Manned Spacecraft Design Principles

(7.75)

$\frac{m_{p,1}}{m_0^I}=k_{p,1}\mathrm{\Delta }{t}_1=0.002889s^{-1}\mathrm{\Delta }{t}_1$ (7.76)

(7.76)

The velocity histories for different values of γ_avg are shown in Figure 7.22 illustrating the effects of gravity as given by sin γ_avg. The time necessary to reach V_E=7.909 km/s for sin γ_avg=0, 0.5, and 1.0 is 287 s, 306 s, and 316 s, respectively. The two extremes are only 29 s apart and because neither is completely accurate we assume that the middle value, sin γ_avg=0.5, may be selected as a reasonable estimate for the gravitational effect. The numerical solution also shown in Figure 7.22 ...