{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "dd43aab3-57f6-4c52-a9f2-34fcd2c77a42",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "696e6ca4-af8f-4288-911d-a4690cc8ac3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "r = a = 6945e3\n",
    "mu_e = 398600e9\n",
    "m=250"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b016073f-a560-4524-8718-3136c2a20428",
   "metadata": {},
   "source": [
    "# finding inclination"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2ec84963-2255-4d37-bc9b-d31bf61e92a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha_dot = 360/365.25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a7d243f6-5dfe-4905-978d-ff48eddab270",
   "metadata": {},
   "outputs": [],
   "source": [
    "def time(a, mu):\n",
    "    return 2*np.pi*np.sqrt(np.power(a, 3)/mu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "97a8ed9f-4635-4f5b-aa3c-d350533a7a94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.000099718506572"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hours = time(a, mu_e)/60/60\n",
    "24/hours"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2faaae5f-0dab-4e7f-9211-0674af454423",
   "metadata": {},
   "source": [
    "# worst case cross section"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "42e29e98-2f6c-4d60-8e24-d51e030b3aa7",
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = np.linspace(0, np.pi/8)\n",
    "\n",
    "# height and width of solar panels\n",
    "h_p = 6.6\n",
    "w_p = 2.2\n",
    "\n",
    "#height and width of bus\n",
    "h_b = 1.63\n",
    "w_b = 3.25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "caa03332-a9f5-4b7b-a77f-109405aa969a",
   "metadata": {},
   "outputs": [],
   "source": [
    "a_p = h_p*np.cos(theta) * w_p\n",
    "\n",
    "a_b = h_b * np.sin(theta) * w_b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "46899560-3013-4b54-9fc2-ffe3592b06bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.5"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ar = a_p + a_b\n",
    "plt.plot(np.degrees(theta), ar)\n",
    "\n",
    "max(ar)\n",
    "\n",
    "np.degrees(np.interp(max(ar), ar, theta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7f9f1d43-1a0b-44ec-b964-a98bf90f5528",
   "metadata": {},
   "outputs": [],
   "source": [
    "def change_in_alt(rho, s, cd, m, a):\n",
    "    frac = s*cd/m\n",
    "    return -2*np.pi*rho*frac*np.power(a, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "0a77b7a3-6948-456c-ac73-f4f549418a5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38449"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alt = 567e3\n",
    "i=0\n",
    "while alt >= 565e3:\n",
    "    alt = alt + change_in_alt(1.9e-13, max(ar), 2.2, m, alt)\n",
    "    i+=1\n",
    "i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "54b42ee3-a6e2-4e15-8544-b23e259d4c09",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.4561328639594"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(ar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "87f92c83-b971-4a4a-ac18-64ab23cde1e8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}