Case Study: Selecting a Launch Vehicle for a Mars Orbiter

"The mission does not begin when the science starts. It begins when you choose the rocket."

Executive Summary

In the previous case study we audited a decision the physics had already made. Here we make one. We take a finished spacecraft — the $1{,}705\ \text{kg}$ Track-C Mars orbiter that Chapter 11 sized down to the last propellant kilogram, aimed at an Earth-departure characteristic energy of $C_3 = 8.7\ \text{km}^2/\text{s}^2$ — and we run the full launch-vehicle selection trade of §30.6 to decide what flies it. We will apply the three hard gates (performance to the required $C_3$, fairing volume, and site/orbit reachability), rank the survivors by the soft preferences (price, schedule, heritage, reliability), compute mass margins, and produce a defensible recommendation. This is exactly the trade a real mission's launch team runs, and the one you will run for your own mission in the capstone.

Skills applied

• Running the hard gates and soft preferences of launch-vehicle selection (§30.6).
• Reading a vehicle's capability to a destination energy ($C_3$), not just to LEO or GTO (§30.2; Ch. 11).
• Computing and interpreting a mass margin, and applying a margin rule (Ch. 29).
• Weighing non-performance factors (price, heritage, schedule) in a real decision.

Background

The payload we must fly

From Chapter 11's design, the orbiter is:

The defining feature is that this is not a LEO or GTO payload: it must be thrown onto an Earth-escape trajectory with a specific positive energy. So the relevant performance number is each vehicle's payload to $C_3 = 8.7$ — not its headline LEO tonnage.

Vehicle $C_3$ capacities below are Tier-2 illustrative, consistent in magnitude with Appendix H and with the class of vehicles that have historically launched Mars orbiters. They are for teaching the method; a real selection uses the operator's current payload-user's-guide $C_3$ curves.

Phase 1: Hard gate 1 — performance to the required $C_3$

We need the vehicle rated to deliver at least the orbiter's wet mass with margin. Applying the Chapter 29 rule of a 10% mass margin, the required capability is

$$ m_{\text{need}} = 1{,}705\ \text{kg} \times 1.10 = 1{,}876\ \text{kg to } C_3 = 8.7. $$

Three candidate vehicles, all Cape-launched and all with interplanetary-capable upper stages:

All three pass the performance gate with comfortable margin. (A recovered — non-expendable — Falcon 9 would deliver less to this energy and could be tight against the margin rule; committing to expend the booster for a high-$C_3$ interplanetary shot is itself a normal trade.)

# Hard gate 1: performance to C3 = 8.7 km^2/s^2, with a 10% mass margin.
c3_capacity = {"Falcon 9 (exp.)": 2500, "Atlas V 401": 2300, "Vulcan VC2": 4000}  # kg, Tier-2
wet_mass = 1705      # kg (Chapter 11 orbiter)
need = wet_mass * 1.10
for name, cap in c3_capacity.items():
    verdict = "PASS" if cap >= need else "FAIL"
    print(f"{name:16s} cap {cap:5d} kg  margin {cap/wet_mass:4.2f}  {verdict}")
# Expected output:
# Falcon 9 (exp.)  cap  2500 kg  margin 1.47  PASS
# Atlas V 401      cap  2300 kg  margin 1.35  PASS
# Vulcan VC2       cap  4000 kg  margin 2.35  PASS

Phase 2: Hard gate 2 — fairing volume

The orbiter's stowed envelope (~$2.6\ \text{m}$ diameter, $3\ \text{m}$ tall) must fit inside the payload fairing with clearance for the separation system and dynamic sway. All three candidates fly standard fairings of roughly $4$–$5\ \text{m}$ external diameter (usable dynamic envelope ~$3.7$–$4.5\ \text{m}$), so a $2.6\ \text{m}$-wide spacecraft fits all of them easily. Gate 2: all pass. For this particular payload, volume is not the binding constraint — but note it could be for a solar-array- or antenna-dominated design, where the folded span, not the mass, decides.

Phase 3: Hard gate 3 — site and orbit reachability

An interplanetary departure adds a subtlety beyond §30.3's inclination rule: the outbound hyperbola leaves Earth along an asymptote with a particular declination (DLA), and the launch site must be able to reach it — the same latitude-versus-inclination geometry, applied to the escape asymptote rather than a parking orbit. For a typical Earth→Mars window the required declination is modest and well within reach of a Cape-launched vehicle using a parking-orbit coast and a timed departure burn. Gate 3: all pass for the assumed window. (A window demanding an extreme departure declination could, in principle, penalize a given site — a check worth making, not assuming.)

Phase 4: Rank the survivors — the soft preferences

All three vehicles clear every hard gate, so the decision moves to the soft preferences of §30.6:

The trade now depends on what the mission values most:

• A cost-driven science program with normal risk tolerance chooses Falcon 9 (expendable): it clears every gate with a healthy $1.47$ margin, flies often, and is the cheapest option — the mass we are throwing is cheap enough that price dominates.
• A risk-averse flagship that cannot be re-flown might pay for Atlas V / Vulcan heritage and accept a higher price for a longer interplanetary track record — reliability is weighted above price when the payload is irreplaceable (Chapter 32).

Phase 5: Recommendation

Recommended vehicle: Falcon 9 (expendable configuration).

• Binding consideration: none of the hard gates bound the choice (all three vehicles pass); the decision is set by the soft preference of price, with the orbiter's modest mass making cost the natural driver.
• Margin: capacity $2{,}500\ \text{kg}$ ÷ wet mass $1{,}705\ \text{kg}$ = 1.47 (47% margin), comfortably above the 10% rule and leaving room for the mass growth Chapter 29 warns is inevitable.
• Documented alternative: Atlas V 401 or Vulcan Centaur, selected instead if the program weights interplanetary heritage and a flawless reliability record above launch price.

This recommendation, its margin, and its one-line rationale go straight into the MDR — the launch-vehicle selection element your capstone in Chapter 40 will assemble with all the others.

🔧 Engineering Reality: A real selection would iterate: the chosen vehicle's injection accuracy and its coast/restart capability feed back into the spacecraft's own delta-v budget (a sloppier drop-off means more clean-up propellant), and its vibration and acoustic environment feed back into the structure (Ch. 23). We checked the gates in one pass for clarity; in practice the launch vehicle and the spacecraft are designed against each other until the whole thing closes.

Discussion Questions

1. Why is "payload to $C_3 = 8.7$" the right performance number for this mission, rather than payload to LEO or GTO? What would using the LEO number instead get wrong?
2. All three vehicles passed every hard gate. In your own words, why does that move the decision to the soft preferences rather than ending it?
3. A recovered (reusable) Falcon 9 delivers less to this high $C_3$ and might fail the 10% margin. Why is expending the booster a reasonable trade for a one-off interplanetary launch, even though reuse is cheaper for LEO work?
4. Under what circumstances would fairing volume, not mass, have become the binding gate for a Mars orbiter?

Your Turn: Extensions

• Option A (analysis). The orbiter's mass estimate grows 12% during design, to $1{,}910\ \text{kg}$. Recompute each vehicle's margin. Does the recommendation survive? Which candidate is most threatened?
• Option B (computation). Extend the Phase-1 code to also flag a WARN when the margin is below $1.2$, and re-run it for a $1{,}910\ \text{kg}$ orbiter. Hand-trace the output; do not run it.
• Option C (your mission). Run the full three-gate-then-rank selection for your Track's spacecraft against Appendix H, compute the winning margin, and write the recommendation into your MDR.

Key Takeaways

1. Select against the destination, not the headline. For an interplanetary mission the performance gate is payload to the required $C_3$, not payload to LEO.
2. Gates first, preferences second. Eliminate every vehicle that fails mass-with-margin, fairing volume, or reachability; only then rank the survivors by price, schedule, heritage, and reliability.
3. Margin is a number you compute and defend. Capacity ÷ wet mass ≥ the mission's margin rule; here $2{,}500 / 1{,}705 = 1.47$ clears the 10% rule with room for growth.
4. The "best" vehicle depends on what the mission values. A cheap science orbiter and an irreplaceable flagship, with identical mass, can rationally choose different rockets.