Earth's Thermal Environment

extracted from Thermal Environments JPL D-8160


Link to: JPL data or GSFC data

Low Earth Orbit (LEO) Thermal Environments

The following table summarizes the range of Direct Solar, Reflected Solar (Albedo), and Planetary Infrared for the planet Earth.


                 Perihelion       Aphelion         Mean
----------------------------------------------------------------
Direct Solar      1414 W/sqM      1323 W/sqM      1367.5 W/sqM
                                                  (433.6 Btu/ft2-hr)

Albedo            0.30+/-0.01     0.30+/-0.01      0.30+/-.01
(global annual
average)

Planetary IR     234 +/-7 W/sqM   234+/-7 W/sqM    234 +/7 W/sqM
(global annual                                     (72 to 76 Btu/ft2-hr)
average)

The variation in solar constant of approximately +3.5% about the mean value of 1367.5 w/m2 is due to the eccentricity of the Earth orbit. Perihelion (closest position to the Sun) occurs on or near December 21 each year and aphelion (furthest position from the Sun) occurs on or near June 21. For spacecraft thermal balance problems, this variation is frequently ignored, and either the perihelion value of 141 w/m2 or the annual mean value of 1367.5 w/m2 is used.

Beta Angle:
Another much more profound effect on Direct Solar energy for LEO missions is that of orbital Beta angle which, in combination with altitude, defines the percentage of time in sunlight. Beta angle is defined as the angle between the orbit plane and the vector from the Sun as shown below.

The extreme effects on orbital shadowing are shown above. For a polar orbit launched at local noon or midnight, the resulting initial Beta angle is 0 degrees which gives maximum Earth shadowing. For an orbit altitutde of 150 nautical miles (~ 280 km), which is the lowest generally practical considering orbital decay physics, the resulting sunlight is 59% of the orbit time (i.e., about 53 minutes sunlight, 37 minutes shadow). Similarly, a polar orbit mission launched at local dawn or dusk results in a 90 degree Beta angle, with 100% sunlight.

Beta angle is a function of all the following variables and is therefore somewhat complex: inclination of the orbit, altitude, time of the mission, time of year of launch, and time of day of the launch. It varies as the mission progresses due to changes in the Earth-Sun inertial relationship (rotation of the Earth about the Sun), and orbit precession effects (non-uniformity of the Earth's gravitational field, etc.). The extreme values of Beta angle over a year's time for a mission launched at a given orbit inclination, I, are +/-(I+23.45)degrees. In other words, for a due east launch from KSC, I=28.5 degrees, and Beta angle will vary from about +52 degrees to -52 degrees over the course of a year.

The fundamental effect of Beta angle is its influence on percent sunlight during any given orbit. Note that the percent sunlight does not fall below 59% for normal LEO missions.

Earth Reflected Solar (albedo):


The variation in the Earth's albedo is a function of latitude, cloud cover, ice fields and perhaps time of year. Table 1 shows variation with latitude and some idea of the annual variation. Note that albedo is lowest (~ 0.23) at the equator and up to ~0.7 at the poles.

The albedo of the Earth is normally treated as fully diffuse, but there has been some theoretical work implying specular (forward scattering) of the polar ice caps.

Most spacecraft thermal balance problems in Low Earth Orbit assume an albedo of 0.3 with a cosine reduction in the reflected energy from the subsolar point of the orbit to the terminator. A more strict integration of albedo from Table 1 for a KSC mission launched due East (i.e., inclination = 28.5 degrees) results in a value of 0.25. The variations shown in Table 1 are seldom of importance except to extremely sensitive instruments or detectors. However, long duration polar orbit missions should probably account for the increase at the poles.

Earth Planetary Infrared:
The Earth's planetary infrared emission is a function of latitude, cloud cover, large area weather phenomena, land masses, forestation, and perhaps time of year. Variations with latitude and annual range are shown in Table 2. Note that the peak values are in the tropical zones about 20 degrees either side of the equator, and the minimums are at the poles where albedo is maximum. As in the case of albedo, most spacecraft thermal balance problems ignore the variations of Table 2 and assume a uniform emission of 241 W/sq M (81 BTU/sq ft-hr). Again, long duration polar missions should consider the reduction at the poles.

Table 1. Zonal Mean Albedos for the Planet Earth
Latitude Range Annual Mean Albedo Annual Range 90 80 0.67 0.44 to 0.75 80 70 0.57 0.49 to 0.83 70 60 0.46 0.39 to 0.78 60 50 0.41 0.37 to 0.56 50 40 -0.36 0.32 to 0.46 40 30 0.31 0.26 to 0.37 30 20 0.26 0.25 to 0.30 20 10 0.24 0.20 to 0.27 10 0 0.25 0.24 to 0.26 0 -10 0.23 0.21 to 0.25 -10 -20 0.23 0.21 to 0.24 -20 -30 0.24 0.23 to 0.25 -30 -40 0.29 0.27 to 0.30 -40 -50 0.35 0.33 to 0.39 -50 -60 0.42 0.41 to 0.47 -60 -70 0.51 0.46 to 0.77 -70 -80 0.64 0.61 to 0.88 -80 -90 0.70 0.40 to 0.80
Table 2. Zonal Mean Planetary Infrared Emission for the Planet Earth
Latitude Range Annual Mean W/Sq M Annual Range W/Sq M 90 80 177 146 to 207 80 70 179 149 to 212 70 60 191 164 to 224 60 50 201 175 to 228 50 40 217 191 to 244 40 30 239 217 to 263 30 20 258 248 to 269 20 10 254 236 to 270 10 0 241 232 to 251 0 -10 251 240 to 261 -10 -20 262 248 to 276 -20 -30 259 254 to 263 -30 -40 239 229 to 253 -40 -50 218 205 to 232 -50 -60 203 187 to 217 -60 -70 185 161 to 209 -70 -80 159 124 to 200 -80 -90 135 94 to 190

Geosynchronous Earth Orbit (GEO) Thermal Environments

The following table summarizes the range of direct Solar, Reflected Solar (Albedo), and Planetary Infrared for a Geosynchronous orbit about Earth.


                   Perihelion     Aphelion       Mean             
----------------------------------------------------------------
Direct Solar      1414 W/sq M    1323 W/sq M    1367.5 W/sq M     
                                                (433.6 BTU/sq ft-hr)
Reflected Solar
(Albedo)*
o  Subsolar Peak  7.19 W/sq M    6.72 W/sq M     6.95 W/sq M      
                                                 (2.2 BTU/sq ft-hr)
o  Orbit Average  2.72 W/sq M    2.54 W/sq M     2.63 W/sq M
                                                 (0.83 BTU/sq ft-hr)
Planetary Infrared*
o  Orbit Average  5.52 W/sq M    5.52 W/sq M     5.52 W/sq M     
                                                 (1.75 BTU/sq ft-hr)

* As received by the spacecraft at GEO compared to the energy at
the planet's thermodynamic system boundary in other tables.

The thermal environment in Geosynchronous Earth Orbit is much simpler to define than in LEO. The direct solar term varies only with time of year except for two occultation periods when the spacecraft enters the Earth shadow each year. These occultations occur each day over a 45- to 50-day period twice a year, and last up to 71 minutes.

Both the reflected solar terms and plantary infrared terms are small in GEO. In the table above, the view factor from a spacecraft at 35,743 km (22,204 st. mi.) has been included since altitude is constant (compared with the LEO section where altitude is a variable). In addition, for the reflected solar term, an orbit average value is shown. The values of these terms are so small at this altitude that they are encompassed by any reasonable uncertainty in the direct solar term.


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