Earth's Thermal Environment

Low Earth Orbit (LEO) Thermal Environments

                 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)

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 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

                   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.

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.