Star tracker viewStar tracker viewReactionwheelReaction wheelReaction wheelTelescopeSpacecraftTelescopeviewFigure 9.5: functional schematic of a satellite observatory, showing three reaction wheelsand two star-tracking cameras for orientation of the telescope and focal plane. The axes ofthe reaction wheels pass through the center of mass of the system. Not shown are thenozzles of compressed-gas thrusters that can exert torque on the spacecraft along thereaction-wheel axes.

Astronomy 203/403, Fall 19991999 University of Rochester6All rights reservedThe classical Cassegrain telescope is shown in Figure 9.7. It is often convenient to define the followingdimensionless parameters associated with the geometry of the telescope. We label the primary andsecondary with the subscripts 0 and 1, in which case the ratios of apex curvatures and diameters areρκκ=01/,kyy=10/.(9.2)The secondary focal lengthsf1andf2are1111/κε±bg. The image at the Cassegrain focus is thereforemagnified laterally with respect to prime focus by the factorCassegrainfocusDeclination orelevation axisCoudé orNasmythfocusTertiary mirror(diagonal flat)Secondary mirrors: convexhyperboloidsFigure 9.6: The classical Cassegrain (left) and coudé (right) configurations of aparaboloid-primary telescope with two interchangeable hyperboloid secondary mirrorsand a flat diagonal tertiary mirror.yzy =kyyDdffff0012001βFigure 9.7: classical Cassegrain telescope, with focal lengths, diameters and otherparameters defined.

Astronomy 203/403, Fall 19991999 University of Rochester7All rights reservedmffk==+−=−211111εερρ,(9.3)and thus the plate scale is smaller than that at prime focus by the factor 1/m. From Equation 9.3 we alsoget a handy expression for the secondary eccentricity:ε111=+−mm.(9.4)The distance from the primary apex to the Cassegrain focal plane isf0β, for which it turns out that11+=+βk maf.(9.5)For example, let the magnification and diameter ratio bem=5andk=15/; then Equations 9.3-9.5 giveρ=0 25.,ε=1 5.andβ=0 2..One can analyze the performance of a Gregorian telescope in a manner different only in sign conventionfrom that of the Cassegrain telescope. Because rays reflected by the primary cross the optical axis (andchange sign iny) on their way to the secondary, and form a real image at the prime focus, thedimensionless constantskandmhave signs opposite those of the corresponding Cassegrain with the samemirror diameters and focal lengths. By the same token, the radii of curvature of primary and secondaryhave opposite signs in Gregorian telescopes. Otherwise the Cassegrain and Gregorian telecopes arebasically the same, optically, so we shall discuss only one of them – the Cassegrain – in the following.The classical Cassegrain has no spherical aberration, and its unblurred field of view is limited by coma, aswe found in Homework Problem Set #2. It is not the only two-mirror configuration that is free of SA,however; we can generate the properties of a whole family of third-order SA-free “Cassegrain” telescopesas follows. Consider a Cassegrain system and another two mirror system with the same apex curvatures

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