This appendix collects the symbols used throughout the book, grouped by topic. Every symbol is defined
where it first appears in the text; this is a reference for when you meet one again.
A standing convention: all mathematics in this book uses standard LaTeX commands, with
$...$ for inline math and $$...$$ for displayed math. No custom macros are defined, so the same
source renders identically in the mdBook and Jupyter Book editions. Vectors are set in bold
($\mathbf{r}$) and their magnitudes in italic ($r = \lvert\mathbf{r}\rvert$). Every physical quantity
carries SI units unless a field-standard unit is noted (specific impulse in seconds; altitudes in km;
delta-v in km/s or m/s).
Mechanics and propulsion
Symbol
Meaning
Typical units
$\Delta v$
delta-v (velocity change)
m/s, km/s
$v_e,\ c$
effective exhaust velocity
m/s
$I_{sp}$
specific impulse
s
$g_0$
standard gravity ($=9.80665$)
m/s²
$m_0,\ m_f$
initial (wet) and final (dry) mass
kg
$m_p,\ m_s,\ m_L$
propellant, structural, payload mass
kg
$m_0/m_f$
mass ratio
—
$\varepsilon$
structural coefficient $m_s/(m_s+m_p)$
—
$\dot m$
mass flow rate
kg/s
$F,\ T$
thrust
N ($T$ also = temperature/period; disambiguate by context)
$T/W$
thrust-to-weight ratio
—
$I_t$
total impulse
N·s
Orbital mechanics
Symbol
Meaning
Typical units
$\mathbf{r},\ \mathbf{v},\ \mathbf{a}$
position, velocity, acceleration vectors
m, m/s, m/s²
$r,\ v$
orbital radius and speed (magnitudes)
m (or km), m/s
$h$
altitude, or specific angular momentum
km; km²/s (disambiguate)
$\mu$
gravitational parameter $GM$ of the central body
km³/s² or m³/s²
$a$
semi-major axis
km
$e$
eccentricity
—
$i$
inclination
deg
$\Omega$
right ascension of the ascending node (RAAN)
deg
$\omega$
argument of periapsis
deg
$\nu$
true anomaly
deg
$E,\ M$
eccentric anomaly, mean anomaly
deg or rad
$T$
orbital period
s
$\varepsilon$
specific orbital energy $-\mu/2a$
J/kg (MJ/kg)
$C_3$
characteristic energy $v_\infty^2$
km²/s²
$v_\infty$
hyperbolic excess velocity
km/s
$\gamma$
flight-path angle
deg ($\gamma$ also = ratio of specific heats; disambiguate)
Propulsion thermodynamics
Symbol
Meaning
Typical units
$p_c,\ T_c$
chamber pressure, chamber temperature
Pa (MPa), K
$p_e,\ p_a$
nozzle exit pressure, ambient pressure
Pa
$A_t,\ A_e$
throat area, exit area
m²
$\epsilon$
nozzle expansion ratio $A_e/A_t$
—
$\gamma$
ratio of specific heats
—
$R_u,\ R$
universal / specific gas constant
J/(mol·K), J/(kg·K)
$\mathcal{M}$
molar mass of exhaust
kg/mol
$M$
Mach number
—
Spacecraft systems
Symbol
Meaning
Typical units
$q$
dynamic pressure $\tfrac12\rho v^2$; or heat flux
Pa; W/m²
$\rho$
atmospheric (or material) density
kg/m³
$C_d$
drag coefficient
—
$\alpha,\ \varepsilon$
absorptivity, emissivity (thermal)
—
$\sigma$
Stefan–Boltzmann constant
W/(m²·K⁴)
$S$
solar flux (solar constant at 1 AU)
W/m²
$G/T$
antenna gain-to-noise-temperature
dB/K
$\text{EIRP}$
effective isotropic radiated power
dBW
Mathematical operators and constants
Symbol
Meaning
$\nabla,\ \partial$
gradient / divergence / curl; partial derivative
$\dot{x},\ \ddot{x}$
first and second time derivatives
$\int,\ \oint$
integral; closed-loop integral
$\times,\ \cdot$
vector cross product; dot product
$\hat{\mathbf{r}}$
unit vector
$\approx,\ \propto,\ \ll,\ \gg$
approximately equal; proportional to; much less/greater than
$\ln,\ \log$
natural logarithm; base-10 logarithm
$e$
base of natural logarithm ($\approx 2.71828$)
$\pi$
$\approx 3.14159$
$\blacksquare$
end of a derivation or proof
A note on reused letters
A handful of letters are traditional in more than one subfield and are reused here rather than
invented around. The book always disambiguates on first use in a section. The most common overlaps:
$T$ — thrust, temperature, or orbital period.
$\gamma$ — flight-path angle (ascent/re-entry) or the ratio of specific heats (nozzle flow).
$h$ — altitude or specific angular momentum.
$\varepsilon$ — specific orbital energy, structural coefficient, or emissivity; $\epsilon$ (a
different glyph) is the nozzle expansion ratio.
$c$ — effective exhaust velocity or the speed of light (the latter only in Chapter 21).
A note for builders of this book: keep to the symbols above and to standard LaTeX. If a chapter
needs a symbol not listed here, add it to this table rather than defining a macro, so that the two
build systems continue to render the mathematics identically.