Fundamentals of Astrodynamics and Applications 3 rd Ed

Transcription

1 Fundaentals of Astrodynaics and Alications 3 rd Ed Errata June 0, 0 This listing is an on-going docuent of corrections and clarifications encountered in the book. I areciate any coents and questions you find. I use RHS for right hand side when referring to equations. You ay reach e at: dvallado@agi.co. Changes in equations are soeties indicated by circles. Page front eqtns, equations for conic sections: The arabolic sei-araeter should be h The eriod equation should also aly for ellises. There should be a negative on the seiajor axis in the hyerbolic ean otion equation. Page 4, First equation: The first and third + signs should be - and the sentence should say for the satellite, and erforing the cross roduct, we have Page 43, Last equation: The last line should read In reality, three quintics are required to find the distance (y) fro each Lagrange oint to the nearest riary (Szebehely, 97:35 38) The sybol (y) relaces (x) in the forula as follows: y 5 + ( 3 * )y 4 + ( 3 * )y 3 *y *y * 0 y 5 ( 3 * ) y 4 + ( 3 * )y 3 *y + *y * 0 y 5 + ( + * )y 4 + ( + * )y 3 ( * )y ( * )y ( * ) 0 Page 4, nd equation: The second ter should not have an e in the denoinator. Page 9, Equation-9: Change the denoinators as follows:. Page 9, Eq -00: Change as follows: dc dw dc dw { wc w 3 c } { c 3c 3 } w h a( e )( COS( i) ) COS( Q) G ( a( e )) SIN( q + Q) H a( e )( COS( i) ) SIN( Q) Page 58, Fig 3-0: Change the erihelion date to ~ Jan :

2 Page 94-95, Footnote and Ex 3-5: Change the nubers to read taking the tie derivative of Eq. (3-45) (with resect to T UT ) and dividing by 3,55. The result gives the nuber of sidereal seconds in one solar day (8, s T UT T UT in the footnote. The Ex 3-5 had too any decial laces. Correct as follows: v GMST 3,984, s Reduce this quantity to a result within the range of 8400 s ( 49, s ). Then convert to degrees by dividing by 40 ( s /40 using Eq. (3-35)). v GMST Add this answer to 30 to get the final answer. v GMST Find LST given v GMST + l ( 04.0 ) v LST Page 04, Ex 3-8: Delete TRUNC fro the last line in the exale. Page 0-03, Ex 3-7: The JD should be,453,40 instead of,453,0 in several laces. This changes the values of T TT and T TDB to and T UT to Page 7, Eq 3-5: The final ter in D L should be raised to the 4th ower. Page 8, st, nd and Last equation: The first equation should have a r ITRF at the end. The s equation should be a negative. The velocity equation should be v CIRS ROT3( v ERA )v TIRS + q K r TIRS. Page, End of last ara: Insert the following addition Note that although Kalan (005:48) shows the true obliquity in Eq equinox000, the narrative suggests it s ore aroriately the ean value, shown below. Page, Para before Eq 3-: Add the following note The A ci and A esi ters reresent out of hase contributions (McCarthy and Petit 003:43), but they are not used in the equinox aroaches (Kalan 005:45-4). Page 5, Last Eq before the Exale: The R atrix should be outside the large left bracket. Page 7, Sec 3.7. and eq 3-5: Insert acceleration into the section heading. Add the following to Eq 3-5. a GCRF [ B] [ P] [ N] [ R] [ W]a ITRF + q K q K r TIRS + q K v TIRS Page 34, Alg 4: The four frae bias ters [B] are not needed and should be reoved. Page 8, nd equation: The Mean anoaly values should have a solar subscrit on each. Page 8-83, Ex 5-: The eclitic longitude value should be reduced to 30 deg, and be deg. The Sun osition vector at the botto of age 8 should have 4,8, as the first coonent.the last sentence in the first ara on age 83 should say is about 8873 k, or AU. The final declination value should be deg. The final digit should be a 7. Page 90-9, Alg 3 and Ex 5-3: The eclitic longitude second ter should have the fractional art 883 instead of the 883. This changes the value slightly in the exale, and the final osition to -34,40., -3,57.590, and -, k. Page 9-95, Alg 3 and Ex 5-4: The constant ter should be in both the text, algorith, and the exale roble. In the algorith, UT te should be t n-. All i values should be 30 deg for consistency. Page 30, nd ara: The ubra and enubra equations should both use Sine instead of Tangent. The values change slightly to and resectively. The distances and ties should be corrected as follows 3098 k and 7 in, and 4 k and 7 in.

3 3 Page 37, Alg 4: The to two lines are not needed for the algorith and should be deleted. The Find line should include i at the end. l trueint Q + Page 477, 478, 48, First ara, Eq 7-43, 7-45 and Eq 7-50: Change te to Dt in.change the equations as follows 3 -- Δt -- s 3 s c Δt +,, 3 s T Δt A -- s n n a n a n Page 478, nd ara: Change the ochhaer index fro n to i. s -- B Δt n n Δt n Page 540, Eq 8-5: There should be a before the suation. r Page 548, Eq 8-7: Add to each coonent for the two-body ters. r 3 Page 558, Eq 8-3: Reove the / in the denoinator. Page 3-3, Equations for dm o /dt: The last equation on g 3 should relace t with (t-t o ). The dn dm o /dt equation on g 3 should have the following ter added: ( t t.the next equation dt o ) dn h dj should be instead of. dt r eh { COS( n) }F R (( + r) SIN( n) )F S dt Page 7, nd Eq: Change the 3rd ter in the brackets to be J - J 3. Page 83, nd Eq for q. : The final ter in the square brackets should be +a instead of the -a. Page 705, Several Equations: Udate and add as follows. J Δr R K SP COS () i 4 e ( ) ecos( v) ecos( v) ) SIN () i COS( u) + e J Δṙ μr K SP 3 () i 4 5 / COS ( )e ( v) e ( + ecos( v) ) SIN e r ṙ + e COS( n) ṙ osc ṙ + Δṙ SP μ --e SIN( n) B ṙ osc μ osc Page 9, Last equations: Change as follows: f i F i h j f i aj aj j j F i h + -- j j k F i h j h k a j a k 3h N 3h na ( a ) N h a 8 a na ( )

4 4 dâ i dt d n + ejn i j j + ef i ( a, l M ) + e ( j + ) f ij ( a, a, a 5, l M ) Page 733, Sentence after the data in Ex 0-: Change the equation to y a + bx for consistency. Page 744, Botto set of equations and g 745 to set of equations: Change the four b sybols to y at the botto of age 744. Change the b atrix equation on the to of g 745 to a r ean (overbar). Add Note that W contains the weights (as aroriate) for each easureent. In ractice, we accuulate easureents so the correlation between ters in the W atrix is siler. Page 757, st equation: Change the equation as follows. Page 798, nd equation fro the botto: Change the equation as follows. j observations f( Xˆ + d i ) f( Xˆ ) Xˆ d i o U f gc -- r R K r { C ( l ) S COS + SIN( l) } TAN( f gc )P + [ SIN( f gc )] 0 + { SEC ( f gc ) + TAN ( f gc ) ( ) ( + + ) }P [ SIN( f gc )]] Page 85, Eq -5 and Eq -: For Eq -5, the a 7/ should be oved down with the nuerator, and add a negative sign before the. For Eq -, ove the a 7/ to the denoinator. Page 859, Eq -5: The denoinator should be changed to 3J R K e. 4 ( 3SIN () i ) 4 5SIN + + ( () i ) Page 875, st equation: Change the equation as follows. 3n -----J R K 8e SIN 3 ( q) ( 4 5SIN () i ) SIN () i e COS () i esin( i) + e SIN() i ( 5SIN () i 3) For the equation in the iddle of the age for e o, the sin(w) ter is not needed. Page 930, Proble 3: The J coonent should have a decial oint 8, Page 95, Interediate equations: Change each r i to x ri in the U(r i ) and W(r i ) equations. Page 958, Eq B-: Delete the negative sign in front of k. Page 97, Matrix inversion exale: The, ter should be Page 99, Para after Eq C-3: Add the following stateent. The second ± sign is not necessarily the sae as the first one, but is deterined as follows: For a given function f, a given value of n, and a given choice of the first (±) sign, the second side will be the sae as the first function for all values of a. Thus, it is only necessary to check the sign for any one value of a, and the forula will be colete. Page 985, Two IF stateents: Both variables should be a qi0 instead of a qi.

5 5 Page 030, 034, References: Add the following: O Conner, John J Methods of Trajectory Mechanics (Second Edition). RCA International Services Cororation. Reort # ESMC-TRR Vallado, David A. and Scott S. Carter Accurate Orbit Deterination fro Short-arc Dense Observational Data. Paer AAS resented at the AAS/AIAA Astrodynaics Secialist Conference. Sun Valley, ID. [0] Page Backcover, Nuerical values: Troical year value has an extra in the fraction. It should be