From 7f86963366887be32b37754b6c9c65b977abc3a5 Mon Sep 17 00:00:00 2001 From: Max Perraudin Date: Fri, 8 May 2020 17:52:10 +0200 Subject: [PATCH] Updated Asteroid_trajectory.py, works with the asteroid 2007 VW266 --- Asteroid_trajectory.py | 195 +++++++++++++++-------------------------- README.md | 7 +- main_GUI.py | 10 +-- screen.png | Bin 168941 -> 180717 bytes 4 files changed, 79 insertions(+), 133 deletions(-) diff --git a/Asteroid_trajectory.py b/Asteroid_trajectory.py index 3c37a9a..8e5322c 100644 --- a/Asteroid_trajectory.py +++ b/Asteroid_trajectory.py @@ -4,7 +4,7 @@ class planet(object): - def __init__(self, m, a, i, e, Omega, omega, M0, t0=0): + def __init__(self, m, a, i, e, Omega, omega, M0): self.m = m self.a = a self.i = np.radians(i) @@ -12,7 +12,6 @@ def __init__(self, m, a, i, e, Omega, omega, M0, t0=0): self.Omega = np.radians(Omega) self.omega = np.radians(omega) self.M0 = np.radians(M0) - self.t0 = t0 self.T = np.sqrt((4 * np.pi ** 2) / (G * (m_sun + self.m)) * self.a ** 3) self.w = 2 * np.pi / self.T @@ -28,7 +27,7 @@ def orbitalparam2vectorList(self, timevector): def completeOrbitalElem2Vector(self, t): self.n = k / np.sqrt(self.a ** 3) - self.M = self.M0 + self.n * (t - self.t0) + self.M = self.M0 + self.n * (t) self.E = self.newton(self.keplerEquation, self.M0) self.bigX = self.a * (np.cos(self.E) - self.e) self.bigY = self.a * np.sqrt(1 - self.e ** 2) * np.sin(self.E) @@ -44,7 +43,8 @@ def completeOrbitalElem2Vector(self, t): self.rotation1(-self.i)), self.rotation3(-self.omega)), np.array([[self.bigXdot], [self.bigYdot], [0]])) - return [self.position[0, 0], self.position[1, 0], self.position[2, 0]] + return [self.position[0, 0], self.position[1, 0], self.position[2, 0], + self.velocity[0, 0], self.velocity[1, 0], self.velocity[2, 0]] def rotation1(self, theta): return np.array([[1, 0, 0], @@ -67,106 +67,76 @@ def keplerEquation(self, E): return E - self.e * np.sin(E) - self.M -class twoBody(): # Only the Sun exerts it's influence on the body. - @classmethod - def func(cls, t, y): # using the state space representation of the equation of motion - y0 = y[3] # velocity on x - y1 = y[4] # velocity on y - y2 = y[5] # velocity on z - r = np.sqrt(y[0] ** 2 + y[1] ** 2 + y[2] ** 2) # norm of the vector r - y3 = -G * (m_sun + m_object) / (r ** 3) * \ - y[0] # equation of motion on x - y4 = -G * (m_sun + m_object) / (r ** 3) * \ - y[1] # equation of motion on y - y5 = -G * (m_sun + m_object) / (r ** 3) * \ - y[2] # equation of motion on z - return np.array([y0, y1, y2, y3, y4, y5]) - - @classmethod - def RK4(cls, time_vector, initial_conditions, h): - # Definition of the Runge-Kutta method at the order 4 - results = [] - yin = initial_conditions - results.append(yin) # set the first value to the initial conditions - for t in time_vector[1:]: - k1 = cls.func(t, yin) - k2 = cls.func(t + h / 2, yin + h / 2 * k1) - k3 = cls.func(t + h / 2, yin + h / 2 * k2) - k4 = cls.func(t + h, yin + h * k3) - yin = yin + h / 6 * (k1 + 2 * k2 + 2 * k3 + k4) - # each value calculated for given t is added to the list - results.append(yin) - return np.array(results) +class MultiBody(): + ''' This class groups together 3 functions : + - the Equation of Motion, which is the core of the program + - The Ruunge Kutta 4 integrator + - The Forward Backward method''' @classmethod - def forward_backward(cls, time_vector, initial_conditions, h): - # allows for error computation. we just need to compute the difference at the starting point - # call RK4 in forward movement - y_forward = cls.RK4(time_vector, initial_conditions, h) - new_y0 = y_forward[-1] # new initial conditions - y_backward = cls.RK4(np.flip(time_vector), - new_y0, -h) # call RK4 backwards - return y_forward, y_backward - + def func(cls, t, y, planets): + ''' State space representation of the Equation of Perturbated Motion + Takes into account every selected planet.''' -class threeBody(): - @classmethod - def func(cls, t, y, planet): y0 = y[3] # velocity on x y1 = y[4] # velocity on y y2 = y[5] # velocity on z r = np.sqrt(y[0] ** 2 + y[1] ** 2 + y[2] ** 2) # norm of the vector r - pos = planet.completeOrbitalElem2Vector(t) - # delta is the difference between r and position_Jupiter (distance between the asteroid and jupiter) - delta = np.sqrt((y[0] - pos[0]) ** 2 + (y[1] - pos[1]) ** 2 + (y[2] - pos[2]) ** 2) - # equation of motion on x - y3 = -G * (m_sun + m_object) / (r ** 3) * y[0] \ - - G * planet.m * ((y[0] - pos[0]) / (delta ** 3) + pos[0] / np.linalg.norm(pos) ** 3) - # equation of motion on y - y4 = -G * (m_sun + m_object) / (r ** 3) * y[1] \ - - G * planet.m * ((y[1] - pos[1]) / (delta ** 3) + pos[1] / np.linalg.norm(pos) ** 3) - # equation of motion on z - y5 = -G * (m_sun + m_object) / (r ** 3) * y[2] \ - - G * planet.m * ((y[2] - pos[2]) / (delta ** 3) + pos[2] / np.linalg.norm(pos) ** 3) + y3 = -G * (m_sun + float(asteroid.m)) / (r ** 3) * y[0] + y4 = -G * (m_sun + float(asteroid.m)) / (r ** 3) * y[1] + y5 = -G * (m_sun + float(asteroid.m)) / (r ** 3) * y[2] + for planet in planets: + pos = planet.completeOrbitalElem2Vector(t) + # delta is the difference between 'r' and 'pos', it is the distance between asteroid & planet + delta = np.sqrt((y[0] - pos[0]) ** 2 + (y[1] - pos[1]) + ** 2 + (y[2] - pos[2]) ** 2) + # equation of motion on x + y3 += - G * planet.m * ((y[0] - pos[0]) / (delta ** 3) + pos[0] / np.linalg.norm(pos) ** 3) + # equation of motion on y + y4 += - G * planet.m * ((y[1] - pos[1]) / (delta ** 3) + pos[1] / np.linalg.norm(pos) ** 3) + # equation of motion on z + y5 += - G * planet.m * ((y[2] - pos[2]) / (delta ** 3) + pos[2] / np.linalg.norm(pos) ** 3) return np.array([y0, y1, y2, y3, y4, y5]) @classmethod - def RK4(cls, time_vector, initial_conditions, h, planet): - # Definition of the Runge-Kutta method at the order 4 + def RK4(cls, time_vector, initial_conditions, h, planets): + ''' Runge kutta 4 integrator : + takes a time vector, an initial conditions vector, a step and a list of planets + as an input, and outputs the list of positions and accelerations''' + results = [] yin = initial_conditions results.append(yin) # set the first value to the initial conditions - for i in range(1, len(time_vector[1:])): - k1 = cls.func(time_vector[i], yin, planet) - k2 = cls.func(time_vector[i] + h / 2, yin + h / 2 * k1, planet) - k3 = cls.func(time_vector[i] + h / 2, yin + h / 2 * k2, planet) - k4 = cls.func(time_vector[i] + h, yin + h * k3, planet) + for t in time_vector[1:]: + k1 = cls.func(t, yin, planets) + k2 = cls.func(t + h / 2, yin + h / 2 * k1, planets) + k3 = cls.func(t + h / 2, yin + h / 2 * k2, planets) + k4 = cls.func(t + h, yin + h * k3, planets) yin = yin + h / 6 * (k1 + 2 * k2 + 2 * k3 + k4) # each value calculated for given t is added to the list results.append(yin) return np.array(results) @classmethod - def forward_backward(cls, time_vector, initial_conditions, h, planet): - # allows for error computation. we just need to compute the difference at the starting point - y_forward = cls.RK4(time_vector, initial_conditions, h, planet) # call RK4 in forward movement + def forward_backward(cls, time_vector, initial_conditions, h, planets): + ''' Calls the RK4 integrator a first time from the initial condition, + and a second time from the results, thus going back to the very + first starting point. By computing the difference between the results + and the initital conditions at the starting point, we obtain the + errors due to the integration''' + + y_forward = cls.RK4(time_vector, initial_conditions, h, planets) # call RK4 forwards new_y0 = y_forward[-1] # new initial conditions - y_backward = cls.RK4(np.flip(time_vector), new_y0, -h, planet) # call RK4 backwards + y_backward = cls.RK4(np.flip(time_vector), new_y0, - h, planets) # call RK4 backwards + return y_forward, y_backward def extract_vectors(results): - # takes the list of outputs from RK4 and extracts a list of position and velocity vectors - r_list = [] - r_dot_list = [] - for i in range(len(results)): - r = [] - r_dot = [] - for j in range(0, 3): - r.append(results[i][j]) - r_dot.append(results[i][j + 3]) - r_list.append(r) - r_dot_list.append(r_dot) + '''takes the list of outputs from RK4 and extracts a list of position and velocity vectors''' + + r_list = [[results[i][j] for j in range(0, 3)] for i in range(len(results))] + r_dot_list = [[results[i][j + 3] for j in range(0, 3)] for i in range(len(results))] return r_list, r_dot_list @@ -215,68 +185,43 @@ def plotOrbitalVariation(a, e, i, t): # initial variables m_sun = 1 # mass of the Sun -m_object = 0 # mass of the object studied -a = (5.2 ** 3 / (3) ** 2) ** (1 / 3) # semi-major axis G = 0.000295824 # gravitation constant expressed in our own system of units k = np.sqrt(G) mu = G * m_sun -# definition of Jupiter orbital parameters +# Creation of the each planet from their orbital parameters at J2000 +# mercury=planet(m_sun / 6023622.047, 0.38709893, 7.00487, 0.20563069, 48.33167, 77.45645, 126.464) +# venus=planet(m_sun / 408544.7263, 0.72333199, 3.39471, 0.00677323, 76.68069, 131.53298, -26.23394) +# earth=planet(m_sun / 332965.0462, 1, 0.00005, 0.01671022, 348.73936, 102.94719, -351.2222) +# mars=planet(m_sun / 3098854.873, 1.52366231, 1.85061, 0.09341233, 49.57854, 336.04084, -30.16606) jupiter = planet(m_sun / 1047.348625, 5.202603, 1.303, 0.048498, 100.46, -86.13, 20.0) - -# initial conditions of the asteroid [pos x, pos y, pos z, v x, v y, v z] -init_state = np.array([a, 0.0, 0.0, 0.0, k / np.sqrt(a), 0.0]) +# saturn=planet(m_sun / 3498.926925, 9.5370703, 2.484, 0.054151, 113.72, 92.43, -156.2) +# uranus=planet(m_sun / 22906.30182, 19.19126393, 0.76986, 0.04716771, 74.22988, 170.96424, 68.0392) +# neptune=planet(, m_sun / 19418.13922, 30.06896348, 1.76917, 0.00858587, 131.72169, 44.97135, 128.19) # integration parameters -tf = 40000 # final time -ti = 0 # starting time +tf = 50000 # Number of days +ti = 5055.5 # starting time (Epoch) step = 1 # step wanted # creation of the list containing each value of time -time = np.arange(ti, tf + step, step) - -# ============================================================================================= -# Start of the computation for 2 body problem -# ============================================================================================= -''' -start_time = chrono.time() -forward, backward = twoBody.forward_backward(time, init_state, step) - -# computation of the error between forward and backward -err_x = 150e6 * abs(forward[0][0] - backward[-1][0]) -err_y = 150e6 * abs(forward[0][1] - backward[-1][1]) -print(' Error on x : ', err_x, ' km\n', 'Error on y : ', err_y, ' km') - -# TODO: Add automatic step adjustment in function of the error ? +time = np.arange(ti, tf + step + ti, step) -# plot of the trajectory -plt.plot(forward[:, 0], forward[:, 1], 'o', color='red', markersize=1) -plt.axis('equal') -plt.title('Unperturbed trajectory around the sun') -plt.show() - -# get the position and velocity from previous results -#r_list, rdot_list = extract_vectors(forward) - -# calculate the orbital parameters from the position and velocity -#a_list, e_list, i_list = orbital_parameters_list(r_list, rdot_list) - -# plot the orbital parameters -#plotOrbitalVariation(a_list, e_list, i_list, time) +# initial conditions of the asteroid [pos x, pos y, pos z, v x, v y, v z] +asteroid = planet(0, 5.454, 108.358, 0.3896, 276.509, 226.107, 146.88) +init_state = np.array(asteroid.completeOrbitalElem2Vector(ti)) -stop_time = chrono.time() -print("Computation time = ", stop_time-start_time, " seconds") -''' # ============================================================================================= # Start of the computation for 3 body problem # ============================================================================================= start_time = chrono.time() -forward2, backward2 = threeBody.forward_backward(time, init_state, step, jupiter) +forward2, backward2 = MultiBody.forward_backward(time, init_state, step, [jupiter]) # computation of the error between forward and backward -err_x2 = 150e6 * abs(forward2[0][0] - backward2[-1][0]) -err_y2 = 150e6 * abs(forward2[0][1] - backward2[-1][1]) -print(' Error on x : ', err_x2, ' km\n', 'Error on y : ', err_y2, ' km') +err_x = 150e6 * abs(forward2[0][0] - backward2[-1][0]) / 2 +err_y = 150e6 * abs(forward2[0][1] - backward2[-1][1]) / 2 +err_z = 150e6 * abs(forward2[0][2] - backward2[-1][2]) / 2 +print(' Error on x : ', err_x, ' km\n', 'Error on y : ', err_y, ' km\n', 'Error on z : ', err_z, ' km') # plot of the trajectory jup_param = jupiter.orbitalparam2vectorList(time) @@ -294,7 +239,7 @@ def plotOrbitalVariation(a, e, i, t): a_list, e_list, i_list = orbital_parameters_list(r_list, rdot_list) # plot the orbital parameters -plotOrbitalVariation(a_list, e_list, i_list, time[1:]) +plotOrbitalVariation(a_list, e_list, i_list, time) stop_time = chrono.time() print("Computation time = ", stop_time - start_time, " seconds") diff --git a/README.md b/README.md index 03e53da..580c6c8 100644 --- a/README.md +++ b/README.md @@ -6,7 +6,7 @@ This project is part of my CIRI (Cours d’Initiation à la Recherche et à l’ The objective is to model the trajectory of an asteroid in the solar system subject to perturbations from Jupiter. We then study the variations of the orbital parameters such as the semi-major axis, the eccentricity and the inclination after a few centuries. This allows us to visualize the resonances. -We went further by adding all the other planets in the solar system, which we can choose from using a Graphical User Interface. The orbital parameters of the asteroid are user-defined, as well as the integration parameters. +We went further by adding all the other planets in the solar system, which we can choose using a Graphical User Interface. The orbital parameters of the asteroid are user-defined, as well as the integration parameters. ## How to use @@ -47,7 +47,7 @@ If you want to re-run the simulation with other parameters, simply change the de - Asteroid parameters : - Circular orbit - User defined orbit with parameters - - User defined orbit with position and velocity + - User defined orbit with position and velocity (bugs) - Plot of the trajectory of every selected body in 3d - Plot of the orbital parameters changes due to perturbation (only if a planet has been selected) @@ -58,7 +58,8 @@ If you want to re-run the simulation with other parameters, simply change the de - Option to choose from simplified or accurate planet trajectory model - more integrators - input proofing and displaying errors instead of crashing the program -- Logging - Saving the results to a file for use in Excel for example - Improve Performance - re-write some functions in C++ to improve performance + +### Contributions are welcome ! \ No newline at end of file diff --git a/main_GUI.py b/main_GUI.py index f541e14..c48ae31 100644 --- a/main_GUI.py +++ b/main_GUI.py @@ -509,9 +509,9 @@ def Start(self): self.err_x = 150e6 * abs(self.forward[0][0] - self.backward[-1][0]) / 2 self.err_y = 150e6 * abs(self.forward[0][1] - self.backward[-1][1]) / 2 self.err_z = 150e6 * abs(self.forward[0][2] - self.backward[-1][2]) / 2 - self.fwbwOutputLabel.setText(f"Error on x: \n{str(round(self.err_x, 2))} km\n\n \ - Error on y: \n{str(round(self.err_y, 2))} km\n\n \ - Error on z: \n{str(round(self.err_z, 2))} km") + self.fwbwOutputLabel.setText("Error on x: \n" + str(round(self.err_x, 2)) + + " km\n\nError on y: \n" + str(round(self.err_y, 2)) + + "km\n\nError on z: \n" + str(round(self.err_z, 2)) + "km") self.results = self.forward # Store the results from the forward integration in a dedicated list else: # if the user did not ask for a fw-bw integration, then only compute the results. @@ -715,7 +715,7 @@ def get_init_state(self, t=0): initial position and velocity vector. All the values are read from the inputs.''' if ui.circularCheckBox.checkState(): # Circular initial orbit - self.a = float(ui.inputAsteroidSmAxis.text()) + self.a = float(ui.inputAsteroidSMaxis.text()) self.init_state = np.array([self.a, 0, 0, 0, k / np.sqrt(self.a), 0]) return self.init_state @@ -729,7 +729,7 @@ def get_init_state(self, t=0): return self.init_state else: # defined by orbital parameters - self.a = float(ui.inputAsteroidSmAxis.text()) + self.a = float(ui.inputAsteroidSMaxis.text()) self.i = np.radians(float(ui.inputInc.text())) self.e = float(ui.inputEcc.text()) self.Omega = np.radians(float(ui.inputLan.text())) diff --git a/screen.png b/screen.png index 608edff0b3a21f8329de9b53ef8c21a6e808a359..59c064daad41cbc628f4327d03780ccc1a27ee8f 100644 GIT binary patch literal 180717 zcmb5W2T)T{_b(c{G*J-{P(cw8sZvBino1F*Hv#EVLy;0ns3L+Oy$OWgd!$PV5fP9Q zItdUUAiYZoJ@5|teeZwYoi}&hV}{`*lbo~9*?X_Geq|A+p{7Vn#XuFeSKh+esF8N+gJN2zwL?oLeC1EK?>q{pDYaK~aU{D}XU~t#o*~R!kAlaZRfkc0g 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