def energy_graph_comparisson(updates):
"""Function used to generate a comparison graph between Euler's method and Beeman's
to show conservation (or not conservation) of energy in both methods
"""
system = SolarSystem(3600, 10.175 * 10**3, Options.NORMAL_RUN,
"CelestialObjects")
energy_1 = [system.get_energy()]
system2 = SolarSystem(3600, 10.175 * 10**3, Options.NORMAL_RUN,
"CelestialObjects")
energy_2 = [system2.get_energy()]
iterate = updates
iterations = [i * 3600 for i in range(iterate + 1)]
for i in range(iterate):
energy_1.append(system.update_beeman())
energy_2.append(system2.update_euler())
plt.xlabel('time(s)')
plt.ylabel('Energy [J]')
plt.plot(iterations, energy_1, iterations, energy_2)
plt.show()
class TestSolarSystem(unittest.TestCase):
def setUp(self):
"""Method that is executed begore each test and that loads all the systems used
"""
self.system_probe = SolarSystem(3600,10000,Options.PROBE_RUN,"CelestialObjects")
self.system = SolarSystem(3600,10000,Options.NORMAL_RUN,"CelestialObjects")
self.system_simple = SolarSystem(3600,10000,Options.NORMAL_RUN,"CelestialObjects")
planetA = CelestialBody("B",1,1,1,"Planet",1,10000,"blue")
star = CelestialBody("A",1,1,1,"Star",0,10000,"blue")
planets = [star,planetA]
self.system_simple.celestial_bodies = planets
self.system_simple.update_initial_acceleration()
def test_initial_accelerations(self):
"""Test used to check that the initial accelerations of the bodies of the systems are
not zero.
"""
for planet in self.system.celestial_bodies:
self.assertNotEqual(0.0,planet.acceleration[0])
self.assertEqual(0.0,planet.acceleration[1],planet.name)
for planet in self.system.celestial_bodies:
self.assertNotEqual(0.0,planet.acceleration[0])
if (planet.name!="Mars" and planet.name != "Probe"):
self.assertEqual(0.0,planet.acceleration[1],planet.name)
def test_potential_energy_simple(self):
"""Test used to check that the value of the potential energy for a siple system is calculated
correctly.
"""
expected_value = -CelestialBody.G
self.assertEqual(expected_value,self.system_simple.get_potential_energy())
def test_kinetic_energy_simple(self):
"""Test used to check that the value of the kinetic energy for a siple system is calculated
correctly.
"""
expected_value = 1/2 * 1 * CelestialBody.G
self.assertEqual(expected_value,self.system_simple.get_kinetic_energy())
def test_kinetic_energy(self):
"""Test used to check that the value of the kinetic energy of a system is calculated
correctly.
"""
expected_value = 0
for body in self.system.celestial_bodies:
expected_value+= 1/2 *body.mass * np.linalg.norm(body.velocity)**2
self.assertEqual(expected_value,self.system.get_kinetic_energy())
def test_potential_energy(self):
"""Test used to check that the value of the potential energy of a system is calculated
correctly.
"""
expected_value = 0
for bodyA in self.system.celestial_bodies:
for bodyB in self.system.celestial_bodies:
if bodyA.name != bodyB.name:
expected_value += -CelestialBody.G * bodyB.mass*0.5 *bodyA.mass/(np.linalg.norm(bodyB.position-bodyA.position))
self.assertEqual(expected_value,self.system.get_potential_energy())
def test_total_energy(self):
"""Test used to check that the value of the total energy of a system is calculated
correctly.
"""
potential = 0
for bodyA in self.system.celestial_bodies:
for bodyB in self.system.celestial_bodies:
if bodyA.name != bodyB.name:
potential += -CelestialBody.G * bodyB.mass*0.5 *bodyA.mass/(np.linalg.norm(bodyB.position-bodyA.position))
kinetic_energy = 0
for body in self.system.celestial_bodies:
kinetic_energy+= 1/2 *body.mass * np.linalg.norm(body.velocity)**2
self.assertEqual(potential+kinetic_energy,self.system.get_energy())
def test_distance_to_earth(self):
"""Test used to check that the initial distance between the probe and the Earth is correctly set
"""
expected_value = 6.371*10**6
self.assertEqual(expected_value,self.system_probe.distance_to_earth())
def test_euler(self):
"""Test used to check that Euler's method works appropiatley.
"""
planetA = CelestialBody("B",1,1,1,"Planet",1,10000,"blue")
star = CelestialBody("A",1,1,1,"Star",0,10000,"blue")
planetB = CelestialBody("B",1,2,1,"Planet",1,10000,"blue")
planetB.position = np.array([-1.0,0.0])
planetB.velocity = np.array([0.0,-planetA.velocity[1]])
system = SolarSystem(3600,1000,Options.NORMAL_RUN,"CelestialObjects")
system.celestial_bodies = [star,planetA,planetB]
system.update_initial_acceleration()
for i in range(100):
system.update_euler()
self.assertEqual(0.0,star.acceleration[0])
self.assertEqual(0.0,star.acceleration[1])
def test_beeman(self):
"""Test used to check that Beeman's method works appropiatley.
"""
planetA = CelestialBody("B",1,1,1,"Planet",1,10000,"blue")
star = CelestialBody("A",1,1,1,"Star",0,10000,"blue")
planetB = CelestialBody("B",1,2,1,"Planet",1,10000,"blue")
planetB.position = np.array([-1.0,0.0])
planetB.velocity = np.array([0.0,-planetA.velocity[1]])
system = SolarSystem(3600,1000,Options.NORMAL_RUN,"CelestialObjects")
system.celestial_bodies = [star,planetA,planetB]
system.update_initial_acceleration()
for i in range(100):
system.update_beeman()
self.assertEqual(0.0,star.acceleration[0])
self.assertEqual(0.0,star.acceleration[1])
def test_timeStep(self):
"""Test used to check that the variable time step is implemented.
"""
self.system_probe.update_beeman()
self.assertEqual(self.system_probe.time_step,20)
for i in range(1000):
self.system_probe.update_beeman()
self.assertEqual(self.system_probe.time_step,3600)
def test_search(self):
for body in self.system.celestial_bodies:
self.assertEqual(self.system.search_body(body.name).name,body.name)
def test_exception_search(self):
with self.assertRaises(ValueError) as context:
self.system.search_body("Probe")
self.assertTrue("The given name is not in the actual list of bodies" in str(context.exception))
def test_variable_time_step(self):
self.assertEqual(self.system_probe.time_step, 20)
self.system_probe.initial = False
self.system_probe.search_body("Probe").position = np.array([1000.0,0.0])
self.system_probe.update_beeman()
self.assertEqual(self.system_probe.time_step, 3600)