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Research in Space Science SBfITHSONIAW INSTITUTION ASTROPHYSICAL OBSERVATORY Research in Space Science 8PICIAL REPORT Number 169 GPO PRICE $ OTS PRICE(S1 $ Hard copy (HC)& Microfiche (MF) I 75 Mch 24, 1965 CAMFB~,MASSACHLEEITS 02138 . SA0 Special Report N9. 169 SATELLITE ORBITAL DATA Material prepared under the supervisim of Beatrice Miller Mathematician, Data Divisim- Smithsonian Institution Astrophysical Observat xy Cambridge, Massachusetts 02138 TABLE OF CONTENTS Orbital Information .............................................................. Orbit a1 Elements Satellite 1958 Alpha (Explorer l), October 1 through December 31, 1963 I. SA0 smoothed elements ............................................. 3 11. SAO mean elements ................................................. 6 Sun-perigee data ....................................................... 7 Satellite 1959 Alpha 1 (Vanguard 2), October 1 through December 31, 1963 I. S.AO smoothed elements ............................................. 8 11. SA0 mean elements ................................................. 10 Sun-perigee data ....................................................... 1.1 Satellite 1959 Eta (Vanguard 3), October 1 through December 31, 1963 I. SA0 smoothed elements ............................................. 12 11. SA0 mean elements ................................................. 14 Sun-perigee data ....................................................... 1.5 Satellite 1960 Iota 1 (Echo l), October 1 through December 31, 1963 SA0 mean elements ...................................................... 16 Sun-perigee data ....................................................... 19 Satellite 1960 Xi 1 (Explorer 8), October 1 through December 31, 1963 I. SA0 smoothed elements ............................................. 23 11. SA0 mean elements ................................................. 25 Sun-perigee data ....................................................... 26 Satellite 1961 Delta 1 (Explorer g), October 1 through December 31, 1963 I. SA0 smoothed elements ............................................. 27 11. SA0 mean elements ................................................. 32 Sun-perigee data ......... ;.. ........................................... 35 Satellite 1962 Alpha Epsilon 1 (Telstw l), October 1 through December 31, 1963 I. SA0 smoothed elements ............................................. 39 11. SA0 mean elements ................................................. 41 Sun-perigee data ....................................................... 42 Satellite 1962 Beta Mu 1 (Anna lB), October 1 through December 31, 1963 I. SA0 smoothed elements ............................................. 43 11. SA0 mean elements ................................................. 45 Sun-perigee data ....................................................... 46 Satellite 1962 Beta Tau 2 (Injun 3), October 1 through December 31, 1963 I. SA0 smoothed elements ............................................. 47 11. SA0 mean elements ................................................. 50 Sun-perigee data ....................................................... 52 L ~ ORBITAL INFORMATION' a The orbital elements have been derived by the indicated staff members or the Sa'cellite Tracking Program, Smithsonian Astmphysical Obser-.-story, employing the SA0 Differential Orbit Impmvement Program (DtI) . Field-reduced photographs from SA0 Baker-Nunn camera.s comprise the majority of observations used in computing these orbital data. SA0 Mooniiatch teams, the NASA Minitrack netvork, foreign observatories, miscellaneous U.S. and foreign observers, a.nd va.rious radar installations also contribute valuable observations. As opposed to osculating elements, the elements presented here are mean elements in the sense that the effects of the short-period perturbations due to the earth's oblateness have been eliminated. SA0 mean elements have been derived from observations covering several days and are given in the form of a table. The successive sets of elements are essentially independent of each other. They are dependent, however, in the sense that high-order coefficients in the secular and the long-periodic terms are generally considej-eG. as knom and as constant for periods of several weeks or months, as dictated by convenience. The times of epoch in the mean elements are reckoned in Julian Days, but for the sake of convenience the number 2400000.5 ha.s been subtracted to pro- vid.e an abbreviated notation which we call "Modified Julian Days," or "MJD. " The units of 'i e orbital elemeiits are degrees for a.ngular clua.ntities, megameters (Mm= 10k meters) for linear quantities, and revolutions for the mean a.nomly M and its derivatives. The tabulated values of the SA0 mean elements give the values of argument of perigee w, right ascension of the ascending node n, inclination i, eccentri- city e, and mean anomaly M as functions of time t = T - To (where To is the reference epoch) expressed in days. The single digit phced at the right of each value represents the standard error for that element and refers to the last digit given. The same tabulation also gives the mean (anomalistic) motion n, the orbital acceleration nf/2 or n' (dn/dt), and the semimajor axis a or the geocentric distance of perigee q (in megameters). Of the last three columns, the one headed N indicates the number of observations used for the computation of a. set of elements; the one headed D, the number of days used; and the one headed 0, the standa.rd eri-or of the representation of the observations relative to their assumed accuracy. 'This work was supported in part by grant NsG 87-60 from the National Aeronautics and Space Admini strat ion. -1- SA0 smoothed elements ha7re been deyi-red Trom observations covering about two :reelis or moi-e. They are Civen as i'uiictions of time and. generally include both secular and periodic terms. The general expression for a.ny element E is E = E + E t + E 2t2 + . + sin (B~+ tit) , 01 IA~ where t = T - TG is again expressed in days. The pi-esence o:L" a, slanda.rd ? e r ror a.s r, CI c i ate d with a parti c ular c oe €'Ti c i e lit i lid. 1c a.te s i; l lal 'ill i s qua.nti t y vas d.etern;iiied. by the process of diffeiaeiitial orbit impyo-\,:meiit; the absence ol a. standard eri*oi-means tha.t the quantity v3.s l;a.lreii frorri sorile o'ilier souxe. In our computer program, the inclination and tlie arpmeri'i or Ijerigee a.re rei'erred to the true equator of date; 'Lhe righi ascension or .the 9.xeiiiline node, however, is reckoned from the mean equinox of 1950.0 aloii.;; the corres- ponding mean equator to the intersection with the moving true equatoy of date, and then along the true equator of da.te. To ti-ansfom from yight aseelision of the node a,s determined by the D$I to 15rht asceilsion ol" tlie iioile rei"errec1 to the mean equinox of date, one uses where MJD stands for the Modi€ied Julian Day of ihe date. The mean (anomlistic) motion n can be ohtdined €i-rsm ilie smoALhei, elemeiit,c by differentiating the expression for M, and the orbiial ti"c>c lcraiioii ri' ran be obtained by twice differentiatinc the same expi-cssioil L'~~*M. The sun-perigee data are related to the perturbin,- eij.'ek:.ts of a.tmokp,he-i.ic drag. From left to right are the Modified Ju1ia.n Da:; (MJD); the pei'illee heizb Z (in kilometers) above the International Ellipsoid ol' Rei'exence; the ;yeocen'ii:'l' latitude of?the perigee (cp); the angular geocentric dista1i'L:e (;) lrom ihe perigee of the sun; and the difference in right ascensioll (D. R.A. ) be'Lirec!ii the perigee and the sun; all these a.ngles are expressed in 6e:;i.ees. In the last column we give the rate of change of the period (P) expressed in da.ys pel- &~y. -2- Satellite 1958 Alpha (Explxer 1) Eleanx Ryan I. SA0 srn3z)thed elements The fAlowing elements are based on 35 observations and are valid fxthe period October 1 through OctDber 15, 1963. To = 38310.0 MJD w = (2130.83 zk 1) + (e640 f 4)t + ?000213t2 + ?3144 C~Sw -4 2 1 n = (114q507 f 6) - (59116 f 1)t - '?37 X 10 t + zoo31 COS U) -6 2 i = (33O.203 f 2) + q97 X 10-4t + ?7l X 10 t - q0039 sin cu e = ( .08792 f 3) - .91 x lam5, + .32 X + .0004980 sin u) -4 2 M = (.32680 f 4) + (13.721805 f 9)t + (.855 f 2) X 10 t + (.228 f 4) X lam5t3- .0008998 cos w Standard error of one observation: CT = f 1!28 The following elements are based on 89 observations and are valid for the period October 15 through November 1, 1963. To = 38326.0 MJD w = (336q09 f 2) + (70.635 f 3)t + ?000213t2 + q3144 cos w 0 (2 = (320.641 f 4) - (50.1175 f 8)t - .37 x 10-4t2 + q0031 cos w -6 2 o i = (330.203 f 1) + '?000120t t q7l X 10 t - .0039 sin w e = ( .08776 f 1) - .81 x + .32 x + .0004980 sin w -3 2 M = (.90348 f 4) + (13.725393 f 7)t + (.1253 f 4) X 10 t -7 + (.46 f 2) x 10-~t~- (.90 f 6) x 10 t 4 - .0008998 cc)s w Standard error of one observation: CT = f 2128 -3 - The following elements are based on 24 observations and are valid for the period November 1. through November 1.5, 1963. To = 38342.0 MJD -4 2 w = (98938 rt 3) + 7965100t + 985 x 10 t + 93144 COS U) 0 -4 2 R = (3104729 f 5) - 5912102t - -79 X 10 t + 90031 COS UI i = (339202 f 3) 995 x 10-5 t - 90039 sin w e = (.08761 f3) - .lo2 x ~o-~t+ .91 x 10-7t2 + .0004980 sin w -4 2 M = (.53888 f 7) + (13.728730 f 5)t + (.969 f 4) xIO t + (.46 f 9) x - .0008998 COS w Standard error of one observation: o = f 2r38 The following elements are based on 76 observations and are valid for the period November 15 through December 1, 1963. To = 38356.0 MJD w = (205q54 f 1) + ($662 f 2)t + 985 x 10-4t2 + 93144 cos w 0 -4 2 R = (2399026 f 3) - (50.1229 f 6)t - .79 x io t + 0.0031 COS w i = (330.2010 f 8) - 9000266t + 995 x 10-5t2 - 90039 sin w e = (.08749 f 1) - .76 x + .91 x 10-7t2 + .0004980 sin w M = (.76119 f 3) + (13.731535 f 5)t + (-9347 f 8) x 10-4 t 2 - (-90 f 2) X - .0008998 cos w Standard error of one observation: CT = f 1175 I -4- The following elements are based on 47 observations and are valid for the period December 1 through Decenber~l5,1963.
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