",
"His velocity starts at 0m/s and will then decrease as he accelerates downward.\n",
"\n",
"These arrays will be filled with the results of the calculations as I use the Euler-Cromer method, and will be used for plotting."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"positions = np.zeros(n)\n",
"positions[0] = earthRadius #You can change this initial height to see how the fall would look like from outer space for example\n",
"\n",
"#This is redundant, as the array is all zeroes. However, you can change this value to see how that changes the results\n",
"startingVelocity = 0\n",
"velocities = np.zeros(n)\n",
"velocities[0] = startingVelocity\n",
"\n",
"accelerations = np.zeros(n)\n",
"\n",
"times = np.linspace(0,n*dt,n)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I have the initial conditions and function for acceleration in order, so all that's left is using the Euler-Cromer method to find the positions, velocities and accelerations of the movement over time:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"for i in range(n-1):\n",
" accelerations[i] = grav(positions[i])\n",
" velocities[i+1] = velocities[i] + accelerations[i]*dt\n",
" positions[i+1] = positions[i] + velocities[i+1]*dt\n",
"accelerations[n-1] = grav(positions[n-1]) #The acceleration at the end is not calculated during the loop"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I use the Euler-Cromer method due to the fact that there is no simple way to get a function for the position. I have no way of finding the exact position and velocity that we will have in the future, so instead I find the acceleration right now and use that to find the velocity Bruce would have after a small time step if the acceleration was constant (which it pretty much is over a small time step). Using this velocity I find the position he would have after a small time step if velocity was constant (which it pretty much is over a small time step). With enough of these time steps I can approximate a movement with a variable acceleration and velocity over a longer period of time."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I can plot the results side by side in subplots:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(19, 4))\n",
"plt.subplot(131)\n",
"plt.plot(times,positions/1000,color=\"blue\")\n",
"plt.xlabel(\"Time [s]\")\n",
"plt.ylabel(\"[km]\")\n",
"plt.title(\"Position\")\n",
"plt.grid()\n",
"\n",
"plt.subplot(132)\n",
"plt.plot(times,velocities,color=\"orange\")\n",
"plt.xlabel(\"Time [s]\")\n",
"plt.ylabel(\"[m/s]\")\n",
"plt.title(\"Velocity\")\n",
"plt.grid()\n",
"\n",
"plt.subplot(133)\n",
"plt.plot(times,accelerations,color=\"green\")\n",
"plt.xlabel(\"Time [s]\")\n",
"plt.ylabel(\"[m/s^2]\")\n",
"plt.title(\"Acceleration\")\n",
"plt.grid()\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now I have all that we need to find out how long it takes to fall through the Earth. To find out the time it takes, I need to find out how long it takes to reach the first dip of the position graph, as that is the \"bottom\" of the Earth."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The time it takes to travel through the Earth is 38 minutes and 10 seconds.\n"
]
}
],
"source": [
"#In order to not find out the time of later dips, I only look at the positions up to a time of 3000, to be safe\n",
"minIndex = np.argmin(positions[:3000]) #Index of the lowest value of positions, when we are at the opposite end of the Earth\n",
"minutes = times[minIndex]/60\n",
"exSeconds = times[minIndex]%60\n",
"print(\"The time it takes to travel through the Earth is {:.0f} minutes and {:.0f} seconds.\".format(minutes,exSeconds))\n",
"#time uses seconds, so I divide by 60 to get minutes, and use %60 to get the remainder of the division"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It takes slightly over 38 minutes to fall through the Earth!\n",
"\n",
"As Bruce leaps into the tunnel, the entirety of the Earth is pulling him down, every atom of the Earth pulling at every atom in him. While he is in the first half of the tunnel, the traitorous parts of the Earth above him start pulling him up again, while the dense and strong core is getting ever closer to Bruce, tightening it's grip. The approaching core barely wins out, making gravity increase slowly, until gravity is at it's strongest right at the edge of the outer core. But then Bruce enters the core, making the parts of the core above him start working against the dwindling rest, resulting in gravity slowly dissipating until he reaches the center. Then, at the very center of the Earth, Bruce is being pulled in every direction equally, by the super dense core, the massive mantle, even by the ocean-filled plasitc. For a single moment in time, everything cancels itself out, as essentially nothing is trying to move Bruce anywhere, except for his blistering speed. Following this, everything happens in reverese, as if someone turned the Earth upside-down and rewinded reality.\n",
"\n",
"With about 22 minutes to spare, Bruce would have plenty of time to make his meeting with Antoni!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The Payoff: Analyzing our results"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The time it takes to fall is not the only thing the calculations found."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The highest speed reached during the fall is 9920 m/s.\n"
]
}
],
"source": [
"topSpeed = np.amax(velocities) #The highest value in velocities\n",
"print(\"The highest speed reached during the fall is {:.0f} m/s.\".format(topSpeed))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On Bruce's way down he reach a top speed of 9,920 m/s. That is equal to 35,712 kilometers per hour, or 22,190 miles per hour. That is only slightly slower than the fastest manned object, the Apollo 10, which reached a top speed of 11,107 m/s when returning from the Moon. It is also a fair bit faster than the typical speed of the ISS and other satellites orbiting the Earth, which travel at around 7,700 m/s (which is about the speed he would reach if the Earth had a constant density).\n",
"\n",
"To better look at how position, velocity and acceleration change in relation to each other throughout the fall, I normalize the arrays by dividing each array by its greatest value and then show them in the same plot. This means that the y-axis only shows how the different sizes relate to themselves. The advantage is that it's then easer to see how one graph affects the shape of the other, even if we don't see the actual values."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(19, 4))\n",
"plt.plot(times,positions/(np.amax(positions)),label=\"Position\")\n",
"plt.plot(times,velocities/(np.amax(velocities)),label=\"Velocity\")\n",
"plt.plot(times,accelerations/(np.amax(accelerations)),label=\"Acceleration\")\n",
"\n",
"plt.xlabel(\"Time [s]\")\n",
"plt.title(\"Normalized graphs for position, velocity and acceleration\")\n",
"plt.legend()\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With nothing stopping him, Bruce would fall all the way through the Earth and then back again, and then back again and so on. Given that gravity is a conservative force, it makes sense that he would never stop moving, but rather fall back and forth around the center.\n",
"\n",
"When he reaches the center (position=0), acceleration is also 0. This is when he reaches his top velocity, as after this point gravity makes the speed decrease.\n",
"\n",
"Gravity is almost constant close to the surface, which can also be seen here. This near constant gravity near the surface is what makes the velocity change so linearly between the sharper turns. The sharp turns of the velocity is due to gravity switching direction.\n",
"\n",
"Bruce would have to be picked out of the air when he arrives floating upside-down on the South-Pole, as he would otherwise fall staright back, trapping him in an eternal fall, the only escape being death, or getting picked up later, whichever works. Despite being affected by an ever-changing force and travelling at blistering speeds, Bruce would not be able to feel much happening at all during the fall. Without any air or ground to push against the force of gravity, he would simply float weightlessly like an astronaut in space, with the Earth's innards moving past him like a blur."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Summary and Conclustion"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using a model of a perfectly spherical Earth with a density given by the Preliminary Reference Earth Model, with no air resistance and no rotation I found that it would take 38 minutes and 10 seconds to fall through the entire Earth, with a top speed of 9,920 m/s along the way.\n",
"\n",
"One would fall back and forth, reaching the same height each time. The model also showed that acceleration would initially increase a little before decreasing nearly linearly while falling towards the center.\n",
"\n",
"These are, of course, estimates. A more accurate picture of a fall through the Earth could include a more accurate density model, air resistance, the coriolis effect, or an earth that is not perfectly spherical. Air resistance would slow down the falling object, and the coriolis effect could make the fall happen in an arch. More accurate models of the Earth's density and shape would not change the behaviour of the fall much, but would provide greater accuracy.\n",
"\n",
"Even though you will probably not be falling through the Earth at any time soon, these calculations can be useful in other places. If one wanted to fly a spacecraft into a gaseous planet, one would have to look at how it would fall under the variable gravity while moving through the gases. One might even want to dig through other celestial objects, like moons or asteroids, where these kinds of calculations could be useful."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Sources and Inspiration"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Preliminary Reference Earth Model - http://ds.iris.edu/ds/products/emc-prem/\n",
"\n",
"The speeds of different things - https://en.wikipedia.org/wiki/Orders_of_magnitude_(speed)\n",
"\n",
"How Long To Fall Through The Earth? - minutephysics - https://www.youtube.com/watch?v=urQCmMiHKQk\n",
"\n",
"Gravity of Earth - https://en.wikipedia.org/wiki/Gravity_of_Earth\n",
"\n",
"Structure of the Earth https://en.wikipedia.org/wiki/Structure_of_the_Earth"
]
}
],
"metadata": {
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"display_name": "Python 3",
"language": "python",
"name": "python3"
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"name": "ipython",
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"file_extension": ".py",
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"name": "python",
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