NavList:

Some clarifications to my posting 12058 in reply to Herman Zevering's posting 12101:

In my formulas, I have assumed that LAT and LONG are the actual position at the time of the observation and thus ALT is the theoretical altitude that a body would have at that moment. It is equivalent to say that DR is exactly on the position circle and the intercept is zero (and that the DR is the basis for calculating the altitude).

Equations (1), (2) and (3) are the pre-requisites of the problem, the two observations and the run between them.

Equation (4') describes how GD-UT is performed: instead of transferring the resulting LOP of the first observation to the time of the second one, with the run in between; you adjust the GP of the first observed body "with the run", i.e. you adjust DEC and GHA valid at the time of the first observation with the shift in latitude and longitude respectively. With these adjusted parameters you solve the first observation as if it was simultaneous with the second one.

It is perfectly true that eq (4) is a restatement of eq (1), the reason is that I want to end up with the same variables in eq (4) as in eq (4'). Then it is easy to compare those two equations. Subtracting one from the other will give a zero result if they are alike. In this case, however, the result is generally not zero.

The reason why GD-UT gives erroneous results is that it is the observer that makes the "run", not the body itself. Thus it should be a part of the position circle in the near vicinity of the observer that should be transferred a certain distance in a certain direction, not the GP. It makes difference transferring each point along the perimeter of the position circle with the course and distance compared to moving the GP the same course and distance.

Lars, 59N 18E
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