🪐 Interplanetary Travel

How to Get from Earth to Mars (and Beyond!)

What You’ll Learn

  1. Hohmann transfer orbits
  2. Delta-V requirements for different destinations
  3. Launch windows and planetary alignment
  4. Why timing is everything in space travel

1. The Challenge of Interplanetary Travel

Getting to another planet isn’t just about going in a straight line. In space, everything is orbiting - Earth orbits the Sun, Mars orbits the Sun, and your spacecraft will orbit the Sun too!

The key insight: Space travel is about changing your orbit to intersect with your destination’s orbit.

Why Can’t We Just Go Straight?

  • A “straight line” to Mars would require ENORMOUS amounts of fuel
  • We’d have to fight the Sun’s gravity the entire way
  • Instead, we use the Sun’s gravity to our advantage
Code 
import numpy as np
import matplotlib.pyplot as plt
plt.style.use('dark_background')

# Solar system constants
AU = 1.496e11  # Astronomical Unit in meters
MU_SUN = 1.327e20  # Sun's gravitational parameter (m³/s²)

# Planet orbital radii (in AU)
PLANETS = {
    'Mercury': 0.387,
    'Venus': 0.723,
    'Earth': 1.000,
    'Mars': 1.524,
    'Jupiter': 5.203,
    'Saturn': 9.537,
}

print("✅ Ready to plan interplanetary missions!")
✅ Ready to plan interplanetary missions!

2. The Hohmann Transfer: The Most Efficient Route

A Hohmann transfer is an elliptical orbit that touches both the starting orbit and the destination orbit. It’s the most fuel-efficient way to travel between two circular orbits.

How It Works

  1. Burn 1 (Departure): At Earth, fire engines to speed up and enter the transfer ellipse
  2. Coast: Travel along the ellipse with NO engine burns (just falling!)
  3. Burn 2 (Arrival): At Mars, fire engines to slow down and match Mars’ orbit

The Math

Transfer orbit semi-major axis: \[a_{transfer} = \frac{r_1 + r_2}{2}\]

Transfer time (half the orbital period): \[T_{transfer} = \pi \sqrt{\frac{a^3}{\mu_{Sun}}}\]

Code 
def hohmann_transfer(r1_au, r2_au):
    """
    Calculate Hohmann transfer parameters between two circular orbits.
    
    Parameters:
    -----------
    r1_au : float - Departure orbit radius (AU)
    r2_au : float - Arrival orbit radius (AU)
    
    Returns: dict with transfer parameters
    """
    r1 = r1_au * AU  # Convert to meters
    r2 = r2_au * AU
    
    # Transfer ellipse semi-major axis
    a_transfer = (r1 + r2) / 2
    
    # Transfer time (half period)
    T_transfer = np.pi * np.sqrt(a_transfer**3 / MU_SUN)
    
    # Velocities
    v1_circular = np.sqrt(MU_SUN / r1)  # Initial circular orbit
    v2_circular = np.sqrt(MU_SUN / r2)  # Final circular orbit
    
    # Transfer orbit velocities at perihelion and aphelion
    v_perihelion = np.sqrt(MU_SUN * (2/r1 - 1/a_transfer))
    v_aphelion = np.sqrt(MU_SUN * (2/r2 - 1/a_transfer))
    
    # Delta-V for each burn
    dv1 = abs(v_perihelion - v1_circular)
    dv2 = abs(v2_circular - v_aphelion)
    
    return {
        'semi_major_axis_au': a_transfer / AU,
        'transfer_time_days': T_transfer / 86400,
        'dv1_km_s': dv1 / 1000,
        'dv2_km_s': dv2 / 1000,
        'total_dv_km_s': (dv1 + dv2) / 1000
    }

# Calculate Earth to Mars transfer
mars_transfer = hohmann_transfer(1.0, 1.524)

print("🚀 EARTH TO MARS HOHMANN TRANSFER")
print("=" * 50)
print(f"Transfer orbit size: {mars_transfer['semi_major_axis_au']:.3f} AU")
print(f"Transit time: {mars_transfer['transfer_time_days']:.0f} days ({mars_transfer['transfer_time_days']/30:.1f} months)")
print(f"\nDelta-V Budget:")
print(f"  Departure burn: {mars_transfer['dv1_km_s']:.2f} km/s")
print(f"  Arrival burn:   {mars_transfer['dv2_km_s']:.2f} km/s")
print(f"  TOTAL:          {mars_transfer['total_dv_km_s']:.2f} km/s")
🚀 EARTH TO MARS HOHMANN TRANSFER
==================================================
Transfer orbit size: 1.262 AU
Transit time: 259 days (8.6 months)

Delta-V Budget:
  Departure burn: 2.95 km/s
  Arrival burn:   2.65 km/s
  TOTAL:          5.60 km/s

3. Compare Missions to Different Planets

Let’s see how delta-V and travel time change for different destinations:

Code 
# Calculate transfers to all planets
print("🪐 HOHMANN TRANSFERS FROM EARTH")
print("=" * 70)
print(f"{'Destination':<12} {'Distance':>10} {'Transit Time':>15} {'Total ΔV':>12}")
print("-" * 70)

destinations = ['Venus', 'Mars', 'Jupiter', 'Saturn']
results = []

for planet in destinations:
    transfer = hohmann_transfer(1.0, PLANETS[planet])
    days = transfer['transfer_time_days']
    
    if days < 365:
        time_str = f"{days:.0f} days"
    else:
        time_str = f"{days/365:.1f} years"
    
    print(f"{planet:<12} {PLANETS[planet]:>8.2f} AU {time_str:>15} {transfer['total_dv_km_s']:>10.2f} km/s")
    results.append((planet, transfer['total_dv_km_s'], days))

print("-" * 70)
print("\n💡 Notice: Outer planets need less delta-V but MUCH more time!")
print("   Jupiter takes ~3 years, Saturn takes ~6 years via Hohmann transfer.")
🪐 HOHMANN TRANSFERS FROM EARTH
======================================================================
Destination    Distance    Transit Time     Total ΔV
----------------------------------------------------------------------
Venus            0.72 AU        146 days       5.21 km/s
Mars             1.52 AU        259 days       5.60 km/s
Jupiter          5.20 AU       2.7 years      14.44 km/s
Saturn           9.54 AU       6.1 years      15.73 km/s
----------------------------------------------------------------------

💡 Notice: Outer planets need less delta-V but MUCH more time!
   Jupiter takes ~3 years, Saturn takes ~6 years via Hohmann transfer.

4. Launch Windows: Why Timing Matters

You can’t just launch to Mars whenever you want! The planets must be aligned correctly.

Phase Angle

Mars must be at a specific angle ahead of Earth when you launch. This angle ensures Mars will be at the right place when your spacecraft arrives ~9 months later.

Phase angle formula: \[\phi = 180° - \omega_{Mars} \times T_{transfer}\]

Synodic Period

Launch windows to Mars open approximately every 26 months (2.14 years).

This is the time it takes for Earth and Mars to return to the same relative positions.

Code 
# Calculate launch windows
T_EARTH = 365.25  # days
T_MARS = 687.0    # days

# Synodic period formula: 1/T_syn = |1/T1 - 1/T2|
synodic_period = 1 / abs(1/T_EARTH - 1/T_MARS)

# Phase angle for Mars
transfer_time = mars_transfer['transfer_time_days']
omega_mars = 360 / T_MARS  # degrees per day
phase_angle = 180 - omega_mars * transfer_time

print("📅 MARS LAUNCH WINDOWS")
print("=" * 50)
print(f"Transfer time: {transfer_time:.0f} days")
print(f"Phase angle required: {phase_angle:.1f}°")
print(f"Synodic period: {synodic_period:.0f} days ({synodic_period/365:.2f} years)")
print(f"\n⏰ Launch windows occur every ~{synodic_period/30:.0f} months!")
print("\nRecent Mars launch windows:")
years = [2018, 2020, 2022, 2024, 2026]
for year in years:
    print(f"  • {year}")
📅 MARS LAUNCH WINDOWS
==================================================
Transfer time: 259 days
Phase angle required: 44.3°
Synodic period: 780 days (2.14 years)

⏰ Launch windows occur every ~26 months!

Recent Mars launch windows:
  • 2018
  • 2020
  • 2022
  • 2024
  • 2026

🎓 Key Takeaways

  1. Hohmann transfers are the most efficient - Use an ellipse touching both orbits

  2. Earth to Mars: ~259 days, 5.6 km/s total delta-V

  3. Launch windows are limited - Must wait for correct planetary alignment

  4. Windows open every ~26 months - Miss one and wait 2+ years!

  5. Outer planets take years - Jupiter ~3 years, Saturn ~6 years

🚀 Try the Simulator!

Run the Mars Mission Simulator to see this in action:

cd ../Projects/Starship_Trajectory_Planner
python mission_planner.py

“Mars is there, waiting to be reached.” — Buzz Aldrin