Re^3: Irrational numbers

[BrowserUk]

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.

[grondilu]

I was thinking of a model from which you could compare differences or something. Even if there is no such thing as a perfect circle or sphere in real life, it's still a very useful concept because it provides a reference frame for observation.

And for docking, I was still thinking of the Kerbal Space Program. Not an actual physical spaceship.

PS. Also, the sun happens to be almost perfectly spherical.

[BrowserUk]

I was thinking of a model from which you could compare differences or something.

And how could we possibly measure millimetric differences in actual orbits in order to compare them against your perfect model?

And for docking, I was still thinking of the Kerbal Space Program. Not an actual physical spaceship.

So you are going to calculate the positions of the simulated spacecraft within your game, to millimetric accuracy, despite that you would need a screen the size of the Earth's orbit around the Sun in order to notice the difference?

PS. Also, the sun happens to be almost perfectly spherical.

I can only assume that you state this in connection with the Sun's gravity?

The variability of the Sun's gravity is not due to the shape of the Sun; but rather to density changes caused by the convection currents that cause the constant churning of the gas.

Look up the Variability of solar IRradiance and Gravity Oscillations (VIRGO) instrument on the SOHO spacecraft; reference g-mode waves.

[grondilu]

So you are going to calculate the positions of the simulated spacecraft within your game, to millimetric accuracy, despite that you would need a screen the size of the Earth's orbit around the Sun in order to notice the difference?

No. The point is to use the same numerical object to represent the position of the spacecraft, all the way from take off on ground level to orbit and docking. I don't know in details how exactly using floating point numbers to do so causes problem, but clearly it did cause problems for KSP.

PS. Also, with a program like KSP, you may not have a screen as big as the solar system, but it's just as if. You have a huge range of numerical values that makes a virtual scene just that big.