142
DETERMINATION OF ELLIPTIC ORBITS.
Applying these corrections to the values of compute the second numerical columns under equations and We do not go on to the computations by equations etc., but content ourselves with the old values of etc., and which with the new residuals
|
|
give
|
|
|
|
This gives
|
|
As the term containing has increased the value of by .00009, we add this quantity to and and get
|
|
With these corrections we compute the third numerical columns under equations etc. This time we recompute the quantities etc., with which we repeat the principal computations of IV, and get the new values
|
|
|
|
|
|
|
|
|
|
|
|
The quantities and we neglect as of no consequence at this stage of the approximation.
With these values the new residuals
|
|
give
|
|
These corrections furnish the basis for the fourth columns of numbers under equations etc., which give the residuals
|
|
and the new corrections
|
|
The corrected values of give
|
|
We have carried the approximation farther than is necessary for the following correction of the formula, in order to see exactly where the uncorrected formula would lead us, and for the control afforded by the fourth residuals.