Isaac Newton

And Newton's third law? (Which is about balance of forces)

They don't work for relativity or for quantum mechanics, so the Euler-Lagrange form of motion laws are more generally useful/findamental - as are Hamilton's.

But how many day-to-day engineering projects involve relativity or quantum mechanics?

Well quite. You're doing pretty well if you can gets the balls in a Newton's Cradle to move at anywhere near the speed of light.

I'd avoid that unless you are up to explaining why dropping 2 balls from one end always results in 2 balls swinging up at the other end. I seem to recall I could have done so once upon a time but I could be dreaming; I know I couldn't explain it now.

The force to stop the first ball sets the next one in motion and so on down the chain until the free one. You do it with just a pair if you want to demonstrate transfer of momentum from one to the other.

Not my problem. Best ask Brian that question. :-)

As for the second point you mentioned, I don't think any future NASA robotic missions to the outer planets and trans Neptunian objects will be affected by relativistic effects of any significance until long after the Sun has become a red giant, collapsed to a white dwarf star and cooled down to just a milli Kelvin or two above Absolute Zero. :-)

Suggest you read the Winky article about it.

AFAIK, all computations for planetary probes have been done using Newton. The most pronounced effect in our Solar System requiring Einstein to explain is the precession of the orbit of Mercury, and even then, some 97% of the effect can be explained without Einstein.

If you mean then yes, thanks, that rang just enough bells to confirm how much I've forgotten :(

Your OK if you drive an inch away or closer (unless they hit something). They can't slow down fast enough for there to be much of an impact before you start pushing them (well not with brakes).

Anything that uses GPS, so most construction projects these days.

The same reason it works for one or three or four. Now more interesting is why steel balls work and rubber ones don't work very well.

NASA's program for computing orbits can take account of relativistic effects but doesn't do so where they are negligible. They certainly weren't seen as negligible for the Messenger flyby. See eg

"So, then, he turned back to the Newton-only formulation for everything, including the Sun, to see what would happen. "The resulting difference was somewhat larger than I expected: The flyby altitude at Mercury increased by about 10 km, but the closest approach time changed by about

NB 10km may not seem much but the spacecraft missed its planned altitude by less than 1.5 kilometers.

I think there may also have been some relativistic corrections for Cassini but can't find now one way or the other.

Prolly because a pressure wave transmits nicely through steel and not that well through rubber?

GPS only uses relativity in the weak field limit as a perturbation.

Moving clocks run slower and clocks further out of the gravitational field run quicker and if you are trying for

It is only when going in towards Mercury that GR frame dragging becomes sufficient to affect orbital trajectories. If we ever get faster probes approaching c/1000 then relativistic effects would matter at ppm levels. The fastest probe we have ever made was Helios at a whopping c/8000 and for comparison the most distant manmade object Voyager is about c/30000.

OTOH observing pulsars the GR light time corrections for ray paths passing close to Jupiter found systematic errors that uncovered a bug in the VSOP87 machine generated FORTRAN code for planetary positions which turned out to be due to >10 continuation cards in one long expression.

anything with a transistor in it, strictly :=)

I think you may be wrong there