Spacecraft bus — structure, power, thermal, ADCS, C&DH, comms, propulsion: Foundations

Before you can read a single formula in the parent note, you need the alphabet those formulas are written in. This page defines every letter — what it means in plain words, what picture it stands for, and why the topic can't do without it. Read top to bottom; each idea uses only the ones above it.

Part 0 — The stage: what "space" removes

This single fact — no air — is why the thermal section only talks about radiation, and why the parent note keeps saying "no convection". Hold onto it.

Figure — Spacecraft bus — structure, power, thermal, ADCS, C&DH, comms, propulsion

Figure s01 — The picture that fixes Part 0: the warm box can shed heat only by the orange radiation arrows; the crossed-out "no air" reminds you convection and conduction-to-air are simply unavailable. Every thermal equation later inherits this restriction.

Part 1 — Numbers that describe amounts

Mass — $m$

Area — $A$

Figure s02 — Why the topic keeps two different areas apart: sunlight power depends on the plum projected (shadow) area $A_{proj}$ , not the larger teal panel. Tilt the panel and its shadow shrinks even though the panel itself is unchanged — that shrinking shadow is exactly what $A_{proj}$ measures.

Length & density — $L$ , $ρ$

Part 2 — Numbers that describe pushes and pulls

Acceleration — $a_{acc}$ , and the launch $g$

Force — $F$ (and Newton's rule)

Stress and yield strength — $σ$ , $σ_{y}$

Part 3 — Efficiency $η$ (define it before any $η$ -ratio)

We meet the Greek letter $η$ before using it in any specialised ratio, because the structural "strength-per-weight" ratio in Part 4 is written with the same letter.

Part 4 — Two amounts combined: efficiency ratios

Structural efficiency — $η_{struct} = σ_{y} / ρ$

Part 5 — Numbers that describe energy, power, and time

Energy $E$ and Power $P$ — the crucial difference

The power symbols this topic uses — $P_{load}$ and $P_{SA}$

Time symbols in orbit — $T_{orbit}, T_{sun}, T_{eclipse}$

Figure s03 — Where the orbit-timing symbols live: the spacecraft rides the dotted loop, bathed in orange sunlight over the arc $T_{sun}$ and swallowed by the plum shadow cone for $T_{eclipse}$ . The whole lap is $T_{orbit}$ . This is the physical stage on which the power-balance derivation below plays out.

Building the array-sizing formula from the balance

Formula Why the array must be oversized — full chain

Step 1 — WHAT the battery must survive. During eclipse the arrays are dead, so the battery alone runs the load $P_{load}$ for a time $T_{eclipse}$ . But pulling energy out leaks, so the battery must actually release more than the load uses: $E_{discharge} = \frac{P _{load} \cdot T _{eclipse}}{η _{discharge}} .$ Dividing by $η_{discharge} < 1$ makes this bigger — you must store extra to cover the leak.

Step 2 — WHAT daylight must bank. During sunlight, the extra array power beyond the load, $P_{SA} - P_{load}$ , charges the battery for a time $T_{sun}$ , but charging also leaks, so only a fraction sticks: $E_{charge} = (P_{SA} - P_{load}) \cdot T_{sun} \cdot η_{charge} .$

Step 3 — WHY they must be equal. Over one steady orbit the battery ends where it began (no net drain), so banked = spent: $(P_{SA} - P_{load}) T_{sun} η_{charge} = \frac{P _{load} T _{eclipse}}{η _{discharge}} .$

Step 4 — solve for $P_{SA}$ . Divide by $T_{sun} η_{charge}$ , then add $P_{load}$ : $P_{SA} = P_{load} + \frac{P _{load} T _{eclipse}}{T _{sun} η _{charge} η _{discharge}} = P_{load} (1 + \frac{T _{eclipse}}{T _{sun} η _{charge} η _{discharge}}) .$ This is exactly the parent note's sizing formula. The bracket is the oversizing factor: the longer the dark ( $T_{eclipse}$ up), or the leakier the battery ( $η$ 's down), the bigger the array must be.

Part 6 — Numbers that describe heat and light

Temperature $T_{temp}$ (Kelvin)

Solar constant $S$ , albedo $a$ , Earth IR $E_{Earth}$

Absorptivity $α$ , emissivity $ϵ$ — the surface's two personalities

The heat inputs $Q_{in}$ and output $Q_{out}$ — one sign convention

The radiation law — Stefan–Boltzmann $σ$ and $T_{temp}^{4}$

Figure s04 — What the $T^{4}$ law adds that words cannot: the orange curve of rejected heat rises ever more steeply, so the horizontal "heat I must dump" line (teal) crosses it at exactly one temperature (plum dot). That crossing IS the spacecraft's settling temperature — nudge the heat load up and the crossing barely moves, which is why the vehicle self-stabilises.

How it all feeds the topic

See the parent Spacecraft Bus topic to see these letters assemble into the full subsystem story.

Equipment checklist

Cover the right side and test yourself — you're ready when each answer comes instantly.

What does

F = m a_{acc}

let you compute at launch?

The axial force the structure must carry: mass times launch acceleration.

Why do we tag acceleration

a_{acc}

on this page?

To keep it distinct from the plain italic

a

used for Earth's albedo.

What is the difference between stress

σ

and force

F

Stress is force divided by area; the same force gives high stress on a thin part, low stress on a fat one.

What does

σ_{y}

mark?

The yield strength — the stress above which the material bends permanently.

What is efficiency

η

, in one phrase?

A goodness ratio — what you want divided by what it costs (often the kept-fraction, 0 to 1).

Why do the units of

σ_{y} / ρ

mean "strength per weight"?

They reduce to newton·metre per kilogram — load-times-reach bought per kilogram lifted.

Why is a wall's mass

m = A L ρ

Volume = cross-section area × length, then mass = volume × density.

What do

P_{load}

and

P_{SA}

each mean?

P_{load}

is the rate all equipment eats power;

P_{SA}

(SA = Solar Array) is the rate the panels generate power.

Why must you not confuse power

P

with energy

E

P

is a rate (watts);

E

is a total (joules);

E = P T

where

T

is a time duration.

Where does the array oversizing factor

1 + T_{eclipse} / (T_{sun} η_{charge} η_{discharge})

come from?

Setting daylight energy banked equal to eclipse energy spent, both corrected for battery leaks.

What removes convection from a spacecraft's heat options?

The vacuum of space — no air, so the only way out is radiation.

Why is temperature written in kelvin for the radiation law?

Because

Q_{out} \propto T^{4}

needs a scale that starts at absolute zero.

What do

α

and

ϵ

each control?

α

= fraction of sunlight absorbed;

ϵ

= how well the surface glows heat away.

What sign convention ties the heat flows together?

All warming flows are positive inputs summed into

Q_{in}

; the only exit is

Q_{out}

, and balance sets

Q_{in} = Q_{out}

Why might effective radiating area be less than the geometric

A

View factors — not every part of the surface sees cold space; some faces the warm Earth or is blocked.

Why does the

T^{4}

law give a stable operating temperature?

A small temperature rise multiplies rejected heat sharply, pushing the balance back.

Which two unrelated quantities both use the symbol

σ

Mechanical stress (pascals) and the Stefan–Boltzmann constant (

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