Technical Note

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1 ES7I Call N. CcpK H. 7 / Technical Nte Cntinuus Cverage f the Nrth Plar Regin with Only Tw Cmmunicatins Satellites J. U. Beusch 4 September 1969 Lincln Labratry MASSACHUSETTS INSTITUTE OF TECHNOLOGY Lexingtn, Massachusetts 0km

2 This dcument has been apprved fr public release its distributin is unlimited.

MASSACHUSETTS INSTITUTE OF TECHNOLOGY LINCOLN LABORATORY CONTINUOUS COVERAGE OF THE NORTH POLAR REGION WITH ONLY TWO COMMUNICATIONS SATELLITES /. U.

3 MASSACHUSETTS INSTITUTE OF TECHNOLOGY LINCOLN LABORATORY CONTINUOUS COVERAGE OF THE NORTH POLAR REGION WITH ONLY TWO COMMUNICATIONS SATELLITES /. U. BEUSCH Grup 67 TECHNICAL NOTE SEPTEMBER 1969 This dcument has been apprved fr public release and sale; its distributin is unlimited. LEXINGTON MASSACHUSETTS

4 The wrk reprted in this dcument was perfrmed at Lincln Labratry, a center fr research perated by Massachusetts Institute f Technlgy. The wrk was spnsred by the Department f the Navy under Air Frce Cntract AF 19(628)-S167. This reprt may be reprduced t satisfy needs f U.S. Gvernment agencies. n

$The system described requires nly tw satellites t prvide bth this cverage and cverage f a cnsiderable fractin f the nrthern hemisphere. Tw rbit planes with 6.$ 4 inclinatin, high eccentricity and ~24 hur perids are emplyed.

4 inclinatin, high eccentricity and ~24 hur perids are emplyed.

5 ABSTRACT The prblem f prviding cntinuus cverage f the nrth plar regin with a small number f cmmunicatins satellites is cnsidered. The system described requires nly tw satellites t prvide bth this cverage and cverage f a cnsiderable fractin f the nrthern hemisphere. Tw rbit planes with 6. 4 inclinatin, high eccentricity and ~24 hur perids are emplyed. The regins f the earth frm which a satellite is cntinuusly visible frm terminals with varius minimum elevatin angles are shwn. The regins in which mutual visibility f a satellite by tw terminals is guaranteed are shwn. A few cmments cncerning satellite design fr this rbit are included. Accepted fr the Air Frce Franklin C. Hudsn Chief, Lincln Labratry Office in

Synchrnus, equatrial satellites prvide cverage t nly lw and mderate latitudes. Satellites in inclined circular rbits can prvide plar cverage but cnsiderably mre than tw satellites are required.

6 Cntinuus Cverage f the Nrth Plar Regin with Only Tw Cmmunicatins Satellites I. Intrductin Cntinuus cverage f the nrth plar regin is desirable, and in sme cases mandatry, fr many satellite cmmunicatins systems. Synchrnus, equatrial satellites prvide cverage t nly lw and mderate latitudes. Satellites in inclined circular rbits can prvide plar cverage but cnsiderably mre than tw satellites are required.* Cnsider the prblem f prviding cntinuus nrth plar cverage using a small number f satellites. It is clear that a single satellite in earth rbit cannt prvide this cverage. T prvide this cverage by keeping a single satellite hvering cnstantly ver the nrthern hemisphere by firing jets n the satellite wuld be prhibitively expensive. In the next sectin we describe a system f nly tw satellites which prvides this cverage and als prvides cntinuus cverage dwn t mderate latitudes f a wide strip f the earth near an arbitrarily selected lngitude. These tw satellites can augment the cverage f synchrnus equatrial satellites r can be used by terminals which perate in an area which includes bth the nrth plar regin and a strip f the earth near a particular lngitude. An example f the latter case is military frces which are deplyed in the plar regin and must cmmunicate with a base lcated in the cntinental United States (CONUS). The system described has the further advantage that, whenever the earth casts its shadw n the slar array f a satellite, the terminals are using the ther satellite. Thus the cmmunicatins transmitter need nt be used during slar eclipse s nly a small strage battery need be included in each satellite. II. Selectin f the Satellite Orbits In synthesizing a system t prvide cntinuus nrth plar cverage with nly tw satellites, ne must cnsider elliptical rbits since circular rbits cannt achieve this bjective. A highly elliptical rbit with its apgee in the nrthern hemisphere is attractive since a satellite spends cnsiderably mre time near its apgee than its perigee. * The advantage f these rbits wuld be that cverage f the suth plar regin wuld als be prvided in thse cases in which it is desired.

In general, such an rbit is unstable in the sense that the apgee will nt remain ver the nrthern hemisphere due t perturbatins caused by the nn-sphericity f the earth.

When i = 6.4, apgee rtatin is zer s this inclinatin has been chsen.

7 In general, such an rbit is unstable in the sense that the apgee will nt remain ver the nrthern hemisphere due t perturbatins caused by the nn-sphericity f the earth. The angular velcity with which the apgee rtates in the rbit plane is prprtinal t 2 5 cs i - 1 where i is the rbit inclinatin, i.e., the angle between the equatrial and rbital planes (Ref. 1). When i = 6.4, apgee rtatin is zer s this inclinatin has been chsen. If tw satellites are placed in the same rbit plane phased such that when ne is at apgee the ther is at perigee, cntinuus nrth plar cverage can be prvided if the apgee height is sufficiently large. When cntinuus cverage f a wide strip f the earth dwn t mderate latitudes near an arbitrarily selected lngitude is als required, tw satellites in the same rbit plane n lnger suffice. This cverage can be prvided if each satellite reaches apgee nly when it is ver the selected lngitude. Figure 1 shws the simplest way f achieving this. Bth rbit planes intersect the equatrial plane in the same line, the line f ndes. Relative t the line f ndes the earth rtates with a perid T «24 hr. The rbital perid f the satellites is als T and they are phased s that ne reaches apgee every T/2 hr. The directin f rtatin f the satellites are chsen s that they fllw the rtatin f the selected lngitude when they are near apgee. If a particular set f terminals can pint antennas tward ne satellite in a particular directin at time t, they can pint tward the ther satellite in the same directin at time t + T/2. This symmetry is use- ful in the cverage analysis f the next sectin. It shuld be nted that T is slightly less than 24 hurs s the satellites reach a particular pint in rbit at slightly different times each day. T insure negligible atmspheric drag the perigee altitude is apprximately 700 km. The effects f drift f perigee altitude is discussed in Sectin VII. A semi-majr axis f earth radii and an eccentricity f prvide an rbital perid f hurs. This is the perid f rtatin f the earth relative t the line f ndes.* As shwn in Fig. 1, the inclinatin f bth rbital planes is 6.4, the ascending ndes are separated by 180 and the argument f perigee is 270. tthe Mlniya satellites use this inclinatin fr high latitude cverage. * Relative t the vernal equinx the earth rtates at a rate f per day. The line f ndes rtates at a rate f per day because f perturbatins f the rbit due t the earth's equatrial bulge. Thus, the earth rtates at per day relative t the line f ndes, i.e., requires 2. 9 hurs t rtate 60.

III. Regin f Cntinuus Visibility The earth's equatrial plane and the line f ndes determine an rthgnal crdinate system; the crdinates are the line f ndes, a line perpendicular t the equatrial plane

Sme higher rder effects including perturbatins due t the sun and mn must be canceled by adjusting the rbit with thrusters in the satellite. Fuel requirements fr these adjustments are fairly small.

8 III. Regin f Cntinuus Visibility The earth's equatrial plane and the line f ndes determine an rthgnal crdinate system; the crdinates are the line f ndes, a line perpendicular t the equatrial plane and a line in the equatrial plane perpendicular t the ther lines. Cnsidering the effects f the secnd harmnic f the earth's gravitatinal field, bth rbit planes are statinary in this crdinate system. Sme higher rder effects including perturbatins due t the sun and mn must be canceled by adjusting the rbit with thrusters in the satellite. Fuel requirements fr these adjustments are fairly small. We assume these adjustments are made. Since the rbital perids and the perids f rtatin f the earth in this crdinate system are equal, the cverage f the satellites during a single perid is repeated exactly in all subsequent perids. Because f the symmetry described in the previus sectin, cverage prvided by ne satellite during ne half-rbit is repeated exactly by the ther satellite in the next half-rbit. Therefre, if a terminal with a particular lcatin and minimum elevatin angle can pint its antenna tward ne satellite fr a half-rbit (~12 hurs) it can always pint tward ne f the satellites, i.e., has cntinuus satellite visibility. Furthermre, if ne satellite is simultaneusly visible frm tw terminals fr a half-rbit, ne f the satellites is always visible frm bth terminals. In Fig. 2, cntinuus visibility cnturs fr terminals with minimum elevatin angles f 0, 5,10, 20 and 0 degrees are shwn. A terminal with a particular minimum elevatin angle lcated n the crrespnding cntur can pint tward ne satellite fr ~12 hurs and thus has cntinuus satellite visibility. A terminal lcated nrth f this cntur als has cntinuus satellite visibility. The cnturs can be mved east r west n the map by changing the lngitude f the ascending ndes f the rbits. IV. Regins f Cntinuus Mutual Visibility A terminal lcated n the cnturs f Figs., 4, and 5 crrespnding t its minimum elevatin angle can pint tward each satellite fr 14, and 21 hurs per rbital perid, respectively. These cnturs prvide mutual visibility infrmatin in the fllwing way. Cnsider the rbit plane f Fig. 6. The satellite is visible frm terminals A and B fr time intervals f length T. and r R. The satellite is visible frm bth terminals fr time T. R and visible frm neither fr time r. R. Frm Fig. 6,

Cnsider tw terminals with'particular minimum elevatin angles. If each is lcated n r nrth f the crrespnding 17. 5 hr. cntur f Fig. 4, cntinuus mutual visibility is prvided.

9 r A + T B- T AB +1 Ai = T ~ 24hr - where T is the rbital perid. Fr cntinuus mutual visibility we require T. R 5 12 hr. s we require r T +T T + T 12 hr A B * T AB nr - ^ + ^.7+12-^. It can be shwn fr the nrthern hemisphere lcatins f interest, TTT > 1 hr. s if T. + r R 5 5 hr., T. R 12 hr. and cntinuus mutual visibility is prvided. Cnsider tw terminals with'particular minimum elevatin angles. If each is lcated n r nrth f the crrespnding hr. cntur f Fig. 4, cntinuus mutual visibility is prvided. If ne is lcated nrth f the crrespnding cntur f Fig. and the ther nrth f the crrespnding cntur f Fig. 5, cntinuus mutual visibility is prvided. As with Fig. 2, the cnturs f Figs., 4, and 5 can be mved east r west n the map. An existing cmputer prgram was emplyed t btain the cnturs. Because f the frm f the prgram, results were cmputed fr particular terminal lcatins and were quantized t 1/ hr. Cnturs were drawn between these particular terminal lcatins using straight lines. T the extent f the quantizatin and f the departure f the straight lines frm smth curves, the results are apprximate. V. Examples In Fig. 7 we shw cverage prvided by tw satellites t terminals with lw (0 r 5 ) minimum elevatin angles. A terminal lcated in the cntinental United States (CONUS) abve the 21 hr. line has cntinuus mutual visibility with all terminals (e.g., aircraft) lcated abve the 14 hr. line. Mst f the nrthern hemisphere is abve the 14 hr. line. In Fig. 8 cverage is shwn prvided by three satellites, tw in 6. 4 inclined rbits and ne in synchrnus equatrial rbit. Assume there are tw 5 elevatin

The terminal in Maine has cntinuus mutual visibility with shipbrne terminals lcated in the Mediterranean Sea, and the Nrth Atlantic, Nrth Pacific and Arctic Oceans. VI.

10 terminals lcated in CONUS as shwn. The terminal in Califrnia has cntinuus mutual visibility with shipbrne terminals lcated inside the curved cnturs in the Pacific and limited t elevatin angles greater than 20 r 0. The terminal in Maine has cntinuus mutual visibility with shipbrne terminals lcated in the Mediterranean Sea, and the Nrth Atlantic, Nrth Pacific and Arctic Oceans. VI. Satellite Design Cnsideratins Relative t the earth's equatrial plane the rbit planes f bth satellites are inclined by Relative t the earth's rbit plane (ecliptic) the inclinatin varies frm 40 t 87. As seen frm the satellite the sun can be lcated in any directin in the ecliptic plane and the earth can be lcated in any directin in the rbit plane. Thus if slar panels n the satellite are sun-riented, an earth-riented antenna must be able t pint in almst all directins relative t the plane f the slar panel. This is nt true f equatrial satellites because their rbit plane is inclined nly 2 relative t the ecliptic. An attractive way t cnfigure the satellite is shwn in Fig. 9. A mmentum wheel r cntrl mment gyr is munted n the slar panels. The wheel spins at a bias speed abut an axis nrmal t the plane f the panels. The wheel axis always pints tward the sun s the angular mmentum vectr must be rtated nce per year by appyling external trque with thrusters. Once per rbit the spacecraft rtates abut the wheel axis and the satellite bdy scillates ±180 abut the slar array shaft. A flexible cable transfers pwer and cntrl signals frm the slar panels t the bdy. Attitude cntrl is accmplished by rienting the antennas tward the earth with earth sensrs while using sun sensrs t rient the slar array. With this cnfiguratin, antennas remain earth riented but they rtate abut an axis frm the satellite t the center f the earth. During the useful part f the satellite's rbit the angle subtended by the earth varies frm ~40 t 9. 5 s use f variable beamwidth antennas wuld be desirable. At X-band (~8 GHz) a reasnable design is t include 4 r 5 antennas, with prgressively narrwer beams, and electrnically switch between them as the satellite traverses its rbit. The antenna apertures wuld vary frm t 12 inches. If a lwer frequency, e.g., UHF (00 MHz), transpnder is included, prviding a variable beamwidth antenna ver the wide variatin f satellite altitude is a mre difficult prblem due t the large aperture invlved.

Thermal design f the satellite bdy is smewhat simpler than fr a synchrnus equatrial rbit satellite because the sun is always in the plane which is perpendicular t the slar array shaft.

4 inclinatin and 700 km (80 nm) rbit and finally cplanar transfer t the highly elliptical rbit. A launch vehicle wuld have slightly mre paylad capability fr this rbit than fr synchrnus equatrial rbit.

11 Thermal design f the satellite bdy is smewhat simpler than fr a synchrnus equatrial rbit satellite because the sun is always in the plane which is perpendicular t the slar array shaft. Launch int the rbits frm Cape Kennedy culd be accmplished by initial launch int a 52 inclined 180 km (100 nautical miles) parking rbit, nn-cplanar transfer t 6. 4 inclinatin and 700 km (80 nm) rbit and finally cplanar transfer t the highly elliptical rbit. A launch vehicle wuld have slightly mre paylad capability fr this rbit than fr synchrnus equatrial rbit. VII. Stability f the Orbits The inclinatin f the rbits relative t the ecliptic varies frm 40 t 87. One f the effects f the secnd harmnics f the luni-slar disturbing functins (Ref. 2) is t cause the perigee height t vary in an irregular but predictable manner. This effect has been examined in Ref. 2 and the authrs have develped cmputer prgrams t btain quantitative results. When a satellite is launched int an rbit such that the perigee height initially decreases, the initial value must be large enugh t insure that, befre this height reaches a value s small that atmspheric drag is encuntered, either it passes thrugh its minimum and begins increasing r the satellite lifetime requirement is fulfilled. Thus, perigee height may be a few hundred kilmeters higher than the 700 km assumed in the cverage analysis. Increasing the perigee height by as much as several thusand kilmeters prduces nly a small change in the cverage if the rbital perid is nt changed. It may be desirable t increase perigee height t avid expsure t radiatin in the Van Allen belts. Fr this rbit, dppler shift due t the velcity f a satellite relative t a terminal is quite high. Depending n the psitin f the satellite in rbit, dppler shift can vary frm 0 t ±200 khz when the satellite frequency is 8 GHz. Lincln Experimental Terminal Number 1 demnstrated the feasibility f predicting, acquiring and tracking dppler shifts f this magnitude several years ag.

REFERENCES I.I. Shapir, H.M. Jnes, and C.W. Perkins, "Orbital Prperties f the West Frd Diple Belt," Prceedings f the IEEE, Vl. 52, 5, p. 472 (May 1964). G.E. Ck and D. W. Sctt, "Lifetimes f Satellites in Large-Eccentricity Orbits, " Planetary Space Science, Vl.

12 REFERENCES I.I. Shapir, H.M. Jnes, and C.W. Perkins, "Orbital Prperties f the West Frd Diple Belt," Prceedings f the IEEE, Vl. 52, 5, p. 472 (May 1964). G.E. Ck and D. W. Sctt, "Lifetimes f Satellites in Large-Eccentricity Orbits, " Planetary Space Science, Vl. 15, p , Pergamn Press Ltd. ACKNOWLEDGMENT The valuable cntributin f Ferenc Nagy, Jr. wh made results frm his cmputer prgrams available is greatly appreciated.

13 LINE OF NODES Fig. 1. The earth, the satellites and their rbital planes.

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18 [ AB Fig. 6. Satellite rbit plane. 1

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$8-6-10051 =7\ SATELLITE BODY SOLAR$

21 =7\ SATELLITE BODY SOLAR ARRAY Fig. 9. Satellite cnfiguratin. 16

UNCLASSIFIED Security Classificatin DOCUMENT CONTROL DATA - R&D (Security classificatin f title, bdy f abstract and indexing anntatin must be entered when the verall reprt is classified) I.

GROUP Nne Cntinuus Cverage f the Nrth Plar Regin With Only Tw Cmmunicatins Satellites 4. DESCRIPTIVE NOTES (Type f reprt and inclusive dates) Technical Nte 5.

22 UNCLASSIFIED Security Classificatin DOCUMENT CONTROL DATA - R&D (Security classificatin f title, bdy f abstract and indexing anntatin must be entered when the verall reprt is classified) I. ORIGINATING ACTIVITY (Crprate authr) Lincln Labratry, M.I.T.. REPORT TITLE 2a. REPORT SECURITY CLASSIFICATION Unclassified 26. GROUP Nne Cntinuus Cverage f the Nrth Plar Regin With Only Tw Cmmunicatins Satellites 4. DESCRIPTIVE NOTES (Type f reprt and inclusive dates) Technical Nte 5. AUTHOR(S) (Last name, first name, initial) Beusch, Jhn U. 8. REPORT DATE 4 September a. CONTRACT OR GRANT NO. AF 19(628)-5167 b. PROJECT NO. 1508A 10. AVAILABILITY/LIMITATION NOTICES 7a. TOTAL NO. OF PAGES 22 9a. ORIGINATOR'S REPORT NUMBER(S) Technical Nte b. NO. OF REFS 96. OTHER REPORT NOISI (Any ther numbers that may be assigned this reprt) ESD-TR This dcument has been apprved fr public release and sale; its distributin is unlimited. 11. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY Nne Department f the Navy 1. ABSTRACT The prblem f prviding cntinuus cverage f the nrth plar regin with a small number f cmmunicatins satellites is cnsidered. The system described requires nly tw satellites t prvide bth this cverage and cverage f a cnsiderable fractin f the nrthern hemisphere. Tw rbit planes with 6.4 inclinatin, high eccentricity and ~24 hur perids are emplyed. The regins f the earth frm which a satellite is cntinuusly visible frm terminals with varius minimum elevatin angles are shwn. The regins in which mutual visibility f a satellite by tw terminals is guaranteed are shwn. A few cmments cncerning satellite design fr this rbit are included. 14. KEY WORDS nrth plar cverage cmmunicatins satellites satellites satellite rbits 17 UNCLASSIFIED Security Classificatin

ASTRODYNAMICS. o o o. Early Space Exploration. Kepler's Laws. Nicolaus Copernicus ( ) Placed Sun at center of solar system

ASTRODYNAMICS. o o o. Early Space Exploration. Kepler's Laws. Nicolaus Copernicus ( ) Placed Sun at center of solar system ASTRODYNAMICS Early Space Explratin Niclaus Cpernicus (1473-1543) Placed Sun at center f slar system Shwed Earth rtates n its axis nce a day Thught planets rbit in unifrm circles (wrng!) Jhannes Kepler