# B Constants and Conversion Factors

- Page ID
- 10995

# 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·sin^{2}(ϕ) – B·sin^{2}(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/m^{2})^{–1} = water-depth evaporation per unit latent-heat flux

B = 3 x10^{9} 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} m^{2}·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 x10^{6} J·kg^{–1} = latent heat of vaporization at 0°C

n = 3.3 x10^{28} 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}·m^{3}·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}·m^{3}·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 x10^{6} (W·m^{–2}) / (K·m·s^{–1})

1 megaton nuclear explosion ≈ 4x10^{15} J

2π radians = 360°

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