Welcome to your journey into rocket science! This notebook will teach you the fundamental concepts needed to understand how rockets work.
Every rocket works because of a simple principle:
“For every action, there is an equal and opposite reaction.”
When a rocket expels hot gas downward (action), the rocket is pushed upward (reaction).
# Let's set up our environment
import numpy as np
import matplotlib.pyplot as plt
# Make plots look nice
plt.style.use('dark_background')
print("✅ Environment ready! Let's learn rocket science!")✅ Environment ready! Let's learn rocket science!This equation tells us how much a rocket’s velocity can change:
\[\Delta v = v_e \cdot \ln\left(\frac{m_0}{m_f}\right)\]
Where: - Δv (delta-v) = Change in velocity (m/s) - vₑ = Exhaust velocity (how fast gas leaves the rocket) - m₀ = Initial mass (rocket + fuel) - mf = Final mass (rocket without fuel) - ln = Natural logarithm
def rocket_equation(exhaust_velocity, initial_mass, final_mass):
"""
Calculate delta-v using the Tsiolkovsky rocket equation.
Parameters:
-----------
exhaust_velocity : float - How fast the exhaust leaves the rocket (m/s)
initial_mass : float - Total mass before burn (kg)
final_mass : float - Mass after fuel is burned (kg)
Returns: The change in velocity (m/s)
"""
mass_ratio = initial_mass / final_mass
delta_v = exhaust_velocity * np.log(mass_ratio)
return delta_v
# Example: A simple rocket
v_exhaust = 3000 # m/s (typical for RP-1/LOX engines like Falcon 9's Merlin)
m_initial = 1000 # kg (rocket + fuel)
m_final = 100 # kg (just the rocket, fuel burned)
delta_v = rocket_equation(v_exhaust, m_initial, m_final)
print(f"🚀 Delta-v achieved: {delta_v:.0f} m/s")
print(f"📊 Mass ratio: {m_initial/m_final:.1f}:1")
print(f"\n💡 This means 90% of the rocket's mass was fuel!")🚀 Delta-v achieved: 6908 m/s
📊 Mass ratio: 10.0:1
💡 This means 90% of the rocket's mass was fuel!Change the values below to see how delta-v changes. Can you reach orbit (9,400 m/s)?
# ============================================
# TRY CHANGING THESE VALUES!
# ============================================
your_exhaust_velocity = 3500 # Try: 2500, 3000, 3500, 4500
your_initial_mass = 500 # Try: 100, 500, 1000, 10000
your_final_mass = 50 # Must be less than initial mass!
# ============================================
your_delta_v = rocket_equation(your_exhaust_velocity, your_initial_mass, your_final_mass)
print("=" * 50)
print("YOUR ROCKET ANALYSIS")
print("=" * 50)
print(f"Exhaust Velocity: {your_exhaust_velocity} m/s")
print(f"Initial Mass: {your_initial_mass} kg")
print(f"Final Mass: {your_final_mass} kg")
print(f"Fuel Mass: {your_initial_mass - your_final_mass} kg")
print(f"Mass Ratio: {your_initial_mass/your_final_mass:.2f}")
print(f"\n🎯 DELTA-V: {your_delta_v:.0f} m/s")
print("=" * 50)
# Can you reach orbit?
if your_delta_v >= 9400:
print("✅ Congratulations! You can reach orbit!")
elif your_delta_v >= 7800:
print("🟡 Almost! You need a bit more delta-v for orbit.")
else:
print("❌ Not enough delta-v for orbit. Try more fuel or better engines!")==================================================
YOUR ROCKET ANALYSIS
==================================================
Exhaust Velocity: 3500 m/s
Initial Mass: 500 kg
Final Mass: 50 kg
Fuel Mass: 450 kg
Mass Ratio: 10.00
🎯 DELTA-V: 8059 m/s
==================================================
🟡 Almost! You need a bit more delta-v for orbit.Let’s see how different engines compare. Better engines (higher exhaust velocity) get more delta-v from the same amount of fuel!
# Compare different engine types
fig, ax = plt.subplots(figsize=(12, 6))
engines = {
'Solid Rocket Motor': 2500,
'Merlin (Falcon 9)': 3050,
'RS-25 (Space Shuttle)': 4400,
'Raptor (Starship)': 3600,
}
mass_ratios = np.linspace(1.5, 15, 100)
colors = ['#ff6b6b', '#feca57', '#48dbfb', '#00d4ff']
for (name, v_e), color in zip(engines.items(), colors):
delta_vs = v_e * np.log(mass_ratios)
ax.plot(mass_ratios, delta_vs/1000, label=f'{name} ({v_e} m/s)',
color=color, linewidth=2.5)
# Reference lines
ax.axhline(y=9.4, color='white', linestyle='--', alpha=0.5, label='LEO (~9.4 km/s)')
ax.axhline(y=11.2, color='lime', linestyle='--', alpha=0.5, label='Earth Escape (11.2 km/s)')
ax.set_xlabel('Mass Ratio (Initial/Final)', fontsize=12)
ax.set_ylabel('Delta-V (km/s)', fontsize=12)
ax.set_title('🚀 The Tyranny of the Rocket Equation', fontsize=14, color='#00d4ff')
ax.legend(loc='lower right', fontsize=9)
ax.grid(True, alpha=0.3)
ax.set_xlim(1, 15)
ax.set_ylim(0, 15)
plt.tight_layout()
plt.show()
print("\n📚 KEY INSIGHT: Higher exhaust velocity = more delta-v for same fuel!")
print(" Notice how the curves flatten out at high mass ratios.")
print(" This is the 'tyranny' - you need exponentially more fuel for linear gains.")
📚 KEY INSIGHT: Higher exhaust velocity = more delta-v for same fuel!
Notice how the curves flatten out at high mass ratios.
This is the 'tyranny' - you need exponentially more fuel for linear gains.\[F = G \cdot \frac{m_1 \cdot m_2}{r^2}\]
At Earth’s surface: g = 9.81 m/s²
Many people think astronauts float because there’s “no gravity” in space. Wrong!
At the International Space Station (400 km altitude), gravity is still 89% as strong as on Earth’s surface. Astronauts float because they’re in free fall - constantly falling around Earth!
# Constants
G = 6.674e-11 # Gravitational constant
M_EARTH = 5.972e24 # Earth's mass (kg)
R_EARTH = 6.371e6 # Earth's radius (m)
def gravity_at_altitude(altitude_km):
"""Calculate gravitational acceleration at a given altitude."""
r = R_EARTH + (altitude_km * 1000)
g = G * M_EARTH / r**2
return g
# Calculate gravity at different altitudes
locations = [
(0, "Earth's Surface"),
(10, "Cruising Airplane"),
(100, "Karman Line (edge of space)"),
(400, "ISS Orbit"),
(35786, "Geostationary Orbit"),
(384400, "Moon's Distance"),
]
print("🌍 GRAVITY AT DIFFERENT ALTITUDES")
print("=" * 60)
for alt, name in locations:
g = gravity_at_altitude(alt)
percent = (g / 9.81) * 100
print(f"{name:30} | g = {g:8.4f} m/s² ({percent:5.1f}%)")
print("\n💡 Key insight: Gravity decreases with the SQUARE of distance!")
print(" Double the distance = 1/4 the gravity")🌍 GRAVITY AT DIFFERENT ALTITUDES
============================================================
Earth's Surface | g = 9.8195 m/s² (100.1%)
Cruising Airplane | g = 9.7888 m/s² ( 99.8%)
Karman Line (edge of space) | g = 9.5184 m/s² ( 97.0%)
ISS Orbit | g = 8.6936 m/s² ( 88.6%)
Geostationary Orbit | g = 0.2243 m/s² ( 2.3%)
Moon's Distance | g = 0.0026 m/s² ( 0.0%)
💡 Key insight: Gravity decreases with the SQUARE of distance!
Double the distance = 1/4 the gravityRockets work by Newton’s Third Law - Push gas out, rocket goes up
The Rocket Equation is fundamental - Δv = vₑ × ln(m₀/mf)
Mass ratio matters - More fuel = more delta-v (but logarithmically!)
Exhaust velocity is key - Better engines = more efficient rockets
Gravity never stops - Even in orbit, you’re still being pulled by Earth
Continue to 02_Orbital_Mechanics_Basics.ipynb to learn: - How orbits work - Circular vs elliptical orbits - How satellites stay in orbit - The vis-viva equation
“The Earth is the cradle of humanity, but mankind cannot stay in the cradle forever.” — Konstantin Tsiolkovsky