Standard Atmosphere

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

The Standard Atmosphere is an internationally recognized reference model that describes how Earth's atmospheric parameters (temperature, pressure, density) vary with altitude. Based on the ideal gas law and empirical measurement data, it provides a unified reference baseline for vehicle aerodynamic calculations, trajectory design, and atmospheric drag estimation.

Core Elements

Atmospheric Layer Structure

Earth's atmosphere is divided into five layers based on temperature variation characteristics:

LayerAltitude RangeTemperature ChangeCharacteristics
Troposphere0–11 kmApprox. −6.5 °C/kmPrimary weather phenomena layer
Stratosphere11–50 kmInitially constant, then risingOzone layer absorbs ultraviolet radiation
Mesosphere50–85 kmApprox. −3 °C/kmColdest region of the atmosphere
Thermosphere85–500 kmSignificant increaseHeated by solar ultraviolet radiation
Exosphere>500 kmApproaches constantAtmospheric particles can escape Earth

Temperature, Pressure, and Density Distribution with Altitude

In the troposphere and standard atmosphere model, the parameters vary with altitude as follows:

Temperature (within the troposphere):

T(h)=T0−βhT(h) = T_0 - \beta h

where T0=288.15T_0 = 288.15 K and β=0.0065\beta = 0.0065 K/m.

Pressure (based on the hydrostatic equation and ideal gas law):

p(h)=p0(1−βhT0)g0βRp(h) = p_0 \left(1 - \frac{\beta h}{T_0}\right)^{\frac{g_0}{\beta R}}

where p0=101325p_0 = 101325 Pa and R=287.05287R = 287.05287 J/(kg·K).

Density:

ρ(h)=ρ0(1−βhT0)g0βR−1\rho(h) = \rho_0 \left(1 - \frac{\beta h}{T_0}\right)^{\frac{g_0}{\beta R} - 1}

where ρ0=1.225\rho_0 = 1.225 kg/m3^3.

Ideal Gas Law

The standard atmosphere model is based on the ideal gas law:

p=ρRTp = \rho R T

This equation relates the three fundamental parameters of pressure, density, and temperature, and serves as the foundation for atmospheric parameter calculations.

Standard Atmosphere Tables

Standard atmosphere tables present temperature, pressure, density, and other parameters in tabular form, covering altitudes from sea level to approximately 1000 km. Commonly used standard atmosphere models include:

  • US Standard Atmosphere 1976: US standard, internationally adopted
  • CIRA: International Reference Atmosphere, incorporating seasonal and latitudinal variations
  • Jacchia series: Precision models for the upper atmosphere (>200 km)

Application Value

The standard atmosphere is a fundamental input for aerospace vehicle aerodynamic calculations and trajectory design. During the powered phase, atmospheric density determines the magnitude of aerodynamic drag. During reentry, atmospheric parameters govern aerodynamic heating and deceleration characteristics. For low-Earth-orbit spacecraft, upper-atmosphere density is a critical parameter for orbital decay analysis.

References

  • Zheng W, An X Y, Zhou X, He R Z. Aerospace Flight Mechanics[M]. National University of Defense Technology, 2026.
  • NOAA. U.S. Standard Atmosphere 1976[S]. 1976.