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jugend-forscht-2026/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()

jugend-forscht-2026/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()