su* dungphuongphaphinhhoc khonggianoe

S U * D U N G P H U O N G P H A P H I N H H O C K H O N G G I A N O E T I N H K H O A N G C A C H G l C T A H A I D I E M ( T R A M O O )

T R E N M A T O A T

Le Thj Minh PhUdng

ABSTRACT

Until now, There are some methods to define the distance (ranging) between two point such as: Very Long Baseline Interferometry - VLBI, Satellite Laser Ranging - SLR, Lunar Laser Ranging - LLR, Global Positioning System - GPS.

The paper presents the solid geometry method to define the distance (rang- ing) between two points on the sphere surface of the earth. This dis- tance defined by the formula follows:

d = R. 2 Hsinip^siiKpj -cosq), cos(p2 cosp Le Thj Minh Phtfong

Trudng dai hoc Kien true Ha Noi Km 10, Nguyen Trai, Thanh Xuan, Ha Noi

E-mail: phuong2000yu@yahoo.com

1. Dat van de

Khi tien hanh do khoang each tren be mat Trai Oat, chung ta thudng do khoang each nam ngang gitfa hai diem. Trai Da't la hinh cau vi vay khoang each thuc chinh xac phai tinh la khoang each cong. Bai bao nay neu len each tinh khoang thang (d) va khoang each cong tren mat cau (I) theo phuang phap hinh hpc khong gian.

2. Cac phuong phap xac dmh khoang each gitfa hai diem

Den nay, cd rat nhieu phuong phap xac djnh khoang each gitfa hai diem (hai tram do) A va B nao do tren mat da't. Nhtfng phtfong phap co ban va thtfdng dupe sd dung la:

- Phuang phap giao thoa day dai (Very Long Baseline Interferometry - VLBI)

- Phuong phap do khoang each laser ve tinh (Satellite Laser Ranging - SLR)

- Phtfong phap do khoang each laser Mat Trang (Lunar Laser Ranging - LLR)

- Phtfong phap he thdng djnh vj toan cau (Global Positioning System -GPS)...

NhUng phtfong phap nay da dtfpc trinh bay trong nhieu tai lieu d ntfdc ta [1,2]. Cac phuang phap tren thtfdng xac djnh khoang each d nam ngang gitfa hai diem. Gpi khoang each AB theo dtfdng thang la d va khoang each cong tren mat

cau la I, thi I >d. I chinh la chieu dai cua cung AB, d la chieu dai cua day AB.Vi vay neu tinh dtfpc khoang each I thi do mdi chinh la khoang each thtfc gitfa hai diem.

De xac djnh khoang each d gitfa A va B ngtfdi ta stf dung phuong phap VLBI. Co sd khoa hpc cua phuang phap nay la thtfa nhan cac thien the vu tru phat ra cac song vo tuyen va cac tram thu tren Trai Da't co the thu nhan dtfpc. Gia stf d tram A, thdi diem nhan sdng la t, va d tram B thdi diem nhan song la t2

(hinh 1) thi dtfa vao khoang tre thdi gian truyen sdng vd tuyen At = t2 - t„ va tren co sd cho rang cac thien the vu tru d rat xa nen dtfdng truyen sdng duoc coi la song song vdi nhau, cac nha khoa hpc Lien Xd (cu) nhtf L.I. Matvenko, H.C. Kardasev va G.B. Solomnhiski (1965, xem [1]) da dtfa ra he thtfc sau de xac djnh khoang each d.

v.At = d.cosp (1) Trong do: v - la van tdc truyen

sdng

At - la khoang each tre thdi gian (3 - la gdc gitfa tia truyen sdng tai B va dtfdng ndi AB (hinh 1).

Khi A va B khdng xa nhau lam (trong trac dja khoang each do dupe chpn bang 20km) thi cd the xem d = I. Khi A va B rat xa nhau thi can xac dinh I tren mat cau cua Trai Dat de nang cao dp chinh xac trong tinh toan.

Bai toan dupe phat bieu nha sau:

18 S N f t f f i B f . 1.2009

Cho hai diem A va B tren mat cau, biet khoang each thang AB = d, can xac djnh dp dai I, tdc la dp dai cua cung chan day AB. Oe giai bai toan nay tru'dc het ta hay tinh d, roi tinh u (gdc AOB), sau dd tinh I. Lay A va B cung nam tren mdt dtfdng trdn tam 0. Gpi A' la diem dd'i xtfng vdi A qua tam 0 tren mat cau. Gia sd cd mdt mat phang P nao dd di qua ba diem AA'B, giao tuyen cua mat phang P vdi mat cau la dUdng trdn tam 0 cd ban kinh la OA = OA' = OB (hinh 2).

Gpi AOB = a. Oudng trdn tam 0 ban kinh OA = OA' = OB = R (ban kinh Trai Oat) cd chu vi la 2icR tfng vdi gdc d tam la 360°. Vay tfng vdi gdc d tam la a bat ki thi chieu dai day cung AB la:

TtRa , , . , ,

• tinh bang dp).

1 = 180

:(a (2)

Muon tinh I ta phai xac dinh a.

Mud'n tinh dupe d, hoac la theo (1) hoac la theo phtfong phap trinh bay (muc 3) dtfdi day.

Ttf hinh 2 ta cd :

d = 2rsin-a (3)

. ct d d Vay: sin— = —dat— = smv(4)

2 2R ' 2R Ttf day ta tinh dtfpc :

a = 2y + 2KJT

Vay muon tinh dupe a, phai xac dinh d. Sau khi tinh dupe a, theo (2) tinh dupe I.

1. Xac dinh khoang each d theo phuang phap hinh hpc khdng gian dtfa vao vi tri dia li (kinh dp va vi dp) cua A va B

Khoang each d cd the tinh theo phuong phap VLBI, SLLR, LLR; vi du theo VLBI theo (1). 0 day xac djnh d theo phuong phap hinh hpc khdng gian, dtfa vao tpa dp dja li cua A va B. Biet dupe vj tri cua A va B nen cd the xac djnh dtfpc kinh tuyen LA, vi tuyen VA di qua A va kinh tuyen LB vi tuyen VB di qua B, ddng thdi, gpi A va B lan lupt la hinh chieu cua A va cua B tren mat phang xich dao, (3 la goc nhi dien gitfa hai mat phang kinh tuyen di qua A va B, va gpi <p, va (j>2 lan Itfpt la vi dp cua A va B, se

tinh dupe d. Tren hinh 3 gdc BOB = cp2, gdc AOA = tp,. Ke dudng BM vudng gdc vdi AA tai M. Gia thiet trai dat la hinh cau, ta cd:

Tren hinh 3 ta cd:

AB = d,AM = AA'-MA' = AA'-BB' Vi MA' = BB'

Trong tam giac thudng A'OB' ta cd A'B'² = OA'² + OB'² -20A'.OB'cosp Vdi AA' = rsincp1;BB' = R sincp2

OA' = Rcoscp, ,OB' = Rcoscp2

De thay: AB² = d² = AM² + BM², chtf y: BM = A'B'

Vay:

d² = AB² = R² cos² cp, + R² cos² cp2

-2R² coscp, coscp2 cosp + +R² (sincp, — sincp2 )² Ttf do ta cd:

d = R 2 1-sincp, sincp2 - -coscp, cos cp2 cosp (5) TrUdng hop A va B nam d hai ban cau khac nhau, gia stf A d Bac ban cau, B d Nam ban cau (hinh 4).

Luc dd, ke dtfdng BM vudng gdc vdi AA' tai M ta cd:

d² = AM² +BM² Vi BM = A'B'

Nen d² = AM² +A⁷B'² Bang each tinh ttfdng ttf nhtf tren ta cd

d2= R2 f²^^{2 S i n (}P l^{S i n t}P 2 - [-2COSCP, coscp2 cosp d = R. 2 i 1 + sincp, sincp2 (6)

Rcoscp, cos q>2 cosPy

Tdng hop ca hai trtfdng hop ta cd:

d R 2 ^{1 Sir}°-^Sin°" _r. ( 7 ) l^-coscp! coscp2cos[:

Dau trtf tfng vdi trtfdng hpp hai diem tren cung mdt ban cau va dau cdng tfng vdi trtfdng hpp hai diem nam d tren hai ban cau khac nhau.

3. Vi du

Tim d va I cua hai diem A va B;

biet tpa dp dia ly cua A (20 dp kinh ddng, 60 dp vi bac) va cua B (80 dp kinh ddng va 30 dp vi bac).

Hinh 1: Xac ctinh khoang each AB = d dtfa vao khoang tre thdi gian BH = vAt theo phtfong phap VLBI.

Hinh 2: Xac dinh moi lien he gitfa d va I (dayAB = d, cung AB = I).

Hinh 3: Xac dinh khoang each d gitfa hai diem tren ciing mpt ban cau.

Hinh 4: Xac dinh khoang each giua hai diem 6 hai ban cau khac nhau.

i S P f f l W I . 1.2009 19

THONG TIN CdNGNGHE

Tren hinh 5 ta co (3 = 80^: - 20" = 60°, tp, = 60^:, cp2 = 30°. BM vuong goc vdi AA¹ goc AOB = a, OH vuong goc vdi AB.

-Tinh d:

A va B tren cung mot ban cau nen theo (5) ta co:

d = R 2 1-cos cp, coscp2 cos[

-sincp1.sincp2

Thay bang so ta dUdc:

d = 6371. 2

1 — 1 V3 1 2 2 '2 2 '2 d = 5333,8 km - Tinh a:

Theo (4) ta co:

sm- d 2R

5333,8

2x6371 : 0,418329,

:5445,79km nhU vay ta duoc: a « 49°

-Tinh I:

Theo (2) ta co:

I _ nRa

~ 180

Dp chenh lech gida I va d la:

5445,79km - 5333,8km gan bang 112km.

Vdi nhUng khoang each Idn, khi xac dinh chieu dai theo I se chinh xac hon so vdi tinh d. Cung cd the dung cdng thdc nay de xac dinh khoang each di ddi cua cac dia mang (geoplate) tU A den B tren

mat dat. •

TAI LIEU THAM KHAO

1. Nguyen Quang Tac, Giao trinh trac dia.

Tai lieu giang day Oai hpc Kien triic Ha Npi, 1998.

2. Dang Nam Chinh, Quan trac chuyen dpng mat dat. Tai lieu giang day cao hpc. Oai hpc Mo - Oia Chat, 1997.

3. Pham Hoang Lan, Bai giang cong nghe GPS. Tai lieu giang day cao hpc. Dai hpc Mo - Oia Chat, 1997.

BE PHOT KIEU M 0 I CUA VIET N A M

DOAT H C V Q U O C T E i

Nhd Uu diem chu ddng ket ndi, thu gom, xd ly nUdc thai va chdng 6 nhiem ngudn nUdc ngam, sang che "Be phot kieu mdi" da doat huy chUOng vang trien lam sang tao qud'c te vda dien ra tai Seoul (Han Qud'c).

Tac gia cua be phot kieu mdi la ky sU Hoang Ddc Thao va cac cdng su tai Cdng ty Thoat nUdc do thj tinh Ba Rja - Vung Tau. L/u diem cua sang che nay la chu ddng ket ndi, thu gom, chuyen tai va xd ly nUdc thai; chdng 6 nhiem ngudn nUdc ngam, nUdc mat; chdng xam thac, an mdn cdng trinh va phat huy triet de cdng suat cac tram bom do Nha nUdc dau tu.

Gia thanh san xua't, lap dat trpn gdi be phot kieu mdi chi bang 1/3 so vdi ham ve sinh truyen thd'ng, tuoi thp cdng trinh cao hon va khoang each hut can gitfa hai chu ky dai gap ddi, thuan tien ddi vdi nha d dd thj.

Cdng trinh nay dtfpc Lien hiep cac Hdi KHKT Viet Nam trao giai ba VIFOTEC 2007 (khdng cd giai nhi va giai nhat). Cdng trinh tren vda doat Huy chuong vang tai trien lam sang tao qudc te lan thd 4 tai Seoul (Han Qud'c) vao trung tuan thang 12. Day la trien lam qudc te Idn va uy tin tren the gidi dupe to chdc 2 nam mdt lan vdi gan 500 to chdc khoa hpc, doanh nghiep cua 38 qud'c gia tren toan the gidi tham dtf.

Hai nam qua, hang tram be phot loai nay da dtfpc lap dat tai TP Vung Tau.

BIEN Ol/OfNG SA T H A N H NGUON

CUNG CAP OIEN 4

De tan dung luc de cua cac phuong tien co gidi, mdt cdng ty tai Israel da che tao he thdng phat dien danh cho dtfdng phd va xa lp.

Tinh the ap dien la loai tinh the tao ra ddng dien khi bj nen va chting cung ttf nen khi cd ddng dien chay qua. Neu chting ta dat cac tinh the ap dien dtfdi Idp nhtfa cua mdt con dtfdng, chung se tao ra ddng dien khi phtfong tien co gidi di qua. Neu dat hang trieu tinh the ap dien dtfdi mat dtfdng, chting se tao ra Itfpng dien nang Idn. Ngudn dien nang nay cd the dtfpc dtfa vao ltfdi dien hoac ket ndi vdi he thd'ng chieu sang va sUdi am.

Innowattech, mdt cdng ty cua Israel, cho biet hp se cho ra mat dUdng san xua't dien dau tien tren the gidi, cd chieu dai 100 met trong vai tuan ntfa.

Cdng ty nay cung se phat trien he thd'ng san xua't dien cho dtfdng ray va via he di ddng d cac san bay. Theo tinh toan cua cac chuyen gia, neu y ttfdng cua Innowattech dupe ap dung tren khap ntfdc Anh, nd cd the tao ra mdt lupng dien nang du de cap cho gan 35.000 xe hoi loai nho.

Nam ngoai cac nha khoa hpc My ttfng trinh dien thtf nghiem tai mdt ga tau hda d thanh phd Turin (bang New York) de chtfng minh rang ltfc giam chan cua con ngudi cd the tao ra dien. Hp dat nhieu tam van d san ga de hanh khach giam len. Ltfc giam nay dtfpc dtfa tdi mdt may phat dien de lam quay turbin. Nhdm chuyen gia khang dinh mdt dam ddng Idn cd the cung cap dien cho mdt tau hda. Neu dat he thdng trong vu trtfdng, nd cd the cung cap du dien nang danh cho cac ne thd'ng chieu sang, dieu hda nhiet dp va am thanh.

20 BKIiiififSf . 1.2009