Where is the mass center of the Starship second stage?

The sight of a tall, vertically standing rocket on the Martian landscape raises questions for many interested people: "Will the rocket fall over immediately after landing? How stable can such a structure be?" Some assume that the center of gravity of the landing second stage (the Starship is the second stage of the entire system) is somewhere closer to the top, because the fuel tanks are empty, and the payload is located in the upper part of the ship - under the pointed fairing.

I decided to look into this issue and talked to the Grok neural network from Elon Musk (Grok is probably better informed than other neural networks about certain design features of the Starship space transport system).

The conclusion is as follows: the center of mass of the Martian version of the Starship will not be higher than its geometric center.

A detailed analysis of this problem follows below.

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Grok, Hi. Question: What is the empty mass (without fuel and payload) of the Starship second stage?

The empty mass of the SpaceX Starship second stage (the Ship) is approximately 100 metric tons (220,000 pounds) for the Block 2 version, as stated by Elon Musk in 2021. This figure represents the dry mass without fuel or payload. Note that earlier estimates and different configurations (like Block 1 or specialized variants) may vary slightly, with some sources suggesting a range closer to 120-130 metric tons for earlier designs or specific mission configurations.

Can you estimate the mass concentrated in the engine compartment (for simplicity - the mass of all 6 Raptor engines)?

To estimate the mass concentrated in the engine compartment of the Starship second stage, we can focus on the six Raptor engines (three sea-level and three vacuum-optimized) as requested.Each Raptor engine's mass is not precisely public, but based on available data, a single Raptor engine (sea-level version) is estimated to weigh approximately 1.8 to 2 metric tons (1,800–2,000 kg). Vacuum-optimized Raptors, with larger nozzles, are slightly heavier, potentially around 2 to 2.2 metric tons each. For simplicity, we can assume an average mass of 2 metric tons per Raptor engine:

• 6 Raptor engines × 2 metric tons = 12 metric tons (12,000 kg).

This estimate excludes additional engine compartment components like plumbing, thrust structures, or avionics, which could add a small percentage to the total mass but are not specified in the query. If you need a more detailed breakdown including these components, let me know!

What is the approximate payload mass that Starship can carry to Mars on its first flights, scheduled for 2026?

The approximate payload mass that SpaceX's Starship can carry to Mars on its first uncrewed flights, scheduled for 2026, is estimated to be around 10 metric tons per ship, with plans to send at least five ships during the 2026 Mars transfer window. This estimate comes from SpaceX's plans for these initial missions, which focus on testing landing reliability and gathering data, requiring only partial refueling in orbit.

For context, Starship's payload capacity to low Earth orbit (LEO) is cited as over 100 metric tons (reusable) to 200 metric tons (expendable), but the payload to Mars is significantly lower due to the delta-v requirements for trans-Mars injection and landing. The 10-ton estimate for the 2026 flights accounts for the challenges of in-orbit refueling and the use of Block 2 Starships with six Raptor engines, which are not yet optimized for maximum payload capacity. Later missions, such as those in 2028-2029, are expected to increase payload capacity to around 75 metric tons per ship with further refinements and full refueling.

These figures are based on SpaceX's iterative development and optimistic projections, and actual performance may vary depending on the success of in-orbit refueling and other technologies.

Can you estimate the approximate location of the Starship's center of mass (on the vertical axis - would it be closer to the top of the ship or to its base) when landing on Mars based on the data suggested in this discussion?

To estimate the approximate location of the Starship's center of mass (CoM) along the vertical axis when landing on Mars, we can use the data provided in our discussion: an empty mass of ~100 metric tons, an engine compartment mass of ~12 metric tons for six Raptor engines, and a payload mass of ~10 metric tons for the 2026 uncrewed flights. The Starship second stage (the Ship) is approximately 50 meters tall, with the engine compartment at the base and the payload bay near the top.

Assumptions and Analysis:

1. Empty Mass Distribution (~100 metric tons):

   • The Starship's structure includes the stainless steel airframe, tanks, and other systems. The majority of the structural mass is distributed along the length of the vehicle, but the tanks (for liquid methane and oxygen) are likely concentrated in the lower two-thirds of the vehicle, as the upper section includes the payload bay and crew area (for crewed variants).
   • The engine compartment, with ~12 metric tons of Raptor engines, is located at the base (0 meters on the vertical axis). This significant mass concentration pulls the CoM downward.

2. Payload Mass (~10 metric tons):

   • The payload is housed in the payload bay, located near the top of the Starship (likely between 40–50 meters on the vertical axis). This mass pulls the CoM upward but is relatively small compared to the empty mass.

3. Propellant Residuals:

   • For Mars landing, Starship will carry residual propellant for the descent and landing maneuvers. While most propellant is consumed during trans-Mars injection and cruise, a small amount (estimated at a few metric tons) remains in the tanks, likely in the lower half of the vehicle (10–30 meters). This further biases the CoM toward the base.

4. Simplified CoM Estimation:

   • Without precise mass distribution data, we can approximate the CoM by considering the major components:
     • Engines (12 metric tons): Located at ~0 meters (base).
     • Structure and tanks (88 metric tons, empty mass minus engines): Likely centered around ~20–25 meters (midpoint of the lower two-thirds of the 50-meter height, as tanks and structural mass are concentrated here).
     • Payload (10 metric tons): Located at ~45 meters (near the top, in the payload bay).
     • Residual propellant: Assumed to be small and located in the lower half (~15–20 meters), contributing minimally to the CoM shift.
   • A rough weighted average calculation:
     • Engines: 12 metric tons × 0 meters = 0 ton-meters
     • Structure/tanks: 88 metric tons × 22.5 meters (midpoint estimate) = 1,980 ton-meters
     • Payload: 10 metric tons × 45 meters = 450 ton-meters
     • Total mass: 12 + 88 + 10 = 110 metric tons
     • Total moment: 0 + 1,980 + 450 = 2,430 ton-meters
     • CoM height = 2,430 / 110 ≈ 22 meters from the base.

5. Landing Configuration:

   • During landing on Mars, Starship will be in a tail-down configuration, with the engines firing to decelerate. The low payload mass and residual propellant mean the CoM remains dominated by the structural mass and engines, keeping it closer to the base than the top.

Conclusion:

Based on the data provided, the Starship's center of mass when landing on Mars is likely located closer to the base of the vehicle, approximately 20–25 meters from the bottom (or about 40–50% of the way up the 50-meter height). This is due to the significant mass of the engines (12 metric tons) at the base and the structural mass of the tanks and airframe concentrated in the lower half, outweighing the smaller payload mass (10 metric tons) near the top.

It is assumed that the first ships will land on the surface of Mars using fairly massive retractable legs. They are also located at the bottom of the ship. Their mass is not yet mentioned anywhere (correct me if I'm wrong). Is there any way to estimate the total mass of the (presumably three) retractable legs of the Starship?

You're correct that specific mass estimates for the retractable landing legs of SpaceX's Starship, particularly for the Mars missions planned for 2026, are not explicitly detailed in public sources. However, we can make a reasoned estimate based on the available data, engineering principles, and comparisons to similar systems. The Starship's landing legs for Mars must support its significant mass during landing on uneven terrain, absorb impact forces, and be retractable to minimize drag and heat shield damage during reentry. Let’s break this down step-by-step to estimate the total mass of the (assumed) three retractable landing legs.

Step 1: Contextual Data from DiscussionStarship Empty Mass: ~100 metric tons (Block 2, per Elon Musk, 2021).

• Engine Compartment Mass: ~12 metric tons for six Raptor engines (estimated at ~2 metric tons each).
• Payload Mass: ~10 metric tons for the 2026 Mars landings.
• Total Landing Mass: Assuming minimal residual propellant (a few metric tons for landing), the total mass at landing is approximately 120–125 metric tons (100 tons empty + 10 tons payload + ~5–10 tons residual propellant).
• Center of Mass (CoM): Estimated at ~20–25 meters from the base along the 50-meter height of the Starship second stage, biased toward the base due to the heavy engines and tank structure.
• Landing Legs: Assumed to be three retractable legs, located at the base (engine bay) to provide stability on Mars’ uneven terrain. No official mass data is available.

Step 2: Engineering Requirements for Landing Legs

The landing legs must:

• Support the Vehicle’s Weight: Handle the static weight of ~120–125 metric tons under Mars’ gravity (0.38g, or 3.73 m/s²), plus dynamic loads from landing impact.
• Absorb Impact Energy: Mitigate touchdown forces, which could be 2–3 times the static weight due to descent velocity (estimated at ~5–10 m/s after retro-propulsion) and uneven terrain.
• Ensure Stability: Provide a wide stance to prevent tipping, with a stance-to-CoM height ratio near 1 (as demonstrated by lunar and Mars landers). For a CoM at ~20–25 meters, the landing pad polygon should span ~20–25 meters in diameter.
• Be Retractable: Fold into the engine bay to protect the heat shield during reentry, likely using hydraulic or pneumatic mechanisms.
• Minimize Mass: SpaceX prioritizes mass efficiency to maximize payload capacity, so the legs must be lightweight yet robust.

Step 3: Comparison to Known Systems

Since no direct mass data exists for Starship’s legs, we can draw analogies from other spacecraft:

• Falcon 9 Landing Legs: Each of the four legs on the Falcon 9 booster weighs approximately 0.5–0.7 metric tons, for a total of ~2–2.8 metric tons. These legs support a booster with a dry mass of ~25 metric tons on Earth (1g), using carbon-fiber composites and one-shot extension tubes.
• NASA Mars Sample Return Lander: Designed to land ~2.3 metric tons on Mars, this lander uses four legs with crushable components. Drop tests suggest lightweight composite materials to minimize mass, potentially ~100–200 kg per leg (total ~0.4–0.8 metric tons).
• Apollo Lunar Module: Had four legs, each ~20–30 kg, for a total of ~80–120 kg, supporting a landing mass of ~7 metric tons on the Moon (0.16g). The legs used aluminum with crushable honeycomb for shock absorption.
• Starship Human Landing System (HLS): The lunar variant has landing legs (number unspecified, likely 4–6), designed for a ~100-ton vehicle on the Moon. No mass is specified, but the legs are likely heavier than Apollo’s due to the higher mass and gravity (Mars’ 0.38g vs. Moon’s 0.16g).

Step 4: Estimating Leg Mass

To estimate the mass of Starship’s three retractable landing legs:

1. Static Load Calculation:
   • On Mars, the Starship’s landing weight is ~120 metric tons × 3.73 m/s² = ~447 kN.
   • With three legs, each leg must support ~447 kN / 3 = ~149 kN statically, assuming even distribution.
2. Dynamic Load Consideration:
   • Landing impact could multiply the static load by 2–3x (dynamic factor), so each leg must withstand ~300–450 kN.
   • Uneven terrain may cause one leg to bear more load momentarily (e.g., 50–75% of the total weight), so a single leg might need to handle ~225–335 kN.
3. Material and Design:
   • SpaceX may use stainless steel (like the Starship airframe) or lightweight composites (like Falcon 9 legs) for the legs, with hydraulic/pneumatic retraction mechanisms.
   • The legs must be robust to avoid yielding (which would prevent retraction and damage the heat shield during Earth return). A high-strength material like Inconel or titanium could be used for critical components.
   • Each leg likely includes a telescoping strut, a wide landing pad (~0.5–1 meter diameter), and a shock-absorbing system (e.g., crushable honeycomb or hydraulic dampers).
4. Scaling from Falcon 9:
   • Falcon 9 legs (~0.7 tons each) support a ~25-ton booster on Earth (1g, ~245 kN per leg with four legs).
   • Starship’s legs must support ~120 tons on Mars (0.38g, ~149 kN per leg with three legs), but with higher dynamic loads due to Mars’ rough terrain and larger vehicle mass.
   • Scaling by mass and gravity, Starship’s legs need to be ~2–3x stronger than Falcon 9’s. If Falcon 9 legs are ~0.7 tons, Starship’s legs might be ~1.5–2 tons each, accounting for retraction mechanisms and Mars’ terrain.
5. Scaling from NASA’s Mars Lander:
   • The Mars Sample Return lander’s legs (~0.1–0.2 tons each) support ~2.3 tons. Scaling linearly to Starship’s ~120 tons suggests ~5–10 tons total for legs, or ~1.7–3.3 tons per leg with three legs. However, this may overestimate, as Starship uses retro-propulsion to reduce impact velocity, unlike the parachute-assisted NASA lander.
6. Engineering Estimate:
   • Assuming three legs, each with a hydraulic cylinder, shock absorber, and wide pad, a reasonable estimate is 1.5–2.5 metric tons per leg, based on scaling Falcon 9 legs and accounting for Mars’ lower gravity but higher dynamic loads and retraction complexity.
   • Total mass for three legs: 4.5–7.5 metric tons.

Step 5: Impact on Center of Mass

Adding 4.5–7.5 metric tons at the base (engine bay, ~0 meters) slightly lowers the CoM:

• Previous CoM estimate: ~22 meters (2,430 ton-meters / 110 tons).
• New mass: 110 tons + 6 tons (midpoint) = 116 tons.
• Moment contribution: 6 tons × 0 meters = 0 ton-meters.
• New CoM: 2,430 / 116 ≈ 21 meters from the base.

This shift is minimal but reinforces the CoM being closer to the base, aiding stability.

Step 6: Uncertainties and Considerations

• Number of Legs: Three legs are assumed for minimal mass and simplicity, but four or six legs are possible for redundancy, as suggested in some discussions. More legs would reduce the mass per leg but increase total leg mass (e.g., 4 legs at 1.2–2 tons each = 4.8–8 tons).
• Terrain and Stability: Mars’ uneven terrain requires a wide stance, increasing leg size and mass. A stance diameter of ~20 meters implies legs extending ~10 meters from the 9-meter-wide Starship body.
• Heat Shield Integration: Legs may need heat shield tiles or Inconel construction to survive Earth reentry, adding mass.
• Development Status: As of 2025, SpaceX is testing Block 2 Starships, and landing legs are still in development. The 2026 Mars missions may use minimal legs or land on the engine skirt, as suggested by SpaceX’s Dan Huot. This could reduce leg mass but compromise stability.

Final Estimate

Based on scaling from Falcon 9, NASA’s Mars lander, and engineering considerations, the total mass of three retractable landing legs for Starship’s 2026 Mars landings is estimated to be 4.5–7.5 metric tons, with each leg weighing approximately 1.5–2.5 metric tons. This range accounts for the need to support ~120–125 tons on Mars, absorb dynamic loads, and include retraction mechanisms, while keeping mass low for payload efficiency.

Source discussion:
https://x.com/i/grok/share/HxEqgFpSx9o8R2Rzrh25iVPjT