{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction: Simulating Asteroid Impacts with a Poisson Process\n", "\n", "In this notebook, we will simulate impacts of near Earth asteroids into Earth using a Poisson process. Through this method, we can come up with a likely number of impacts during an individual's life and figure out how long it will be until the Earth is hit by a massive asteroid! " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2019-02-03T13:38:07.152343Z", "start_time": "2019-02-03T13:38:05.968588Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/vnd.plotly.v1+html": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/vnd.plotly.v1+html": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/vnd.plotly.v1+html": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import pandas as pd\n", "import numpy as np\n", "\n", "# Options for pandas\n", "pd.options.display.max_columns = 20\n", "pd.options.display.max_rows = 10\n", "\n", "# Display all cell outputs\n", "from IPython.core.interactiveshell import InteractiveShell\n", "InteractiveShell.ast_node_interactivity = 'all'\n", "\n", "# Interactive plotting\n", "import plotly.plotly as py\n", "import plotly.graph_objs as go\n", "from plotly.offline import iplot, init_notebook_mode\n", "init_notebook_mode(connected=True)\n", "\n", "import cufflinks as cf\n", "cf.go_offline(connected=True)\n", "cf.set_config_file(theme='pearl')\n", "\n", "# Used for calculating theoretical value\n", "from scipy.special import factorial" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data on Impacts\n", "\n", "The data on impact frequency, impact energy, and number of objects is from the NASA 2017 Report of the Near Earth Object Science Definition Team. It is available [online here](https://cneos.jpl.nasa.gov/doc/2017_neo_sdt_final_e-version.pdf).\n", "\n", "\n", "\n", "The average impact frequency for all asteriods is $1.66 x 10^{-9} yr^{-1}$. To get the rate per size category per year, we just multiple the impact frequency times the number of asteroids in the size category. \n", "\n", "According to the overall frequency rate, a single Near Earth Asteroid (NEA) will impact the Earth once in 600 million years. Or, if there are 600 million NEAs, there should be one collison every year. The impact frequency in a category is the rate is the Poisson equation. To get the expected number of impacts in a time period, we multiple the rate per year times the number of years. For example, we can use 100 years as a standard human lifetime and then find the number of expected asteriods in one human lifetime. We can also use the rates to find the expected waiting time between asteriod impacts in each class.\n", "\n", "### Acronyms\n", "\n", "* NEA: Near Earth Asteroid\n", "* NEO: Near Earth Object\n", "* PHA = Potentially Hazardous Asteroids" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "ExecuteTime": { "end_time": "2019-02-03T13:45:11.971911Z", "start_time": "2019-02-03T13:45:11.579117Z" } }, "outputs": [ { "data": { "text/html": [ "
\n", " | range_diameter | \n", "diameter | \n", "range_absolute_magnitude | \n", "absolute_magnitude | \n", "impact_energy | \n", "cumulative_number_greater | \n", "number | \n", "impact_frequency | \n", "undiscovered_fraction | \n", "undiscover_number | \n", "undiscovered_impact_frequency | \n", "
---|---|---|---|---|---|---|---|---|---|---|---|
0 | \n", ".0200–.0251 | \n", "0.0224 | \n", "25.75–26.25 | \n", "26.0 | \n", "4.523-01 | \n", "5220000.0 | \n", "2850000.0 | \n", "0.004730 | \n", "1.000 | \n", "2850000.0 | \n", "0.004730 | \n", "
1 | \n", ".0251–.0316 | \n", "0.0282 | \n", "25.25–25.75 | \n", "25.5 | \n", "9.02e-01 | \n", "2370000.0 | \n", "1350000.0 | \n", "0.002240 | \n", "1.000 | \n", "1350000.0 | \n", "0.002240 | \n", "
2 | \n", ".0316–.0398 | \n", "0.0355 | \n", "24.75–25.25 | \n", "25.0 | \n", "1.80e+00 | \n", "1020000.0 | \n", "526000.0 | \n", "0.000873 | \n", "0.999 | \n", "525000.0 | \n", "0.000872 | \n", "
3 | \n", ".0398–.0501 | \n", "0.0447 | \n", "24.25–24.75 | \n", "24.5 | \n", "3.59e+00 | \n", "493000.0 | \n", "263000.0 | \n", "0.000437 | \n", "0.997 | \n", "262000.0 | \n", "0.000435 | \n", "
4 | \n", ".0501–.0631 | \n", "0.0562 | \n", "23.75–24.25 | \n", "24.0 | \n", "7.16e+00 | \n", "230000.0 | \n", "116000.0 | \n", "0.000193 | \n", "0.994 | \n", "115000.0 | \n", "0.000191 | \n", "
\n", " | range_diameter | \n", "diameter | \n", "absolute_magnitude | \n", "impact_energy | \n", "number | \n", "impact_frequency | \n", "min_diameter | \n", "max_diameter | \n", "
---|---|---|---|---|---|---|---|---|
0 | \n", ".0200–.0251 | \n", "0.0224 | \n", "26.0 | \n", "4.523-01 | \n", "2850000.00 | \n", "4.730000e-03 | \n", ".0200 | \n", ".0251 | \n", "
1 | \n", ".0251–.0316 | \n", "0.0282 | \n", "25.5 | \n", "9.02e-01 | \n", "1350000.00 | \n", "2.240000e-03 | \n", ".0251 | \n", ".0316 | \n", "
2 | \n", ".0316–.0398 | \n", "0.0355 | \n", "25.0 | \n", "1.80e+00 | \n", "526000.00 | \n", "8.730000e-04 | \n", ".0316 | \n", ".0398 | \n", "
3 | \n", ".0398–.0501 | \n", "0.0447 | \n", "24.5 | \n", "3.59e+00 | \n", "263000.00 | \n", "4.370000e-04 | \n", ".0398 | \n", ".0501 | \n", "
4 | \n", ".0501–.0631 | \n", "0.0562 | \n", "24.0 | \n", "7.16e+00 | \n", "116000.00 | \n", "1.930000e-04 | \n", ".0501 | \n", ".0631 | \n", "
... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "
22 | \n", "3.16–3.98 | \n", "3.5500 | \n", "15.0 | \n", "1.80e+06 | \n", "36.80 | \n", "6.110000e-08 | \n", "3.16 | \n", "3.98 | \n", "
23 | \n", "3.98–5.01 | \n", "4.4700 | \n", "14.5 | \n", "3.59e+06 | \n", "20.40 | \n", "3.390000e-08 | \n", "3.98 | \n", "5.01 | \n", "
24 | \n", "5.01–6.31 | \n", "5.6200 | \n", "14.0 | \n", "7.16e+06 | \n", "12.20 | \n", "2.030000e-08 | \n", "5.01 | \n", "6.31 | \n", "
25 | \n", "6.31–7.94 | \n", "7.0800 | \n", "13.5 | \n", "1.43e+07 | \n", "2.03 | \n", "3.370000e-09 | \n", "6.31 | \n", "7.94 | \n", "
26 | \n", "7.94–10.0 | \n", "8.9100 | \n", "13.0 | \n", "2.85e+07 | \n", "2.02 | \n", "3.350000e-09 | \n", "7.94 | \n", "10.0 | \n", "
27 rows × 8 columns
\n", "\n", " | range_diameter | \n", "diameter | \n", "range_absolute_magnitude | \n", "absolute_magnitude | \n", "impact_energy | \n", "cumulative_number_greater | \n", "number | \n", "impact_frequency | \n", "undiscovered_fraction | \n", "undiscover_number | \n", "undiscovered_impact_frequency | \n", "min_diameter | \n", "max_diameter | \n", "
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | \n", ".0200–.0251 | \n", "0.0224 | \n", "25.75–26.25 | \n", "26.0 | \n", "4.523-01 | \n", "5220000.00 | \n", "2850000.00 | \n", "4.730000e-03 | \n", "1.0000 | \n", "2850000.000 | \n", "4.730000e-03 | \n", ".0200 | \n", ".0251 | \n", "
1 | \n", ".0251–.0316 | \n", "0.0282 | \n", "25.25–25.75 | \n", "25.5 | \n", "9.02e-01 | \n", "2370000.00 | \n", "1350000.00 | \n", "2.240000e-03 | \n", "1.0000 | \n", "1350000.000 | \n", "2.240000e-03 | \n", ".0251 | \n", ".0316 | \n", "
2 | \n", ".0316–.0398 | \n", "0.0355 | \n", "24.75–25.25 | \n", "25.0 | \n", "1.80e+00 | \n", "1020000.00 | \n", "526000.00 | \n", "8.730000e-04 | \n", "0.9990 | \n", "525000.000 | \n", "8.720000e-04 | \n", ".0316 | \n", ".0398 | \n", "
3 | \n", ".0398–.0501 | \n", "0.0447 | \n", "24.25–24.75 | \n", "24.5 | \n", "3.59e+00 | \n", "493000.00 | \n", "263000.00 | \n", "4.370000e-04 | \n", "0.9970 | \n", "262000.000 | \n", "4.350000e-04 | \n", ".0398 | \n", ".0501 | \n", "
4 | \n", ".0501–.0631 | \n", "0.0562 | \n", "23.75–24.25 | \n", "24.0 | \n", "7.16e+00 | \n", "230000.00 | \n", "116000.00 | \n", "1.930000e-04 | \n", "0.9940 | \n", "115000.000 | \n", "1.910000e-04 | \n", ".0501 | \n", ".0631 | \n", "
... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "
22 | \n", "3.16–3.98 | \n", "3.5500 | \n", "14.75–15.25 | \n", "15.0 | \n", "1.80e+06 | \n", "77.50 | \n", "36.80 | \n", "6.110000e-08 | \n", "0.0221 | \n", "0.081 | \n", "1.350000e-09 | \n", "3.16 | \n", "3.98 | \n", "
23 | \n", "3.98–5.01 | \n", "4.4700 | \n", "14.25–14.75 | \n", "14.5 | \n", "3.59e+06 | \n", "40.70 | \n", "20.40 | \n", "3.390000e-08 | \n", "0.0202 | \n", "0.410 | \n", "6.800000e-10 | \n", "3.98 | \n", "5.01 | \n", "
24 | \n", "5.01–6.31 | \n", "5.6200 | \n", "13.75–14.25 | \n", "14.0 | \n", "7.16e+06 | \n", "20.30 | \n", "12.20 | \n", "2.030000e-08 | \n", "0.0170 | \n", "0.021 | \n", "3.400000e-10 | \n", "5.01 | \n", "6.31 | \n", "
25 | \n", "6.31–7.94 | \n", "7.0800 | \n", "13.25–13.75 | \n", "13.5 | \n", "1.43e+07 | \n", "8.07 | \n", "2.03 | \n", "3.370000e-09 | \n", "0.0140 | \n", "0.030 | \n", "4.700000e-11 | \n", "6.31 | \n", "7.94 | \n", "
26 | \n", "7.94–10.0 | \n", "8.9100 | \n", "12.75–13.25 | \n", "13.0 | \n", "2.85e+07 | \n", "6.04 | \n", "2.02 | \n", "3.350000e-09 | \n", "0.0100 | \n", "0.020 | \n", "3.400000e-11 | \n", "7.94 | \n", "10.0 | \n", "
27 rows × 13 columns
\n", "