01 - Units and Quantities.ipynb

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    "AMUSE tutorial on units and quantities\n",
    "====================\n",
    "\n",
    "Here we will start up an AMUSE service in Jupyter notebook and run some example operations."
   ]
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    "%%capture _preamble\n",
    "!pip show amuse-framework || pip install amuse-framework\n",
    "# Make sure the required packages are installed"
   ]
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   "cell_type": "code",
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   "source": [
    "# Load in the amuse units module\n",
    "from amuse.units import units"
   ]
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   "source": [
    "# Declare some variables\n",
    "star_mass = 1 | units.MSun\n",
    "star_radius = 1 | units.RSun"
   ]
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    "# calculate surface escape speed\n",
    "# this requires the gravitational constant to be declared\n",
    "G = 6.67e-11 | units.m**3 * units.kg**-1 * units.s**-2\n",
    "velocity_escape = (2 * G * star_mass / star_radius).sqrt()"
   ]
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   "source": [
    "print(f\"The escape speed is {velocity_escape}\")"
   ]
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    "This looks weird, right?\n",
    "But it is the right answer.\n",
    "AMUSE will operate on \"lazy calculating\", meaning that it will only perform the actual calculation once it is explicitely asked for it.\n",
    "Now try converting the unit to something more readable."
   ]
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    "print(f\"The escape speed is: {velocity_escape.in_(units.kms)}\")"
   ]
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    "You may realise that you used the wrong value for the gravitational constant G.\n",
    "The values of the most relevant constants are stored in the AMUSE framework.\n",
    "They can be accessed by loading in the appropriate module."
   ]
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   "cell_type": "code",
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    "from amuse.units.constants import G\n",
    "vesc = (2*G*star_mass/star_radius).sqrt()\n",
    "print(f\"The escape speed is: {velocity_escape.in_(units.kms)}\")"
   ]
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   "source": [
    "You have now calculated the escape speed from the Solar surface."
   ]
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    "Assignments and questions:\n",
    "---------------\n",
    "\n",
    "### Assignment 1:\n",
    "Calculate the orbital velocity of the planet Earth in orbit around the Sun.\n",
    "\n",
    "### Assignment 2:\n",
    "Calculate the escape speed of the supermassive black hole in the Galactic center from the pericenter of S2 (the star famously used to characterize the central supermassive black hole).\n",
    "\n",
    "### Question 1:\n",
    "What is the range in velocities with which you expect an asteroids to hit the Earth's surface?\n",
    "Assume that there are asteroids with semimajor axes between 0 and 3.5 AU (the outer edge of the asteroid belt), with eccentricities between 0 and 0.4.\n",
    "Note that for an elliptic orbit, the peri- and apocentric distances are $(1\\pm e)a$, and the peri- and apocentric speeds are $\\sqrt{\\frac{(1\\pm e)\\cdot GM}{(1\\mp e)a}}$.\n",
    "Is the acceleration due to the Earth's gravitational well important?\n",
    "\n",
    "### Question 2:\n",
    "With a photospheric effective temporature of 5772K (see [Wikipedia](https://en.wikipedia.org/wiki/Sun)), what is the Sun's luminosity?\n",
    "*note here that the Stefan-Bolzmann constant in AMUSE is available in the units.constants package under the name of Stefan_hyphen_Boltzmann_constant.*\n",
    "\n",
    "Calculate the difference with the standard in AMUSE available solar luminosity (1 | units.LSun).\n",
    "Why are the two values different?\n",
    "\n",
    "If the discrepancy originates from the photospheric effective temperature from Wikipedia, what would be the correct temperature to match the Solar luminosity?"
   ]
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