Calculation of Distance Between Two Points on the Earth(Ellipsoid of Revolution)

Keyword

First Eccentricity,Second Eccentricity,Ellipticity,Curvature Radius of Prime Vertical,Curvature Radius of Meridian,Average Curvature Radius,Linear Distance,Sea Surface Height,Approximation of Geodetic line,3-Dimension Cartesian Coordinate,Geodetic Latitude,Longitude,Geocentric Latitude.

Reference

[1]:『測地学の基礎』(佐藤裕).
[2]:『測地学の方法』(大野重保).
[3]:『理科年表』(国立天文台編).
[4]:『測地学入門』(萩原幸男).

Remarks

・First Eccentricity:e=((A^2-B^2)/A^2)^0.5.
・Second Eccentricity:e'=((A^2-B^2)/B^2)^0.5.
・Ellipticity:f=(A-B)/A.
・W=(1-e^2*(sinθ)^2)^0.5.
・V=(1+e'^2*(cosθ)^2)^0.5.
・Curvature Radius of Prime Vertical:N=A/W.
・Curvature Radius of Meridian:M=A*(1-e^2)/W^3.
・Average Curvature Radius:R=(N*M)^0.5.
・r=B/(1-e^2*(cosφ)^2)^0.5.Distance from center of Earth to Point.
・Linear Distance:L=((x2-x1)^2+(y2-y1)^2+(z2-z1)^2)^0.5.
・Linear Distance(Sea Surface Height=0):L0=((x02-x01)^2+(y02-y01)^2+(z02-z01)^2)^0.5.
・Approximation of Geodetic line:S0=2*(r1+r2)/2*arcsin(L0/2/((r1+r2)/2)).
・x=(N+H)*cos(θ)*cos(λ).In 3-Dimension Cartesian Coordinate.
・y=(N+H)*cos(θ)*sin(λ).In 3-Dimension Cartesian Coordinate.
・z=(N*(1-e^2)+H)*sin(θ).In 3-Dimension Cartesian Coordinate.
・tanφ=(1-e^2/(1+h/N))*tanθ.
・tanφ'=(1-e^2)*tanθ.

History

・2014/08/01:Layout change.
・2009/11/15:BugFix
・2009/11/14:Adding Reference books.
・2009/11/14:Modification about calculation of S0.
・2009/11/14:Modification about description of equation on S0 in Remaks.
・2009/11/14:Modification about calculation of Geocentric Latitude.
・2009/11/14:Modification about description of equation on Geocentric Latitude in Remaks.
・2009/11/13:Upload.