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Author: devNull-bootloader

calculation of v1 and v2.py

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+import math
+import matplotlib.pyplot as plt
+import numpy as np
+
+# ========== Constants ==========
+mu_earth = 3.986e14  # gravitational constant × Earth’s mass
+r_earth = 6371e3      # Earth radius (m)
+
+# ========== Example orbits ==========
+r1 = r_earth + 200e3   # Low Earth Orbit (200 km)
+r2 = r_earth + 35786e3 # Geostationary Orbit (35,786 km)
+
+def hohmann_delta_v(r1, r2, mu=mu_earth):
+    # ========== Hohmann transfer Δv (two burns) ==========
+    v1 = math.sqrt(mu / r1)
+    v2 = math.sqrt(mu / r2)
+    a_transfer = (r1 + r2) / 2
+
+    v_perigee = math.sqrt(mu * (2/r1 - 1/a_transfer))
+    v_apogee = math.sqrt(mu * (2/r2 - 1/a_transfer))
+
+    delta_v1 = abs(v_perigee - v1)
+    delta_v2 = abs(v2 - v_apogee)
+    return delta_v1, delta_v2, delta_v1 + delta_v2
+
+dv1, dv2, total = hohmann_delta_v(r1, r2)
+print(f"Δv1 = {dv1/1000:.2f} km/s")
+print(f"Δv2 = {dv2/1000:.2f} km/s")
+print(f"Gesamtes Δv = {total/1000:.2f} km/s")
+
+def rocket_equation(delta_v, Isp=320, m0=1000):
+    g0 = 9.80665
+    mf = m0 * math.exp(-delta_v / (Isp * g0))
+    fuel_used = m0 - mf
+    return fuel_used, (fuel_used / m0) * 100
+
+fuel, percent = rocket_equation(total)
+print(f"Verbrauchtes Treibstoff: {fuel:.2f} kg ({percent:.1f}% von Gesamtmasse)")
+
+
+isp_values = np.linspace(200, 450, 100)
+
+
+fuel_list = []
+for i in isp_values:
+    f, _ = rocket_equation(total, Isp=i)
+    fuel_list.append(f)
+
+
+plt.figure(figsize=(8, 4))
+plt.plot(isp_values, fuel_list, color='blue', linewidth=2)
+plt.title(f'Treibstoff für LEO -> GEO Transfer ({int(total)} m/s)')
+plt.xlabel('Spezifischer Impuls (s)')
+plt.ylabel('Treibstoffmasse (kg)')
+plt.grid(True, linestyle='--', alpha=0.6)
+
+
+plt.scatter([320], [fuel], color='red', zorder=5)
+plt.text(330, fuel, f'Mein Satellit\n(Isp=320s, Treibstoff={int(fuel)}kg)', color='red')
+
+plt.show()

sim_v2.py

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+# Der Code ist in Englisch, da ich eher Englisch spreche.
+
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.animation import FuncAnimation
+
+# ================== CONSTANTS ==================
+mu = 3.986e14
+r_earth = 6.371e6
+g0 = 9.80665
+
+Isp = 320
+m0 = 1000
+
+r1 = 7e6
+r2 = 4.2e7
+
+# ================== HOHMANN TRANSFER ==================
+a_t = (r1 + r2) / 2
+e_t = (r2 - r1) / (r1 + r2)
+
+T1 = 2*np.pi*np.sqrt(r1**3 / mu)
+Tt = np.pi*np.sqrt(a_t**3 / mu)
+T2 = 2*np.pi*np.sqrt(r2**3 / mu)
+
+N1, Nt, N2 = 200, 300, 200
+
+# ================== ORBIT 1 ==================
+t1 = np.linspace(0, T1, N1)
+theta1 = 2*np.pi*t1/T1
+x1 = r1*np.cos(theta1)
+y1 = r1*np.sin(theta1)
+
+# ================== TRANSFER ORBIT ==================
+def kepler(M, e):
+    E = M.copy()
+    for _ in range(10):
+        E -= (E - e*np.sin(E) - M) / (1 - e*np.cos(E))
+    return E
+
+t_t = np.linspace(0, Tt, Nt)
+M = np.sqrt(mu/a_t**3) * t_t
+E = kepler(M, e_t)
+
+theta_t = 2*np.arctan2(
+    np.sqrt(1+e_t)*np.sin(E/2),
+    np.sqrt(1-e_t)*np.cos(E/2)
+)
+
+r_t = a_t * (1 - e_t*np.cos(E))
+x_t = r_t*np.cos(theta_t)
+y_t = r_t*np.sin(theta_t)
+
+# ================== ORBIT 2 ==================
+T2 = 2*T2
+t2 = np.linspace(0, T2, N2)
+theta2 = theta_t[-1] + 2*np.pi*t2/T2
+x2 = r2*np.cos(theta2)
+y2 = r2*np.sin(theta2)
+
+# ================== COMBINE ==================
+x = np.concatenate([x1, x_t, x2])
+y = np.concatenate([y1, y_t, y2])
+r = np.sqrt(x**2 + y**2)
+
+# ================== SPEED & ENERGY ==================
+v = np.zeros_like(r)
+
+v[:N1] = np.sqrt(mu / r1)
+v[N1:N1+Nt] = np.sqrt(mu * (2/r[N1:N1+Nt] - 1/a_t))
+v[N1+Nt:] = np.sqrt(mu / r2)
+
+energy = 0.5*v**2 - mu/r
+
+# ================== FIGURE ==================
+fig = plt.figure(figsize=(11, 6))
+gs = fig.add_gridspec(2, 2)
+
+ax_orbit = fig.add_subplot(gs[:, 0])
+ax_speed = fig.add_subplot(gs[0, 1])
+ax_energy = fig.add_subplot(gs[1, 1])
+
+# ================== ORBIT VIEW ==================
+ax_orbit.set_aspect('equal')
+lim = r2 * 1.15
+ax_orbit.set_xlim(-lim, lim)
+ax_orbit.set_ylim(-lim, lim)
+ax_orbit.set_title("Hohmann-Transfer")
+
+ax_orbit.add_patch(plt.Circle((0,0), r_earth, color='skyblue', zorder=0))
+ax_orbit.plot(x1, y1, '--', color='gray')
+ax_orbit.plot(x_t, y_t, '--', color='orange')
+ax_orbit.plot(x2, y2, '--', color='gray')
+
+sat, = ax_orbit.plot([], [], 'ro', markersize=6)
+
+# ================== SPEED GRAPH ==================
+ax_speed.set_title("Geschwindigkeit vs Zeit")
+ax_speed.set_ylabel("m/s")
+ax_speed.set_xlim(0, len(x))
+ax_speed.set_ylim(v.min()*0.95, v.max()*1.05)
+line_v, = ax_speed.plot([], [], 'r')
+
+# ================== ENERGY GRAPH ==================
+ax_energy.set_title("Spezifische Energie")
+ax_energy.set_xlabel("Zeitschritt")
+ax_energy.set_ylabel("J/kg")
+ax_energy.set_xlim(0, len(x))
+ax_energy.set_ylim(energy.min()*1.05, energy.max()*0.95)
+line_e, = ax_energy.plot([], [], 'b')
+
+# ================== ANIMATION ==================
+def update(i):
+    sat.set_data([x[i]], [y[i]])
+    line_v.set_data(np.arange(i), v[:i])
+    line_e.set_data(np.arange(i), energy[:i])
+    return sat, line_v, line_e
+
+anim = FuncAnimation(
+    fig,
+    update,
+    frames=len(x),
+    interval=20,
+    blit=False
+)
+
+plt.tight_layout()
+plt.show()

visualisation.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+# ========== Constants ==========
+mu = 3.986e14         # gravitational constant × Earth’s mass
+R_earth = 6371e3      # Earth's radius (m)
+
+# ========== Orbit altitudes (from 200 km to 36,000 km) ==========
+h = np.linspace(200e3, 36000e3, 200)
+r = R_earth + h
+
+# ========== Orbital velocity at that altitude ==========
+v_orbit = np.sqrt(mu / r)
+
+# ========== Approximate Δv to reach that orbit from Earth ==========
+v_surface = np.sqrt(mu / R_earth)
+print(v_surface)
+delta_v = v_orbit - v_surface  # not realistic, but only for comparison
+delta_v = np.abs(delta_v)
+
+# ========== Plot ==========
+plt.figure(figsize=(8, 5))
+plt.plot(h/1000, delta_v/1000, color='royalblue', linewidth=2)
+plt.title("Δv vs Orbit Altitude", fontsize=14)
+plt.xlabel("Orbit altitude (km)")
+plt.ylabel("Δv (km/s)")
+plt.grid(True)
+plt.show()