in reply to Re^2: Irrational numbers
in thread Irrational numbers
Say you have a spaceship in a circular orbit around the sun ... and request a result with a millimeter precision.
Sorry, but your misunderstandings are legion.
It would be impossible to pre-calculate such an encounter, regardless of the precision of the calculations.
The gravitational field of the Sun is neither uniform nor constant; and we do not yet have, and never will have, an accurate mapping of it; nor any way to produce one.
For a start, in order to produce such a map, it would be necessary to have an identifiable reference point or line, but the Sun's surface and its interior rotate at different speeds; and the surface rotates at different speeds relative to latitude, with the poles rotating almost 50% faster than the equator. The surface is constantly changing so there is no way to denote a fixed reference point.
In addition, solar radiation has a profound affect upon small craft in orbit around the Sun; and it is entirely unpredictable.
These, and many other factors, are why all long distance space flights have in-transit correction burns built into them. Not to correct for inaccuracies in precalculations; but rather to correct for the unknowable and unpredictable affects of gravitational perturbations and variable solar pressures.
And that is why all docking maneuvers in space require either manual corrections or programmed, active corrections using vehicle to vehicle sensing during final approach.
The polite assessment of your idea is that it is a solution looking for a problem to solve. If implemented, it would at best be, an unnecessary drain on computing resources; at worst, completely pointless.