Find the variation with orbit altitude of the heat loads on a perpendicular plate, due to Earth’s IR emission and albedo, assuming the planet emits as a grey-body with Tp=288 K and =0.6, and has an albedo of =0.3 against a solar irradiance of E=1370 W/m2.
a) Find the variation with orbit altitude of the heat loads on a perpendicular plate, due to Earth’s IR emission and albedo.
The view factor for a frontal planar patch is F12=1/h2.
i.e., the first plot shows the view factor (from the plate to the planet) vs. distance in planet-radii, from LEO (h-1<<1) to GEO (h=6.6, or H=36 000 km). The second plot is a closeup for LEO.
Planet IR load is constant along a circular orbit with this simple model. It depends on IR-absorptance of the plate (equal to plate emissivity by Kirchhoff's law):
i.e. the outgoing longwave radiation (OLR) from Earth is 234 W/m2 (207 W/m2 at H=400 km LEO-altitude, 14 W/m2 at GPS-altitude, and 5.5 W/m2 at GEO-altitude).
Albedo is solar reflection in a planet. We consider it diffuse (i.e. a given patch reflects in all directions according to the cosine law, what yields a uniform radiance, like for a blackbody), but the albedo load on a satellite depends not only on altitude but on angular position to the Sun-Earth directuion, phi, with a maximum at the subsolar point (phi=0).
i.e. albedo load on the plate at the subsolar point (maximum in the orbit), is 364 W/m2 at H=400 km LEO, 24 W/m2 at GPS, and 9.3 W/m2 at GEO. The efect of altitude and of orbit angle are:
i.e. the albedo load is larger than the planet-IR (for a blackbody) at the subsolar point, but in the average it is the opposite (e.g. at h=400 km, the orbital mean is 207 W/m2 for IR but only 116 W/m2 for albedo.