Uydu Jeodezisi Ders Notları
Uygulama 9 : Uydu Lazer Uzunluk (SLR: Satellite Laser Ranging) ve Uydu Yükseklik (Satellite Altimeter)
Ölçülerinin değerlendirilmesi, Deniz Yüzeyi Topografyasının (DYT, SST: Sea Surface Topography) belirlenmesi.
Şekil 1. Yörüngesi SLR ölçüleri ile belirlenen Yükseklik Ölçme Uydusu (Satellite Altimetry, Geosat).
VERĐLER
SN
==
1
2
3
4
5
6
SLR-NN
========
ankr
bucu
dyng
nico
trab
tubi
t [ms]
========
0.000
73.920
147.840
221.760
295.680
369.600
443.520
517.440
591.360
665.280
739.200
813.120
887.040
960.960
1034.880
1108.799
1182.719
1256.639
1330.559
1404.479
X [m]
==========
4121934.26
4093760.99
4595220.60
4359417.88
3705250.47
4211318.52
S1 [m]
===========
807238.6887
807247.5794
807256.9196
807266.6977
807276.9559
807287.7238
807298.9436
807310.5723
807322.7840
807335.3691
807348.5062
807362.1452
807376.2284
807390.9020
807406.0356
807421.6990
807437.8657
807454.5285
807471.7644
807489.4891
Y [m]
==========
2652189.81
2007793.67
2039433.74
2874117.01
3084421.65
2377865.76
S2 [m]
===========
920824.9152
920602.4759
920379.5513
920156.0911
919932.2132
919707.7793
919482.9829
919257.6065
919031.8025
918805.4587
918578.7883
918351.5190
918123.8683
917895.7384
917667.1260
917438.1391
917208.6299
916978.7178
916748.4105
916517.6283
Z [m]
==========
4069034.91
4445129.86
3912627.02
3650778.27
4162044.65
4144664.46
S3 [m]
===========
959218.2600
959473.6279
959730.2838
959988.1378
960247.1335
960507.4620
960769.0109
961031.7174
961295.6955
961560.8933
961827.3121
962094.9793
962363.9078
962634.0462
962905.4536
963178.1338
963452.0644
963727.2491
964003.6869
964281.3386
S4 [m]
============
1054484.3215
1054773.4518
1055063.8691
1055355.5784
1055648.5452
1055942.8750
1056238.5212
1056535.4478
1056833.6519
1057133.2142
1057433.9921
1057736.1602
1058039.6330
1058344.4390
1058650.5567
1058957.9920
1059266.7796
1059576.8521
1059888.2919
1060201.0653
S5 [m]
===========
177943.4434
177784.4789
177625.2010
177465.6126
177305.7168
177145.5165
176985.0149
176824.2149
176663.1196
176501.7321
176340.0554
176178.0927
176015.8470
175853.3215
175690.5193
175527.4435
175364.0973
175200.4838
175036.6063
174872.4680
S6 [m]
===========
749952.5855
749948.7581
749945.3701
749942.4265
749939.9321
749937.8921
749936.3114
749935.1950
749934.5479
749934.3753
749934.6820
749935.4733
749936.7542
749938.5298
749940.8053
749943.5858
749946.8765
749950.6826
749955.0092
749959.8615
hA [m]
==========
749969.907
749971.706
749971.975
749974.720
749976.368
749977.187
749979.486
749980.526
749983.051
749984.578
749987.038
749988.668
749989.728
749991.525
749994.225
749996.274
749997.617
749999.207
750001.641
750002.937
Yrd.Doç. Dr. Orhan KURT ( 1 / 3 )
Uydu Jeodezisi Ders Notları
BĐLGĐ
0) Sabitler:
GM
wE
awgs
bwgs
=
=
=
=
3.986005e+14
7.2921151467e-5
6378137.0
6356752.31425
m3s-2
rad s-1
m
m
1) SLR Ölçülerinin Değerlendirilmesi:
t ={0.000, 73.920, …, 1404.479}[ms]
S j ( t ) = ( X ( t ) − X j )2 + ( Y ( t ) − Y j )2 + ( Z ( t ) − Z j )2
j ={1,2,3,4,5,6}
S j 0 ( t ) = ( X 0 ( t ) − X j )2 + ( Y0 ( t ) − Y j )2 + ( Z 0 ( t ) − Z j )2
X 0 ( t ) = Y0 ( t ) = Z 0 ( t ) =6378000.000m
vj(t ) =
[
X 0 ( t )− X j
S j0( t )
Y0 ( t )−Y j
S j0( t )
Z0 ( t )− Z j
S j0( t )
]
δ X ( t )
δ ( t ) − S ( t ) − S ( t )
j
j0

 Y
δ Z ( t ) 
[
]
Pj ( t ) = 1.0
{
δ( t ) = A T ( t ) A( t )
}
−1
v( t ) = A( t ) δ( t ) − l( t )
P( t ) = I
X( t ) = X 0 ( t ) + δ( t )
X( t ) = [ X 0 ( t ) Y0 ( t ) Z 0 ( t )]
δ( t ) = [δ X ( t ) δ Y ( t ) δ Z ( t )]
v( t ) = A( t ) δ( t ) − l( t )
m0 ( t ) = v T ( t ) v( t ) / 3
T
X( t ) = [ X ( t ) Y ( t ) Z ( t )]
T
A T ( t ) l( t )
T
2) Jeodezik Koordinatlara Dönüşüm:
X( t ) = [ X ( t ) Y ( t ) Z ( t )]
T

Z( t ) 
2 
 p (1 − e ) 
(1) B0 = arctan
(2) N =
(3)
a
1 − e 2 sin 2 B0
→
⇒ B( t ) = [B( t ) L( t ) h( t )]
T
e 2 = 1 − ( b / a )2
h( t ) =
p = X 2( t ) + Y 2( t )


p
Z( t ) / p
− N → B( t ) = arctan

2
cos B0
 1 − e N / {N + h( t )} 
B( t ) − B0 > 1e − 14 ⇒ B0 = B( t )
→
(2)
 Y( t ) 

 X ( t )
(4) L( t ) = arctan 
3) Deniz Yüzeyi Topografyasının Hesaplanması: DYT ( t ) = h( t ) − hA ( t ) − EGM 08( B( t ) , L( t ) )
Yrd.Doç. Dr. Orhan KURT ( 2 / 3 )
Uydu Jeodezisi Ders Notları
ÇÖZÜM
SN
===
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
===
t [ms]
===========
0.0000
73.9200
147.8400
221.7600
295.6800
369.6000
443.5200
517.4400
591.3600
665.2800
739.2000
813.1200
887.0400
960.9600
1034.8800
1108.7990
1182.7190
1256.6390
1330.5590
1404.4790
===========
h [m] m0 [cm]
N [m]
=========== ======= =========
750006.7645
1.34
37.499
750008.4612
0.61
37.489
750010.1811
0.66
37.479
750011.8868
2.21
37.469
750013.6017
1.49
37.460
750015.3406
2.71
37.452
750017.1150
1.73
37.445
750018.8367
1.20
37.439
750020.6028
1.95
37.433
750022.3352
1.17
37.428
750024.1122
0.75
37.424
750025.8677
0.87
37.420
750027.6424
1.68
37.417
750029.4276
1.10
37.415
750031.2032
1.10
37.414
750033.0123
0.95
37.413
750034.8035
0.56
37.413
750036.6007
1.67
37.414
750038.4263
0.63
37.415
750040.2268
2.57
37.417
=========== ======= =========
DYT [m]
=========
-0.6415
-0.7338
0.7271
-0.3022
-0.2263
0.7016
0.1840
0.8717
0.1188
0.3292
-0.3498
-0.2203
0.4974
0.4876
-0.4358
-0.6747
-0.2265
-0.0203
-0.6297
-0.1272
=========
3
m0 [cm]
DYT [m]
2
1
0
1500
1250
1000
750
500
250
0
-1
Şekil 2. m0 ve DYT (Deniz Yüzeyi Topografyası).
Yrd.Doç. Dr. Orhan KURT ( 3 / 3 )
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Şekil 1. Yörüngesi SLR ölçüleri ile belirlenen Yükseklik Ölçme