2 Outline Sub-satellite point Motion of sub-satellite point Calculation of elevation and azimuthLook angle calculation spreadsheetLook angles to geo-synchronous satellitesExamplesImportant note: Slides present summary of the results. Detailed derivations are given in notes.
3 Sub-satellite pointPoint at which a line between the satellite and the center of the Earth intersects the Earth’s surfaceLocation of the point expressed in terms of latitude and longitudeIf one is in the US it is common to useLatitude – degrees north from equatorLongitude – degrees west of the Greenwich meridianLocation of the sub satellite point may be calculated from coordinates of the rotating system as:
4 Examples of sub-satellite point trajectories sub-satellite point used for 2D map display of satellite pathFor most satellites the trajectory is part of sinusoidalFor geo-stationary satellites the trajectory is a pointSirius radio – two geo stationary and three highly inclined orbit satellitesNote: maps are generated using STK by Analytic Graphics, Inc.International space station – LEO orbit
5 Look angles – elevation (El) and azimuth (Az) Az – angular distance of the satellite from the northAz is between 0 and 360 degreesEl – angular distance of the satellite from the local horizontal planeEl is between 0 and 90 degreesAz and El are required for proper pointing of the Earth station antennaIf the satellite is geo-stationary the antenna is pointed onceIf the satellite is on non stationary orbit, the ground system needs to track the Az and El in timeDefinition of Az and El
6 Calculation of elevation Given:Le – latitude of Earth Stationle – longitude of Earth stationLs – latitude of sub-satellite pointls – longitude of sub-satellite pointrs – distance to satelliteExample: Calculate El for the following dataES: latitude: N ( rad)longitude: W ( rad)SSP: latitude: N ( rad)longitude: W ( rad)radius, rs = 38000kmStep 1:Step 1:Step 2:Step 2:Where re is the radius of the Earth (6370km)
7 Calculation of azimuth - cases Eight cases to considerNorthern hemisphere – 4 casesAt least one of the two points (Earth station, sub-satellite point) is in the northern hemisphereSouthern hemisphere – 4 casesBoth points (Earth station and sub-satellite point) are in the southern hemisphereGiven:Le – latitude of Earth Stationle – longitude of Earth stationLs – latitude of sub-satellite pointls – longitude of sub-satellite pointrs – distance to satelliteNote: presented algorithm accommodates general case
8 Calculation of azimuth – northern hemisphere whereA west of BB west of ANote: B chosen to be north of ACaseSSPESRelationsAz (degrees)1ABA west of B360-Y2X3B west of AY4360-XSolve tan equations for X and YIdentify the case and use table to determine the AZSSP- sub-satellite pointES – Earth station
9 Calculation of azimuth – southern hemisphere whereA west of BB west of ANote: B chosen to be south of ACaseSSPESRelationsAz (degrees)1ABA west of B180+Y2180-X3B west of A180-Y4180+XSolve tan equations for X and YIdentify the case and use table to determine the AZSSP- sub-satellite pointES – Earth station
10 Azimuth calculation - example Example: Calculate Az for the following dataES: latitude: N ( rad)longitude: W ( rad)SSP: latitude: N ( rad)longitude: W ( rad)radius, rs = 6738kmThis is Case 2 of Northern hemisphere calculation:C = | |= radLB= radLA= radtan[0.5(Y-X)]=0.82510.5(Y-X)= radtan[0.5(Y+X)]=5.41000.5(Y-X)= radX= radY= radFor Case 2 of northern hemisphere:Az = X = rad
12 Look angles to geo-stationary satellites Occupy non-inclined geo-synchronous orbitAlways above same equatorial pointLocation specified using longitude of the sub-satellite point and distance to the satelliteThe El/Az calculation spreadsheet “works” for geo-stationary satellitesThere are also many websites that calculate El/Az pairsExample site:VSAT broadcast terminals are usually operating with Geo-stationary satellitesExample of “dish pointer” websiteNote: compare pointing results between class spreadsheet and dish-pointing websites
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