Fundamental of Atrodynamic and Application 4 th Ed Conolidated Errata July 2, 207 Thi liting i an on-going document of correction and clarification encountered in the book. I appreciate any comment and quetion you find. I ue RHS for right hand ide when referring to equation and N/A for not applicable. You may reach me at: dvallado@agi.com or davallado@gmail.com. Change in equation are ometime indicated by circle. I have tried to indicate change that were preent in previou edition a I know many of you have thoe copie. For many correction in the 2 nd edition, the firt and econd printing had identical page, unle otherwie noted with the firt printing page being in parenthee. The exact decription may differ, but it hould get you cloe enough. Page xiv, Algorithm : The cro reference hould ay pg 63, not 7. Page 07, Fig 2-9: (3 rd pg 5, 2 nd pg 5, t pg 42) The unit for Mean motion hould be (rev/day 2 / 2) and for Mean motion econd derivative (rev/day 3 /6). The Mean motion econd derivative hould have a negative ign in the box before the 0 exponent. The upercripted value were miing. The checkum for the firt line hould be 9 and the check um for the econd line hould be 6. Page 0, 2 nd equation: (3 rd pg 8) The velocity equation hould be COS( a) SIN( d) COS( b) COS( ) SIN( a) SIN( b) COS( ) + COS( a) SIN( ) v SIN( a) SIN( d) COS( b) SIN( ) + COS( a) SIN( b) COS( ) + SIN( a) SIN( ) COS( a) COS( ) + SIN( d) COS( ) Page 20, Poition and velocity vector: (3 rd pg 27-28, 2 nd pg 26) the lat 2 decimal place of the poition and velocity vector component hould be 68, 32, 9 and 79, 40, and 0. Page 58, Firt paragraph: (3 rd pg 66, 2 nd pg 63, t pg 44) It hould be jut clockwie. Page 73, Algorithm 3: (3 rd pg 80, 2 nd pg 78) The equation for b hould be corrected a follow: 2 b R K ( e b )SIGN( r K ) r b Page 93, Eq 3-52: (3 rd pg 99) The lat term hould be intead of + (TDB 0 ). Page 208, Fig 3-26: The IAU 976 preceion matrix element hould be revered and of oppoite ign. Page 23, Lat para: (3 rd pg 29, 2 nd pg 22) The ummation hould go from 0-4, not 0-5. Page 26, Eq 3-67: (3 rd pg 22) The contant hould be -0.000 029 956T 4. Page 225, Eq 3-82: (3 rd pg 230, 2 nd pg 20, t correct) The equation actually were from 996 value and are thu a little different. They hould be a follow:
2 2 5 3 M z 34.962 98 39 + ( 325r + 98.867 398 )T TT + 0.008 697 2T TT +.78 0 T TT M L 357.527 723 33 + ( 99r + 359.050 340 0)T TT 0.000 60 3T TT 3.3 0 T TT u Mz 93.27 90 28 + ( 342r + 82.07 538 )T TT 0.003 682 5T TT + 3. 0 T TT D L 297.850 363 06 + ( 236r + 307. 480 0)T TT 0.00 94 2T TT + 5.3 0 T TT Q z 25.044 522 ( 5r + 34.36 260 8) T TT + 0.002 070 8T TT + 2.2 0 T TT Page 226, Sentence after Eq 3-86: The end hould ay the equation after Eq. (3-72). Page 232, Text of table 3-6: The velocity unit hould be m/, not mm/. Page 277-28, Sun algorithm: (3 rd pg 279-283, 2 nd pg 265-269 (263-267), t 8-84) The equation hould be made identical to the Almanac verion, which i TOD, not MOD. The development how where the equation come from, but the accuracy i lightly better uing the truncated term from the Almanac. It change the example problem lightly, and thi i evident in the Matlab approach which ha been updated. Page 284, firt paragraph of text after the example: (3 rd pg 287, 2 nd pg 273 (27)) The and 3000 m in altitude can be deleted becaue it i not needed for the problem. Page 288-289, Eq for magnitude of the Moon: (3 rd pg 290-29, 2 nd pg 276-277 (274-275), t 87-88) The numerator hould be R Kz, not. Page 298, Example 5-5: (3 rd pg 300, 2 nd pg 286 (284), t 90-92) The TU hould be replaced by day. Thi caue everal calculation to be different. r XYZ 4.075 93 Xˆ 3.578 308 Ŷ + 0.05 970 Ẑ AU r, v ROT( e) r v XYZ XYZ r 4.075 93 Î 3.325 69 Ĵ.326 86 Kˆ AU 609,750,543 I ˆ 497,438,245 Ĵ 98,394,607 Kˆ km v 0.004 889 Î 0.004 846 Ĵ 0.002 97 Kˆ AU/day 8.46560 I ˆ 8.3937 Ĵ 3.80323 Kˆ km/ Page 299, Lat Eq: (3 rd pg 30, 2 nd pg 287 (285)) The umbra and penumbra equation hould not have the ign before the anwer in degree. Page 362-364, Eq 6-38, Algorithm 44, and Ex 6-8 and Ex 6-9: (3 rd pg 363-366, 2 nd pg 348-352 (346-350), t 38-32) The equation hould be c p a L in each. In Ex 6-8, the target i in front of the interceptor, q tgt 0.000 438 rad/, the phaing value i maller than the original orbit, and the interceptor enter a lower orbit. In Ex 6-9, the target i in front of the interceptor, q tgt 0.000 072 9 rad/, q int 0.000 438 rad/, and the target atellite begin in front of the interceptor. Page 369, Ex 6-0: (3 rd pg 37, 2 nd pg 357 (355), t 326) q tgt 0.000 072 9 rad/, and q int 0.00 045 7 rad/, Page 386, Eq 6-55: (3 rd pg 388, 2 nd pg 373 (37), t 342) The two ummation hould be divided, not multiplied. Page 388, Ex 6-3 v acc equation: (3 rd pg 388, 2 nd pg 374 (372)) The v acc equation hould be 0.75 (6578.36) / (845.0472). (remove the / ) Page 44-46, Alg 49 and 50 (3 rd pg 42-46, 2 nd pg 397-399(395-397), t pg 366-368) There have been everal update to match the final form given in Vallado and Alfano. 204. Curvilinear Coordinate
3 Tranformation for Relative Motion. 8 (3):253-27, Celetial Mechanic and Dynamical Atronomy and the few errata in (206) 25:263 264. Page 445, 2 nd Eq after ELSE: (3 rd pg 44, 2 nd pg 425 (423), t 399) The denominator hould be changed a follow: e SIN( n 2 ) ( ) e COS( n 3 ) -------- COS( Δn 32 )e COS n 2 SIN( Δn 32 ) Page 473, 475, After 2 nd para, and in Alg 56: (3 rd pg 47, 2 nd pg 454 (452), t 428) Add the following para and equation: To find the minimum time with, new value of a e and b e are required. Pruing and Conway (992, 72) how the reult. p b min SIN --------- 2 c Change the a e and b e ubcript to min in Alg. 56. Page 489, 3 rd full para (3 rd pg 486, 2 nd pg 46(460), t pg 436) The reference i for pg 23-236, not 93-98. Page 496, Alg 59: (3 rd pg 493, 2 nd pg 468 (466), t 443) If a > 0.0, calculate the minimum value firt, then find the ubcripted e value. p b min SIN --------- 2 c IF Δn > π b min b min -- 2 t min 3 a --------- min { a m min b min + SIN( b min )} a e SIN ---- 2 ----- 2a b e SIN ---- 2 c 2a The K(U) n coefficient hould alo be corrected a: n 0,, 2, IF 2n even 23n ( + ) ( 6n ) c U --- 94n ( ) ( 4n + ) n 0,, 2, IF 2n + odd 23n ( + 2) ( 6n + ) c U ---- 94n ( + ) ( 4n + 3) Page 542, 544, Eq 8-5, Eq 8-7: (3 rd pg 54, 2 nd pg 56 (53), t 490). In Eq 8-5, the 2 i not needed outide the ummation. Inide the ummation, there hould be a (2-d k ) term defined a k
4 wa in Eq 8-22. In Eq 8-7, the (2-d k ) term hould be inide the integral. All three equation hould ue the d k parameter for conitency. Page 550, Eq 8-27: (3 rd pg 548, 2 nd pg 524 (52), t 497) The final term hould be component of the poition vector a follow: a I r ------ K U U mr r r ------ r 2 r r I + r f I ------ I rj -------- gcat r J I + r lat J r 3 a J r ------ K U U r r ------ r 2 r r I + r f J + ------ ri mr -------- J gcat r J I + r lat J r 3 a K r I + r J U mr ------r r r K K + r 2 --------- f gcat r 3 Page 559, Next to lat Eq: (3 rd pg 557) The final Kp 4 and ap 4 term hould be divided by 6. Page 575, Eq 8-35: The firt equation denominator hould be magnitude, not vector. Page 589, Eq 8-50: (3 rd pg 587, 2 nd pg 550 (546), t 524) The F thrut equation hould have a g before I p. Page 600, Lat paragraph: (3 rd pg 596, 2 nd pg 559) verification hould be validation. Page 626, 2 nd equation: (3 rd pg 622, 2 nd pg 584 (582), t 557) The Mean anomaly rate hould have a n a the firt term on the RHS. Page 635, firt equation: (3 rd pg 63, 2 nd pg 593 (59), t 566) The F term hould have a SIN(n) a well. Page 636, firt unnumbered equation: (3 rd pg 632, 2 nd pg 594 (592), t 567) The bracket hould be a follow: dn ------ dt h ---- r 2 + ----- p COS( n) F eh R ( p + r) SIN( n) F S Page 709, lat line of SP radial rate term: (3 rd pg 705) The term hould be (+eco(n)) 2. Page 75, Center equation and text: (3 rd pg 745, 2 nd pg 694 (692), t 672) The text hould be changed a follow For N unique enor and obervation type combination, and Note that W contain the weight (a appropriate) for each meaurement. For example, if one enor record right acenion-declination, and another record range azimuth and elevation, and each enor produce meaurement, the W matrix would be 5 5. If each enor took 6 meaurement, the W matrix would be 30 30! In practice, we accumulate meaurement o the ize of the W matrix i much maller. In the example above, the W matrix would till be jut 5 5 for all 6 meaurement. The equation hould read w i ------ w. j A i N A Page 802-803, lat equation and top equation (803): (3 rd pg 793, 2 nd pg 743 (740)) The azimuth numerator and denominator are witched. Both term in the numerator of the 3,3 matrix poition hould be quared. Page 80, footnote equation: (3 rd pg 80, 2 nd pg 750) The Dt hould be quared.
5 Page 865, firt equation: (3 rd pg 854, 2 nd pg 788 (784), t 760) The emimajor axi hould be 778.363 intead of.2532. Page 898-899, Eq -44: (3 rd pg 887, 2 nd pg 89 (85), t 79) The econd negative ign from the left hould be +. Top of 899, the Danielon reference hould be from 2003. Page 96, Ex 2-8: (3 rd pg 44, 2 nd pg 44 (44), t 26) The lat entence hould be came within about 340,000 km of Jupiter certainly far enough out to avoid encountering the atmophere. Thi i cloe to the actual value due to ome approximation ued in thi example.. Page 972, econd equation: (3 rd pg 44, 2 nd pg 44 (44), t 26) The firt term hould be /2 - u*.