Foundations — Space environment — LEO radiation (SAA, Van Allen), atomic oxygen, MMOD debris

Before you can read the parent note, you must be able to read its symbols. This page builds every one of them from nothing, in an order where each brick rests on the brick below it. If a smart 12-year-old reads from line one, they should never meet a squiggle they have not been shown.

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1. Numbers that describe "where" and "how big"

Look at Figure 1. The picture is the whole reason we distinguish the two words: orbital physics cares about pull from Earth's centre, so it always uses $r$ measured from the middle — but engineers quote altitude because that is what a person standing on the ground would call "how high."

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2. Scientific notation and the units you will meet

Space numbers are absurdly big or tiny, so we write them compactly.

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3. Rate vs. total: the single most important pattern

Almost every hazard formula in the parent note is the same shape: a rate (per second) multiplied by time, or — if the rate changes — a sum over time written with the integral sign.

Figure 2 makes this concrete: the total is literally the area under the rate-vs-time curve.

Recall Why is fluence like TID?

Both are a rate integrated over the whole mission — cumulative damage. ::: They share the identical structure: something arriving per unit time, summed over the mission. TID sums energy; fluence sums atoms.

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4. Vectors and the arrow picture

Radiation trapping needs vectors — quantities with a direction, drawn as arrows.

Figure 3 splits one velocity arrow into an along-field piece and an across-field piece — because only the across-field piece ${\vec{v}}_{\perp }$ appears in the gyration-radius formula.

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5. The cross product and the Lorentz force

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6. Kinetic energy — the "how hard does it hit" number

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7. Chance: the Poisson idea

Recall If

$\lambda =10^{-3}$, what is the chance of at least one impact? $1-e^{-0.001}$ ::: $\approx 0.001=0.1\%$ — small for 1 mm particles, but $\lambda$ scales with flux, and tiny particles are $10^4\times$ more common, making their impacts near-certain.

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8. How it all feeds the topic

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Equipment checklist

Self-test: can you answer each before revealing?

• What is the difference between altitude and radius $r$? ::: Altitude is height above the surface; $r$ is measured from Earth's centre, larger by $R_{\text{Earth}}\approx 6371$ km.
• What does the dot in $\dot{D}$ mean? ::: "Per second" — a rate of change; $\dot{D}$ is dose arriving each second.
• What does ${\int }_0^{T}fdt$ compute, in words? ::: The total accumulated amount = area under the rate-vs-time curve from 0 to T.
• Why does $\vec{v}\times \vec{B}$ trap a particle instead of speeding it up? ::: The cross product points perpendicular to $\vec{v}$, so the force only steers, curving the path into a circle.
• In $r_L=m{v}_{\perp }/(qB)$, what makes the circle wider vs tighter? ::: Bigger $v_{\perp }$ or mass $m$ widens it; bigger charge $q$ or field $B$ tightens it.
• Why does 7.7 km/s make atomic oxygen dangerous when a still O atom is harmless? ::: Kinetic energy $\frac{1}{2}m{v}^2$ scales with $v^2$; at orbital speed each atom carries ~4.9 eV, above chemical bond energies.
• Write the probability of at least one debris impact given expected count $\lambda$. ::: $P(\ge 1)=1-e^{-\lambda }$.
• What does $\gg$ mean and where is it used? ::: "Much greater than"; used in $\rho v^2\gg \sigma$ to say impact pressure vastly exceeds material strength.