Advances in Computers, Vol. 3

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As shown in Hildebrand [23] this advantage is illusory since the total propagated error is only of order h4. 10) for the free-flight problem. 10). 4 Accumulated Round-off Error Since a machiiie works wilh a finite number of digits, and since some sort of rounding is involved in each calculatioii, it is clear that some significance will be lost due to round-off. Indeed the loss due to round-off can be disastrous in some problems, aiid every effort should be made to assess the extent of such loss.

The reference orbit is continually rectified. In general, for earth satellites one would expect the orbital elements to change more slowly than rectangular coordinates. This in turn implies that a larger integrating step size can be taken for a required accuracy. Several sets of orbital elements have been proposed and are described in the literature under the names of Stromgren, Merton, Hansen, and Oppolzer [34]. More recently S. Herrick has introduced a specially chosen set of parameters which define the osculating orbit a t each epoch.

27) to to where the perturbative variations a', b', n', M' are to be defined. 27) determine the mean anomaly. 27) is redundant since only six independent equations are needed to describe the motion but the redundancy is used as a check on the computations. To relate the Herrick elements to the rectangular coordinates of the vehicle we proceed as follows. a. 27) the variations a', b', M' must be obtained. Letting F,, F,, F,, be the components of the perturbations, we compute: n', diD' = d&' = + yF, + zF, 2 f .

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