Folks, I don't know how to post a message to Ac44ck so I'll post it here.
The radius needs to be included in the equation:
1) In the central Angle equation, the chord has units of length which is divided by a scalar "2" causing one to attempt to take the arcsin of a length. By adding the radius back in the equation the length units cancel and one can then take the arcsin of a dimensionless number.
2) The next equation on Great Circle Distance includes the radius. From a standpoint of parallel development, shouldn't this radius be set to one and dropped out of the equation as well? It doesn't seem correct to me to do so; the equations become degenerate and useless since the distance now becomes equal to the great circle angle.
Folks, I don't know how to post a message to Ac44ck so I'll post it here.
The radius needs to be included in the equation:
1) In the central Angle equation, the chord has units of length which is divided by a scalar "2" causing one to attempt to take the arcsin of a length. By adding the radius back in the equation the length units cancel and one can then take the arcsin of a dimensionless number.
2) The next equation on Great Circle Distance includes the radius. From a standpoint of parallel development, shouldn't this radius be set to one and dropped out of the equation as well? It doesn't seem correct to me to do so; the equations become degenerate and useless since the distance now becomes equal to the great circle angle.