q_emis = (A)(e)(s)(T_s)⁴

s=Stefan-Boltman Constant = 5.67x10^-8 W/msK⁴

e=Emissivity (0.90)

T_s = Surface Temperature   =  700K

q_abs < q_emis

Eqn. D2 is the thermal energy the shuttle loses from that same surface area when the orbiter is in the earths shadow.  The exposed surface area is assumed to be the same for both scenarios and is then constant for both equations and can be factored out.  When the shuttle is on the dark side of the Earth the shuttles skin and thermal tiles radiate more heat than it absorbs from the sun.  Therefore the temperature of the shuttles skin should drop to absolute 0K (-273°F) before it reaches the sunny side of the earth again.