B.3. Earth Characteristics

1° latitude = 111 km = 60 nautical miles (nm) [Caution: This relationship does NOT hold for degrees longitude.]

a = 149.598 Gm = semi-major axis of Earth orbit

A = 0.306 = Bond albedo (NASA 2015)

A = 0.367 = visual geometric albedo (NASA 2015)

b = 149.090 Gm = semi-minor axis of Earth orbit

d = 149.5978707 Gm = average sun-Earth distance = 1 Astronomical Unit (AU) (NASA 2015)

d_aphelion = 152.10 Gm = furthest sun-Earth distance, which occurs about 4 July (NASA 2015)

d_perihelion = 147.09 Gm = closest sun-Earth distance, which occurs about 3 January (NASA 2015)

d_r = 173 = 22 June = approx. day of summer solstice

e = 0.0167 = eccentricity of Earth orbit around sun

g = –9.80665 m·s^–2 = average gravitational acceleration on Earth at sea level (negative = downward) (from 2014 CODATA)

|g| = g_o· [1 + A·sin²(ϕ) – B·sin²(2ϕ)] – C·H

= variation of gravitational-acceleration magnitude with latitude ϕ & altitude H (in meters) above mean sea level. g_o = 9.7803184 m·s^–2, A = 0.0053024, B = 0.0000059, C = 3.086x10^–6 s^–2.

M = 5.9726 x1024 kg = mass of Earth (NASA 2015)

P_earth = 365.256 days = Earth orbital period (2015)

P_moon = 27.3217 days = lunar orbital period (2015)

Ps_idereal = 23.9344696 h = sidereal day = period for one revolution of the Earth about its axis, relative to fixed stars

R_earth = 6371.0 km = volumetric average Earth radius (from NASA 2015)

= 6378.1 km = Earth radius at equator

= 6356.8 km = Earth radius at poles

S = 1367.6 W ·m^–2 = solar irradiance (solar constant) at top of atmosphere (NASA 2015)

≈ 1.125 K ·m ·s^–1 = kinematic solar constant (based on mean sea-level density)

T_e = 254.3 K = effective radiation emission black-body temperature of Earth system (NASA 2015)

Φ_r = 23.44° = 0.4091 radians = tilt of Earth axis = obliquity relative to the orbital plane (2015)

Ω = 0.7292107 x10^–4 s^–1 = sidereal rotation frequency of Earth (NASA 2015)

2·Ω = 1.458421 x10^–4 s^–1 = Coriolis factor

2·Ω / R_earth = 2.289 x10^–11 m^–1 ·s^–1 = beta factor

B.4. Air and Water Characteristics

a = 0.0337 (mm/day) ·(W/m²)^–1 = water-depth evaporation per unit latent-heat flux

B = 3 x10⁹ V·km^–1 = breakdown potential for dry air

C_vd = 717 J·kg^–1·K^–1 = specific heat for dry air at constant volume

C_pd = 1003 J·kg^–1·K^–1 = specific heat for dry air at constant pressure at –23°C

= 1004 J·kg^–1·K^–1 = specific heat for dry air at constant pressure at 0°C

= 1005 J·kg^–1·K^–1 = specific heat for dry air at constant pressure at 27°C

C_pv = 1850 J·kg^–1·K^–1 = specific heat for water vapor at constant pressure at 0°C

= 1875 J·kg^–1·K^–1 = specific heat for water vapor at constant pressure at 15°C

C_liq = 4217.6 J·kg^–1·K^–1 = specific heat of liquid water at 0°C

C_ice = 2106 J·kg^–1·K^–1 = specific heat of ice at 0°C

D = 2.11x10^–5 m²·s^–1 = molecular diffusivity of water vapor in air in standard conditions

e_o = 0.611 kPa = reference vapor pressure at 0°C

k = 0.0253 W·m^–1·K^–1 = molecular conductivity of air at sea level in standard conditions

L_d = 2.834x106 J·kg^–1 = latent heat of deposition at 0°C

L_f = 3.34 x105 J·kg^–1 = latent heat of fusion at 0°C

L_v = 2.501 x10⁶ J·kg^–1 = latent heat of vaporization at 0°C

n = 3.3 x10²⁸ molecules ·m^–3 for liquid water at 0°C

n_air ≈ 1.000277 = index of refraction for air

n_water ≈ 1.336 = index of refraction for liquid water

n_ice ≈ 1.312 = index of refraction for ice

P_STP = 101.325 kPa = standard sea-level pressure (STP = Standard Temperature & Pressure)

ℜ_d = 0.287053 kPa·K^–1·m³·kg^–1 = C_pd – C_vd

= 287.053 J·K^–1 ·kg^–1 = gas constant for dry air

ℜ_v = 461.5 J·K^–1·kg^–1 = water-vapor gas constant

= 4.61 x10^–4 kPa·K^–1·m³·g^–1

Ri_c = 0.25 = critical Richardson number (dimensionless)

s_o = 343.15 m·s^–1 = sound speed in standard, calm air

T_STP = 15°C = standard sea-level temperature

ε = 0.622 g_water·g_air^–1 = ℜ_d / ℜ_v = gas-constant ratio

γ = 0.0004 (g_water·g_air^–1)·K^–1 = C_p / L_v

= 0.4 (g_water·kg_air^–1)·K^–1 = psychrometric constant

Γd = 9.75 K·km^–1 = |g|/C_p = dry adiabatic lapse rate

ρ_STP = 1.225 kg·m^–3 = standard sea-level air density

ρ_avg = 0.689 kg·m^–3 = air density averaged over the troposphere (over z = 0 to 11 km)

ρ_liq = 999.84 kg·m^–3 = density of liquid water at 0°C

= 1000.0 kg·m^–3 = density of liquid water at 4°C

= 998.21 kg·m^–3 = density of liquid water at 20°C

= 992.22 kg·m^–3 = density of liquid water at 40°C

= 983.20 kg·m^–3 = density of liquid water at 60°C

= 971.82 kg·m^–3 = density of liquid water at 80°C

= 958.40 kg·m^–3 = density of liquid water at 100°C

ρ_sea-water = 1025 kg·m^–3 = avg. density of sea water (sea water contains 34.482 g of salt ions per kg of water, on average)

ρ_ice = 916.8 kg·m^–3 = density of ice at 0°C

σ = 0.076 N·m^–1 = surface tension of pure water at 0°C

B.5. Conversion Factors & Combined Parameters

C_pd / C_vd = k = 1.400 (dimensionless) = specific heat ratio

C_pd /|g| = 102.52 m·K^–1

C_pd / L_v = 0.0004 (g_water·g_air^–1)·K^–1 = γ

= 0.4 (g_water·kg_air^–1)·K^–1

= psychrometric constant

C_pd / ℜ_d = 3.50 (dimensionless)

C_vd / C_pd = 1/k = 0.714 (dimensionless)

|g|/C_pd = Γ_d = 9.8 K·km^–1 = dry adiabatic lapse rate

|g|/ ℜ_d = 0.0342 K·m^–1 = 1/(hypsometric constant)

L_v / C_pd = 2.5 K/(g_water·kg_air^–1)

L_v / ℜ_v = 5423 K = Clausius-Clapeyron parameter for vaporization

ℜ_d / C_pd = 0.28571 (dimensionless) = potential-temperature constant

ℜ_d /|g| = 29.29 m·K^–1 = hypsometric constant

ρ_air ·C_{pd air} = 1231 (W·m^–2) / (K·m·s^–1) at sea level

= 12.31 mb·K^–1 at sea level

= 1.231 kPa·K^–1 at sea level

ρ_air ·|g| = 12.0 kg·m^–2·s^–2 at sea level

= 0.12 mb·m^–1 at sea level

= 0.012 kPa·m^–1 at sea level

ρ_air ·L_v = 3013.5 (W·m^–2) / [(g_water·kg_air^–1)·(m·s^–1)] at sea level

ρ_liq ·C_liq = 4.295 x10⁶ (W·m^–2) / (K·m·s^–1)

1 megaton nuclear explosion ≈ 4x10¹⁵ J

2π radians = 360°

(1–ε)/ε = 0.61 = virtual temperature constant