PYTHON · NUMPY

Composing the budget

Your payload fraction comes out negative. What does that mean physically?

Pay the budget down with reusable infrastructure and autonomous in-space transport, and reach destinations a single vehicle cannot.

01Challenge

Reusable, shared infrastructure and autonomous in-space transport can each supply part of the budget, so the vehicle carries only the remainder. Implement the composition and reach Mars.

Predict firstYour payload fraction comes out negative. What does that mean physically?

02Model

You do not have to pay the whole budget with the onboard rocket. A launch handoff, a tether boost, an orbital-transfer stage, an aerocapture at arrival: each supplies a slice of delta-v the vehicle no longer carries. Because the rocket equation is exponential, dropping the onboard share pays back out of all proportion, and a destination that was unreachable becomes reachable. the way to report the result is the payload mass fraction itself, not a ratio against an infeasible baseline, and to label a destination the vehicle could never reach alone rather than invent a big multiplier for it.

03Guided practice

1. The remainder. With offload segments deltas (km/s) against a budget T, the onboard budget is T - sum(deltas), floored a little above zero.

2. Payload from the remainder. The vehicle's payload fraction follows from that reduced onboard budget by the same rocket equation as Lesson 1.

3. Reach Mars. Stack a sled, a skyhook, a depot, and an aerocapture, and watch the Mars payload fraction turn positive.

04Feedback

PASS WHEN PASS once every destination prints a positive composed payload fraction, including the ones a single vehicle could not reach.

If your run fails, check:

If a payload fraction is still negative, add another offload segment: the onboard remainder is too large.
Remember to floor the onboard budget above zero, or the exponential blows up.

05Retrieve & space

Why does offloading a few km/s help so much more than it seems? (the mass ratio is exponential, so shrinking the onboard budget lifts the payload fraction nonlinearly).
How should you report the win honestly when a single vehicle can't reach the destination at all? (as a payload mass fraction, and label the baseline unreachable rather than quoting an unbounded ratio).
Which part of the composed stack is infrastructure many missions can share? (the launch assist and the in-space transport, e.g. sled, skyhook, depot).

06Mastery & project

You can compose a velocity budget from offload segments and report the payload fraction honestly, including for destinations no single vehicle can reach.

The habit: when a budget is too large for one vehicle, decompose it into shared infrastructure plus a small onboard remainder, and price the payload from the remainder.

GO FURTHER · THE LIVE PLAYGROUND

Compose the journey (live) ↗ · Stack segments per destination and read the same numbers.

← The rocket-equation wall Relative motion: Clohessy-Wiltshire →

PYTHON · NUMPY

Composing the budget

Implement the composition and reach each destination with a stack of offload segments.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you