Page "Orbit" Paragraph 49
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Wikipedia
: The differential equation form is used for scientific or mission-planning purposes.
According to Newton's laws, the sum of all the forces will equal the mass times its acceleration ( F = ma ).
Therefore accelerations can be expressed in terms of positions.
The perturbation terms are much easier to describe in this form.
Predicting subsequent positions and velocities from initial values corresponds to solving an initial value problem.
Numerical methods calculate the positions and velocities of the objects a short time in the future, then repeat the calculation.
However, tiny arithmetic errors from the limited accuracy of a computer's math are cumulative, which limits the accuracy of this approach.
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