Individual Assignment Geospatial Reference System Material

Assignment 03 1. The positions of point 1 and point 2 are located on one meridian. Calculate the arc length along the meridian from point 1 to point 2 accurately, respectively on the Bessel ellipsoid and WGS 84! Point 1 : ϕ1 = 11° 15’ 39,76208’’ LS λ1 = 126° 10’ 36,781995’’ BT Point 2 : ϕ2 = 4° 45’ 16,081343’’ LU λ2 = 126° 10’ 36,781995’’ BT Answer : Known Data : a. Conversion ϕ Degree ϕ1 = - ( 11 + 15/60 + 39,76208/3600 ) ° = - 11,261045 ° ϕ2 = ( 4 + 45/60 + 16,081343/3600 ) ° = 4,754467 ° b. Ellipsoid parameters Bessel a = 6.377,397 km b = 6.356,078 km WGS 84 a = 6.378,137 km b = 6.356,752 km Looking for eccentricity (e) eBessel = 2 2 √𝑎 −𝑏 eWGS84 = 𝑎 = 0,0817 2 2 √𝑎 −𝑏 𝑎 = 0,0832 Finding the length of the arc In the Bessel ellipsoid ( e used is eBessel ) 𝐶 sin4ϕ – sin4ϕ ) Sϕ = aBessel ( 1 – e2 )[A(ϕ - ϕ ) - 𝐵 (sin2ϕ - sin2 𝐷 ϕ ) + ( 1 2 2 1 2 1 4 2 𝐸 (sin6ϕ2 – sin6ϕ1) + 8 (sin8ϕ2 – sin8ϕ1) - 𝐹 6 (sin10ϕ2 – sin10ϕ1) ] + ....... 10 With, 3 45 4 175 6 11025 8 43659 4 64 256 16384 65536 A = 1 + e2 + 3 B= 4 e2 + C= e + e + e + 15 4 e 16 + 525 6 2205 8 e + e 512 2048 + 15 4 e 64 + 105 6 e 256 + 35 D= 512 + e6 + 2205 8 e 4096 315 2048 16384 e10 + ..... 65536 e8 + 315 E= 72765 e10 + ..... 10395 e10 + ..... 16384 31185 e10 + ..... 131072 e8 + 3465 65536 693 F= 131072 e10 + ..... e10 + ..... By substituting the known data into the formula above, we get that Sϕ = 1770,9 km. Thus, the length of the meridian arc between point 1 and point 2 on the Bessel ellipsoid is 1770,9 km. In the WGS 84 ellipsoid (e used is eWGS 84 ) 𝐵 sin2ϕ - sin2 𝐶 sin4ϕ – sin4ϕ ) Sϕ = aWGS 84 ( 1 – e2 )[A 𝐷 ϕ1) + ( (ϕ2 - ϕ1) - ( 2 2 1 2 4 𝐸 (sin6ϕ2 – sin6ϕ1) + 8 (sin8ϕ2 – sin8ϕ1) - 𝐹 (sin10ϕ2 – sin10ϕ1) ] + ....... 10 With, 3 A = 1 + e2 + 4 45 4 e 64 + 175 6 e 256 + 11025 8 e 16384 + 43659 65536 e10 + ..... 6 3 B= 4 C= D= e2 + 15 4 e 16 + 525 6 2205 8 e + e 512 2048 + 15 4 e 64 + 105 6 e 256 + 35 512 + e6 + 2205 8 e 4096 315 2048 65536 e8 + 315 E= 72765 16384 e10 + ..... 10395 16384 e10 + ..... 31185 131072 e8 + 3465 65536 e10 + ..... e10 + ..... 693 F= 131072 e10 + ..... By substituting the known data into the formula above, we get that Sϕ = 1771,1 km. Thus, the length of the meridian arc between point 1 and point 2 on the WGS 84 ellipsoid is 1771,1 km. It is concluded that the length of the meridian arc between point 1 to point 2 on the WGS 84 ellipsoid is 0.2 km longer than the length of the meridian arc from point 1 to point 2 on the Bessel ellipsoid. 2. The coordinates of the boundary points of Bandung City can be obtained through various methods and sources. In this assignment, take the coordinate data of the boundary points of Bandung City from Google Maps. Next, calculate the area of Bandung City approximately with the grid dimensions on the ellipsoid surface Δϕ = 1’ and Δλ = 1’! Calculate the area of Bandung City using the WGS 84 ellipsoid (the reference ellipsoid used by Google Maps) as a reference. Answer : Picture of Bandung City on Google Earth Known data: a. Ellipsoid parameters WGS 84 a = 6.378,137 km b = 6.356,752 km b. Samples taken ϕ = 107°39’ LS λ = 6°55’ BT Δϕ = 1’ Δλ = 1’ c. Data Conversion Degree ϕ1 = ( 107 + 39/60 ) ° = 107,65° ϕ2 = ( 6 + 55/60 ) ° = 6,9166° Δϕ = 0,016666° Δλ = 0,016666° Radiant Δϕ = 0,016666° / 180 ° x π = 0,0002908 rad Δλ = 0,016666° / 180 ° x π = 0,0002908 rad d. Number of grids = 68 pieces Finding the eccentricity value (e) 2−𝑏2 e = √𝑎 𝑎 = 0,0832 Find the radius of curvature of the meridian a ( 1 – e2 ) M= ( 1 – e2 ( sin ϕ))3/2 = 6.375,033236 km Finding the radius of the main vertical curve a N= ( 1 – e2 ( sin ϕ2))3/2 = 6.398,299237 km Approximate area of Bandung City Grid area L = M x N x cos ϕ x Δϕ x Δλ = 2,3143 km Bandung city area = area grid x 68 = 158,3755 km Approximate area of Bandung City 158,3755 km.