Appendix B: Physical Constants and Astronomical Data

The numbers a rocket scientist reaches for constantly. Values are standard, rounded to the precision this book needs; for mission-grade work, use the full-precision values from a current ephemeris (e.g. NASA JPL). Gravitational parameters $\mu = GM$ are given directly, because for orbit work you almost always want $\mu$, not $G$ and $M$ separately.

Fundamental constants

Constant	Symbol	Value
Standard gravity	$g_0$	$9.80665\ \text{m/s}^2$
Gravitational constant	$G$	$6.674\times10^{-11}\ \text{m}^3\,\text{kg}^{-1}\text{s}^{-2}$
Speed of light	$c$	$2.998\times10^{8}\ \text{m/s}$
Stefan–Boltzmann constant	$\sigma$	$5.670\times10^{-8}\ \text{W}\,\text{m}^{-2}\text{K}^{-4}$
Boltzmann constant	$k_B$	$1.381\times10^{-23}\ \text{J/K}$
Universal gas constant	$R_u$	$8.314\ \text{J}\,\text{mol}^{-1}\text{K}^{-1}$
Solar constant (flux at 1 AU)	$S$	$1{,}361\ \text{W/m}^2$
Astronomical unit	AU	$1.496\times10^{8}\ \text{km}$

Earth

Quantity	Value
Gravitational parameter $\mu_\oplus$	$3.986\times10^{5}\ \text{km}^3/\text{s}^2$ ($=3.986\times10^{14}\ \text{m}^3/\text{s}^2$)
Equatorial radius	$6{,}378\ \text{km}$
Mean radius	$6{,}371\ \text{km}$
Mass	$5.972\times10^{24}\ \text{kg}$
Surface gravity	$9.81\ \text{m/s}^2$
Escape velocity (surface)	$11.19\ \text{km/s}$
Sidereal rotation period	$86{,}164\ \text{s}$ ($23^\text{h}56^\text{m}$)
Equatorial rotation speed	$0.465\ \text{km/s}$
Oblateness coefficient	$J_2 = 1.0826\times10^{-3}$
Obliquity (axial tilt)	$23.4^\circ$

Reference Earth orbits

Orbit	Radius / altitude	Speed	Period
Low Earth orbit (400 km)	$r = 6{,}778\ \text{km}$	$7.67\ \text{km/s}$	$92.6\ \text{min}$
Low Earth orbit (200 km)	$r = 6{,}578\ \text{km}$	$7.79\ \text{km/s}$	$88.5\ \text{min}$
Geostationary (GEO)	alt $35{,}786\ \text{km}$, $r = 42{,}164\ \text{km}$	$3.07\ \text{km/s}$	$23^\text{h}56^\text{m}$
GPS (MEO)	alt $20{,}200\ \text{km}$	$3.87\ \text{km/s}$	$11^\text{h}58^\text{m}$
Karman line (edge of space)	alt $100\ \text{km}$	—	—

The Sun and Moon

Body	$\mu$ (km³/s²)	Mean radius (km)	Escape velocity (km/s)	Notes
Sun	$1.327\times10^{11}$	$695{,}700$	$617.5$ (surface)	mass $1.989\times10^{30}\ \text{kg}$
Moon	$4.903\times10^{3}$	$1{,}737$	$2.38$	mean distance from Earth $384{,}400\ \text{km}$; surface $g = 1.62\ \text{m/s}^2$

The planets

Planet	$\mu$ (km³/s²)	Mean radius (km)	Semi-major axis (AU)	Escape velocity (km/s)
Mercury	$2.203\times10^{4}$	$2{,}440$	$0.387$	$4.25$
Venus	$3.249\times10^{5}$	$6{,}052$	$0.723$	$10.36$
Earth	$3.986\times10^{5}$	$6{,}371$	$1.000$	$11.19$
Mars	$4.283\times10^{4}$	$3{,}390$	$1.524$	$5.03$
Jupiter	$1.267\times10^{8}$	$69{,}911$	$5.203$	$59.5$
Saturn	$3.793\times10^{7}$	$58{,}232$	$9.537$	$35.5$
Uranus	$5.794\times10^{6}$	$25{,}362$	$19.19$	$21.3$
Neptune	$6.835\times10^{6}$	$24{,}622$	$30.07$	$23.5$

The standard atmosphere (Earth, sea level, 1976 US Standard)

Quantity	Value
Pressure	$101.325\ \text{kPa}$
Temperature	$288.15\ \text{K}$ ($15\,^\circ\text{C}$)
Density	$1.225\ \text{kg/m}^3$
Speed of sound	$340\ \text{m/s}$
Approx. density scale height	$\sim 8.5\ \text{km}$ (density falls by $1/e$ each scale height)

A useful exponential model for quick estimates: $\rho(h) \approx \rho_0\, e^{-h/H}$ with $\rho_0 = 1.225\ \text{kg/m}^3$ and $H \approx 8.5\ \text{km}$.

Handy conversions and reference delta-v

From	To	Multiply by
specific impulse $I_{sp}$ (s)	exhaust velocity $v_e$ (m/s)	$9.81$
km/s	m/s	$1000$
AU	km	$1.496\times10^{8}$
degrees	radians	$\pi/180 \approx 0.01745$
$^\circ$C	K	add $273.15$

Representative delta-v costs (the full "delta-v map" is Appendix G): Earth surface → LEO $\approx 9.4$ km/s; LEO → GTO $\approx 2.5$; GTO → GEO $\approx 1.5$; LEO → trans-lunar injection $\approx 3.1$; LEO → Earth escape $\approx 3.2$; LEO → trans-Mars injection $\approx 3.6$.

A note on precision: the figures here are teaching values. Gravitational parameters and radii are known to many more digits; planetary positions require a time-dependent ephemeris (planets are not at fixed distances). When a worked example needs a launch window or a precise transfer, the text says so and uses the appropriate model.