Q^{\downarrow}_{AQ}(t) = \int_0^t q^{\downarrow}_{AQ}(t) dt = \theta \cdot r_e \cdot h_a \cdot M_a \cdot \cdot \int_0^t \frac{\partial p_a(t,r)}{\partial r} \bigg|_{r=r_e} dt = \theta \cdot r_e \cdot h_a \cdot M_a \cdot \int_0^t \frac{1}{r_e} \frac{\partial p_a(t \cdot \frac{r_e^2}{\chi_a},R_E \cdot r_D)}{\partial r_D} \bigg|_{r=r_e} \frac{r_e^2}{\chi_a} dt_D = \theta r_e^2 \cdot h_a \cdot c_t \phi \cdot \int_0^t \frac{\partial p_a(t \cdot \frac{r_e^2}{\chi_a},r_e \cdot r_D)}{\partial r_D} \bigg|_{r_D=1} dt_D |