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This scaling provides us with a crude estimate for an equivalent single-stage-average speciﬁc impulse, (Isp)avg . e. 7 Interpretation of the Level-1 estimate This result, À54,600 kg, of course, makes no physical sense! Our single stage model does predict that the total payload mass which can be lifted into orbit by this hypothetical single stage vehicle is 45,400 kg. This low Sec. 4 Quick-Fire estimate of cargo mass delivered to orbit 21 payload mass indicates that a single stage Shuttle vehicle, with a 2 million kg initial mass, driven by an engine with an average speciﬁc impulse of 400 s and supporting a 100,000 kg Orbiter spacecraft, could never reach orbit, no matter how small the cargo mass might be.
The magniﬁcation m2 is written here as ‘‘m’’. Simple ray geometry shows that ‘‘m’’ is equal to the ratio of the secondary mirror’s image distance L to Às2 , the object distance. We use the small angle approximation applicable to any light ray that is close to and nearly parallel to the optical axis. This is the paraxial approximation. It is central to the derivation of the optical equations presented in all ﬁrst-year optics courses. In the paraxial optical approximation it can be shown that ‘‘m’’ is the equivalent focal length of the entire optical system, feq , divided by f1 , the focal length of the primary mirror.
4 Interpretation of the Level-2 estimate This two stage model result, 3,200 kg, is positive and therefore makes some physical sense (unlike our previous single stage model). However, this is far too small a cargo Sec. 4 Quick-Fire estimate of cargo mass delivered to orbit 23 magnitude for a viable rocket system the size of the Shuttle. It would mean that the Shuttle could send into orbit only the smallest of satellites. The Shuttle was initially designed to be capable of orbiting the largest Air Force satellites, typically !