Starship Trajectory for a 2024 Mars Mission
Imagine we’re embarking on one of the most incredible adventures of our age—traveling to Mars in 2024 with SpaceX’s Starship. Today, I want to take you on a journey through our star system, explaining how we can harness the power of astrodynamics to carve out a trajectory for Starship, turning science fiction into science fact.
We’ll start with the basics of a heliocentric Hohmann Transfer Orbit—a route that could make Mars not years but months away. Whether you’re a student dreaming of space, a teacher guiding future pioneers, or an enthusiast captivated by the stars, let’s plot our course to the Red Planet, learning about physics and the boundless possibilities of interplanetary travel.
Starship's Launch to Orbit
As the dawn of an ambitious journey approaches, SpaceX’s Starship, perched atop the formidable Super Heavy Rocket, stands ready at Kennedy Space Center’s Launch Complex 39A. It’s early October 2024, and the countdown to a historic Mars-bound mission is underway. With over 1,200 tons of fuel and 100 tons of payload, this engineering marvel boasts a total lift-off mass of 5,300 tons.
The launch window is critical—only 109 days remain until Earth and Mars align perfectly, a condition known as Opposition, essential for the most efficient path to Mars. Every second counts as the engines of the Super Heavy Rocket roar to life, propelling the Starship into the sky. During its ascent, the rocket faces its greatest challenge, the point of maximum aerodynamic pressure, known simply as max Q, between 11 and 13 km altitude.
Successfully navigating this, the rocket continues its powered climb until it reaches between 80 to 100 km above Earth. Here, a pivotal moment—the main engine cut-off (MECO)—occurs. Moments later, the Super Heavy detaches and begins its precise, vertical return to an offshore landing pad, leaving Starship on its course to carve a path through Low-Earth Orbit to Mars.
Parking the Starship in Earth Orbit
Moments after detaching from the Super Heavy Rocket, the Starship ignites its engines, setting its sights on a 200-kilometer (about 108-nautical-mile) parking orbit. This critical phase, known as the Parking Orbit Maneuver Injection (POMI), ensures the Starship adjusts its trajectory towards the intended circular orbit. During this maneuver, the Starship fine-tunes its path to align perfectly with its target orbit.
As Starship nears the desired altitude, it must reach a circular speed of 7.784 kilometers per second to achieve and maintain the stable 200 km orbit. Approaching this critical velocity, a precise engine cutoff is triggered, allowing Starship to transition into its orbital coast seamlessly. Here, the spacecraft embarks on orbit verification, confirming its successful positioning and readiness for the next phase of its mission to Mars.
Refueling Starship
Upon achieving its parking orbit, Starship conducts a comprehensive system-wide status check (SSC). Having depleted its fuel in the ascent, SpaceX has engineered a novel in-orbit refueling strategy. The spacecraft aligns itself using a Guided System Reference Alignment (GSRA) to prepare for docking with a waiting Tanker-ship.
The rendezvous is meticulously timed: the Tanker-ship, already in orbit or arriving shortly thereafter, aligns with Starship. Following a successful docking, the critical refueling process commences. After the tanks are replenished, Starship disconnects from the Tanker, which then returns to Earth. As Starship readies for the Trans-Mars Injection (TMI), it undertakes a final system update and status check, ensuring all systems are ‘go’ for the next leg of its historic journey to Mars.
Starship in Earth Geocentric Trajectory
As Starship aligns along its parking orbit, it approaches the critical Trans-Mars Injection (TMI) coordinate. At this point, the craft is positioned at the perigee of the injection path, where the angle η1—149.18 degrees—between Earth’s orbital velocity vector and the injection radius vector (r0=6578 km) is optimal. Here, Starship’s engines ignite for TMI-0, propelling it to a necessary escape velocity of 11.45235 km/sec.
This velocity is precisely calculated to break free from Earth’s sphere of influence while ensuring Starship maintains sufficient speed to enter a heliocentric transfer orbit towards Mars. Achieving this velocity, the engines cut off, and Starship coasts along a hyperbolic trajectory, marked by a semi-major axis of 40,003.16852 km and an eccentricity of 1.1644369. With Earth as the focal point of this hyperbola, Starship will navigate using a specific angular momentum of 4.98212 km²/sec², an eccentric anomaly of 212.4719917 degrees, and an angular separation of 118.360677 degrees between the trajectory’s asymptotes.
Starship Approaches ESoI
As Starship navigates through its hyperbolic trajectory, it systematically performs system checks and navigation sightings. Nearly a month later, 29.369 days to be exact, it nears the edge of Earth’s sphere of influence (ESoI). At this juncture, Starship’s velocity includes a hyperbolic excess speed of Δv = 3.1566185 km/sec relative to Earth. Considering Earth’s orbital velocity of 29.78 km/sec, Starship’s total speed relative to the Sun reaches 32.9366185 km/sec as it transitions to a heliocentric path aimed at Mars.
Upon reaching the ESoI boundary, Starship executes a critical Trans-Mars Injection-1 (TMI-1) to fine-tune its course. Additional TMIs may follow, ensuring precise navigation as it embarks on its journey towards the Red Planet
Starship’s Heliocentric Launch
As Starship navigates through its hyperbolic trajectory, it systematically performs system checks and navigation sightings. Nearly a month later, 29.369 days to be exact, it nears the edge of Earth’s sphere of influence (ESoI). At this juncture, Starship’s velocity includes a hyperbolic excess speed of Δv = 3.1566185 km/sec relative to Earth. Considering Earth’s orbital velocity of 29.78 km/sec, Starship’s total speed relative to the Sun reaches 32.9366185 km/sec as it transitions to a heliocentric path aimed at Mars.
Upon reaching the ESoI boundary, Starship executes a critical Trans-Mars Injection-1 (TMI-1) to fine-tune its course. Additional TMIs may follow, ensuring precise navigation as it embarks on its journey towards the Red Planet
Starship in Hohmann Transfer Orbit
As Starship ventures on its journey to Mars, it follows a precisely calculated heliocentric Hohmann transfer orbit. This trajectory has a semi-major axis of approximately 192.493567 million kilometers and an eccentricity of 0.22283299, with the Sun at the focus. The specific angular momentum for this path is 344.7269487 km²/sec², and the semi-minor axis extends roughly 187.653631 million kilometers.
Throughout its voyage, Starship conducts periodic navigation sightings, system-wide checks, and updates, ensuring alignment with its trajectory. As it traverses Earth’s orbital plane, which is tilted at 1.85 degrees relative to Mars’s orbit, Starship performs crucial mid-course corrections.
At a critical point 192.493567 million kilometers from the Sun, it realigns its attitude and executes a brief engine burn (TMI-3), adjusting its velocity by 0.8477779373 km/sec. This maneuver is designed to maintain the required momentum and speed for its heliocentric coast towards Mars.
Starship - Mars Sphere of Influence (MSoI)
After a journey of 266.5629 days (approximately 8.67 months) through space, Starship nears the Mars Sphere of Influence (MSoI), which extends about 578,000 kilometers. Arriving with a slight offset of 5,812.3 km from Mars’s orbital velocity vector and traveling at a speed of 20.9327468 km/sec, Starship prepares for a crucial maneuver. The spacecraft initiates TMI-4 to adjust its course from a heliocentric trajectory to a Mars-centric one. This shift is necessary because Mars’s orbit, unlike a perfect circle, is elliptical, requiring Starship to enter the MSoI at an angle of 5.05 degrees. As it begins its final approach, Starship adjusts to a Mars-relative velocity of 3.708637927 km/sec, setting the stage for its hyperbolic entry into Mars’s orbit.
Starship Coasts Hyperbolic Mars Intercept Orbit
As Starship nears Mars, it enters a hyperbolic trajectory designed for an aerobraking maneuver just 100 km above the Martian surface. This critical path has a semi-major axis of 3113.858856 km and an eccentricity of 2.117584374, with Mars as the focal point of the hyperbola. The trajectory’s specific angular momentum is 6.8769976 km²/sec², and it has an eccentric anomaly of 295.8416269 degrees and an angular separation of 56.3591 degrees between the hyperbola’s asymptotes.
Approaching the closest point to Mars, the hyperbolic perigee at 3380 km from the planet’s center, Starship aligns with an angle of 113.129554 degrees relative to Mars’s orbital velocity vector. Here, it reaches a velocity of 6.1941735 km/sec, setting the stage for the precise execution of its aerobraking maneuver to slow down and enter Mars orbit.
Starship Approaches Mars
As Starship prepares for Mars entry, SpaceX has engineered it to withstand the intense heat and structural stress from atmospheric drag, all while maintaining the safety of its payload and crew. Entering the atmosphere at a velocity of 7.5 km/sec, Starship’s current velocity of 6.1941735 km/sec is below the designated safe entry speed, giving it two options: to land immediately or to enter orbit.
Due to a sandstorm at the planned landing site, the decision is made to enter a parking orbit until conditions improve. To establish a stable circular orbit 100 km above Mars, Starship needs to adjust to a velocity of 3.5081 km/sec. Currently, as it ends its reentry hyperbolic trajectory at a velocity of 6.1941735 km/sec, Starship maneuvers towards Mars for atmospheric reentry.
Starship 1st Atmospheric Aerobraking
As Starship descends to just 100 km above the Martian surface at the hyperbolic perigee, it encounters significant atmospheric drag. This aerobraking effectively reduces its velocity to 4.794172 km/sec as it exits the Martian atmosphere, positioning it into an elliptical orbit with Mars as the focal point. The new orbit has a semi-major axis of 26,279.825 km and an eccentricity of 0.867579, with a specific angular momentum of 0.8148456 km²/sec².
This elliptical journey around Mars takes approximately 14.97 days to complete one full cycle. During this period, Starship will conduct regular system checks, adjust its navigational bearings, and continuously monitor Martian weather conditions to prepare for the subsequent atmospheric entry.
Starship Parks in Orbit Around Mars
Given suboptimal conditions, Starship performs another aerobraking maneuver to adjust its trajectory, exiting the Martian atmosphere with a reduced velocity of 3.794173 km/sec. This adjustment places it into a one-day elliptical orbit around Mars, characterized by a semi-major axis of 41,914.11 km, an eccentricity of 0.16973, and a specific angular momentum of 5.10910935 km²/sec².
Following a second pass, Starship utilizes the natural decay of velocity and atmospheric drag for another orbital parking maneuver, achieving a new velocity of 3.5081186 km/sec. This precise speed sets it into a stable, circular orbit at 100 km altitude. To secure its position in this stable orbit, Starship methodically performs several minor maneuvers over subsequent orbits, ensuring each adjustment enhances orbital stability.
Starship Lands on Mars
When conditions on both the Starship and Mars are deemed optimal, Starship will initiate its final descent. This begins with the Mars Entry Maneuver Injection (MEMI), transitioning smoothly into a controlled, free-fall atmospheric entry. At approximately 15 km above Mars, Starship shifts into Horizontal Mode to stabilize its descent. Its Raptor engines ignite for the entry burn, guiding the spacecraft through aerodynamic maneuvers. This precise sequence of operations culminates in a vertical landing on the Martian surface, marking the end of a meticulously calculated journey.
Conclusion
As we have traversed through the complexities and precise calculations required for Starship’s journey to Mars, it’s clear that each maneuver from launch to landing is meticulously planned to ensure safety and success. This exploration not only pushes the boundaries of human ingenuity and technological advancement but also opens up new possibilities for future interplanetary travel. As Starship touches down on the Martian surface, it marks not just a triumph of engineering, but a bold step into the future of humanity’s place in our solar system.