Using the REBOUND Kepler Solver

KeplerSolver.ipynb

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   "source": [
    "# Using the Kepler Solver in REBOUND"
   ]
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   "cell_type": "markdown",
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   "source": [
    "First, let's import REBOUND and a few wrapper functions from the ctypes library."
   ]
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     "text": [
      "Date on which REBOUND was compiled: Jul  8 2018 23:01:09.\n"
     ]
    }
   ],
   "source": [
    "import rebound\n",
    "import numpy as np\n",
    "from ctypes import c_double, byref, c_int\n",
    "print(\"Date on which REBOUND was compiled: {}.\".format(rebound.__build__))"
   ]
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   "cell_type": "markdown",
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   "source": [
    "Next up, we create a `Simulation` object. This is needed because the Kepler solver needs to know the gravitational constant (which is a property of the `Simulation` object and defaults to 1). "
   ]
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   "cell_type": "code",
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   "metadata": {},
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   "source": [
    "sim = rebound.Simulation()"
   ]
  },
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   "source": [
    "Next up, we create the particle we want to evolver with the Kepler solver. Only the x, y, z, and vx, vy, vz properties of this particle matter."
   ]
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   "cell_type": "code",
   "execution_count": 3,
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   "outputs": [],
   "source": [
    "p = rebound.Particle(x=1.,vx=1.)"
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "The mass of the particle is not used by the Kepler solver. It expects a mass as a separate argument when calling it (this allows you to use different coordinates systems). Here, we simply use:"
   ]
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   "cell_type": "code",
   "execution_count": 4,
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   "source": [
    "M = 1."
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "The last argument that we pass to the Kepler solver is the timestep. As a test, let's evolve for one full orbit. In units where $G=1$ and the mass in the system is $M=1$, an orbit takes $2\\pi$ time units."
   ]
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   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "dt = 2.*np.pi"
   ]
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   "metadata": {},
   "source": [
    "We can now finally call the Kepler solver with this command:"
   ]
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   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "rebound.clibrebound.reb_whfast_kepler_solver(byref(sim),byref(p),c_double(M),c_int(0),c_double(dt));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function will not return anything, but it will change the Particle that we pass it. To see the difference, let us print out the coordinates of `p`:"
   ]
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   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<rebound.Particle object, m=0.0 x=1.0000000000000044 y=0.0 z=0.0 vx=0.9999999999999991 vy=0.0 vz=0.0>\n"
     ]
    }
   ],
   "source": [
    "print(p)"
   ]
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   "cell_type": "markdown",
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   "source": [
    "As you can see we almost get exactly back what we put in, except a small difference at the 15th or 16th digit. This is because of floating point precision, which limits us to a relative precision of $\\approx 10^{-16}$. "
   ]
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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