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Author: devNull-bootloader

Orbital Mechanics.py

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+import math
+import matplotlib.pyplot as plt
+from matplotlib.animation import FuncAnimation
+
+# Constants
+G = 6.674e-11  # Gravitational constant
+dt = 3600*24  # Time step (seconds)
+
+# Inputs
+mass_star = 1.989e30  # Mass of the star (e.g. the Sun)
+mass_planet = 5.972e24  # Mass of the planet (e.g. the Earth)
+num_steps = 2000  # Number of simulation steps
+
+# Initial Conditions
+planet_position = [1.5e11, 0]     # Start at 1 AU (same as Earth)
+velocity = [3000, 25000]   # Initial velocity (m/s)
+star_position = [0, 0]  # Star is at the origin
+
+# Lists to store the path for plotting
+x_positions = []
+y_positions = []
+trail_positions = []
+trail_lines = []
+
+# Create the figure
+fig, ax = plt.subplots()
+planet_dot, = ax.plot([], [], 'bo')  # Planet as blue dot
+star_dot, = ax.plot(0, 0, 'yo', label='Star')  # Star as yellow dot
+orbit_path, = ax.plot([], [], 'b-', linewidth=0.5)  # Planet's full path
+ax.set_xlim(-3e11, 3e11)
+ax.set_ylim(-3e11, 3e11)
+ax.set_aspect('equal')
+ax.grid(True)
+ax.set_title("Orbital Animation")
+ax.set_xlabel("X position (m)")
+ax.set_ylabel("Y position (m)")
+ax.legend()
+
+def update(frame):
+    global planet_position, velocity, trail_lines
+
+    # Compute distance components
+    dx = star_position[0] - planet_position[0]
+    dy = star_position[1] - planet_position[1]
+    magnitude = math.sqrt(dx**2 + dy**2)
+
+    # Compute gravitational force
+    force = G * mass_star * mass_planet / magnitude**2
+
+    # Unit vector from planet to star
+    unit_vector = [dx / magnitude, dy / magnitude]
+
+    # Force vector
+    force_vector = [force * unit_vector[0], force * unit_vector[1]]
+
+    # Acceleration = F / m
+    acceleration = [force_vector[0] / mass_planet, force_vector[1] / mass_planet]
+
+    # Update velocity
+    velocity[0] += acceleration[0] * dt
+    velocity[1] += acceleration[1] * dt
+
+    # Update position
+    planet_position[0] += velocity[0] * dt
+    planet_position[1] += velocity[1] * dt
+
+    # Store position for full orbit
+    x_positions.append(planet_position[0])
+    y_positions.append(planet_position[1])
+
+    # Store position for fading trail
+    trail_positions.append(planet_position.copy())
+    max_trail_length = 100
+    if len(trail_positions) > max_trail_length:
+        trail_positions.pop(0)
+
+    # Remove previous trail lines
+    for line in trail_lines:
+        line.remove()
+    trail_lines = []
+
+    # Draw fading trail
+    for i in range(1, len(trail_positions)):
+        alpha = i / len(trail_positions)
+        line, = ax.plot(
+            [trail_positions[i-1][0], trail_positions[i][0]],
+            [trail_positions[i-1][1], trail_positions[i][1]],
+            color='blue',
+            alpha=alpha,
+            linewidth=2
+        )
+        trail_lines.append(line)
+
+    # Update planet and orbit
+    planet_dot.set_data([planet_position[0]], [planet_position[1]])
+    orbit_path.set_data(x_positions, y_positions)
+
+    return planet_dot, orbit_path, *trail_lines
+
+# Animate!
+ani = FuncAnimation(fig, update, frames=num_steps, interval=10, blit=False)
+plt.show()