In The Relativity of Wrong, Asimov makes the point that the accuracy of the Voyager spacecraft was pure Newton.
Hmmm, I would dispute this. The cathode-ray tube oscilloscope was invented in 1897 by Karl Ferdinand Braun, who clearly knew nothing of Relativity. Of course, the early models used accelerating voltages that did not result in electron velocities for which relativistic calculations were particularly necessary, but they still worked.
If one were to design a state-of-the-art oscilloscope with Apollo-era technology but without knowledge of relativity, it would still function, but with the following caveats:
[ol]
[li]If the “X” and “Y” deflection plates are equidistant from the electron gun, then the resulting image will be the same shape, but of a slightly different size from that expected if relativistic effects had been accounted for. This would not be a problem because oscilloscopes are always calibrated for “X” and “Y” amplitude using test signals.[/li][li]If the “Y” deflection plates are further from the electron gun than the “X” plates (or vice versa), there will be a horizontal/vertical gain discrepancy leading to aspect-ratio distortion; in such a configuration there is always a variable delay adjustment between X and Y plate voltage waveforms.[/ol]In either case, ignorance of Relativity would lead to a slight change in displayed image at the phosphor, which might cause a few raised eyebrows and shrugged shoulders for the calibration team, but certainly wouldn’t have prevented Apollo-era CRTs from functioning. Standard calibration procedures would correct for the time-of-flight issues, even though the designers wouldn’t have known why the electrons weren’t following the exactly-predicted paths.[/li]
[Nowadays, almost all high-performance oscilloscopes digitize the incoming signal(s) in real time, and then display the waveform(s) on a comparatively slow CRT or LCD monitor.]
I was about to say that.
I might go to a thread I understand :rolleyes:
Scientific theories aren’t really necessary to carry out any engineering project; they’re just necessary to do so efficiently. The Medieval cathedrals, for example, were built without any knowledge of Newtonian physics or advanced mathematics; the builders just ridiculously over-engineered them, and if they collapsed anyway they tried a different approach. If any part of sending men to the moon relied on knowledge of relativity, we could have gotten by without it by substituting trial and error, though it may have been ridiculously inefficient (i.e., multiple failed missions until we got it right).
I think we’re comparing apples and oranges, hajario. The unmanned probes were important, no question, and were being used to test all sorts of applications that had to work right for the Apollo program.
But, again, without the better ability to predict oribital mechanics that Relativity brought us, I’m not so sure that we’d have been able to fudge things enough to make up for what might have been as much as a half percent error because our math wasn’t up to the task. IOW, I contend that the errors that would occur by simply using straight Newtonian physics, instead of Einsteinian physics would have been at most an error of less than one half of one percent. But it’s my understanding that some things that the Apollo program had to get right had to be correct within fractions of a tenth of a percent, or we would end up with dead astronauts. Specifically, hitting the rentry window for the command module was hugely difficult - come in too fast and even the heat shield would burn up, come in too shallow and the module would bounce off the atmosphere.
psychonaut, I agree with you. I’m trained as a chem and radcon guy. If anyone knows about the effectiveness of a good estimate based on incomplete understandings, it would be me. I would add one caveat to your statement, though - losing two or more missions in succession would probably have killed Apollo deader than Pharaoh. Just look at the effect of losing Challenger and then Columbia each had on the Space Shuttle program.
Though, considering the point that Bryan Ekers brings up - I’ll admit I may be wrong about the need for Relativity for the fine tuning that such calculations would require.
If the relative velocities of the observers is small compared to the speed of light, though, the two formulas become indistinguishable. More precisely, the shifts in the frequency will be the same to one part in (speed of light)/(relative velocity), or one part in about 30,000 for the Apollo astronauts. So while light/radio Doppler shift is properly described by relativistic mechanics, in practice the non-relativistic version was good enough — just like many other aspects of the mission.
I don’t want to claim credit, of course. The relevant passage from Asimov’s The Relativity of Wrong is:
>Doppler shift is not a relativistic effect.
It’s a relativistic effect, in Galilean relativity and all the ones since. It’s not an effect in Einsteinian relativity in particular.
>In either case, ignorance of Relativity would lead to a slight change … and shrugged shoulders … but certainly wouldn’t have prevented Apollo-era CRTs from functioning.
Yes, actually, I guess that’s true, as far as I know. Good point. I retract the statement.
In fact, I wonder what other Big Truths we have missed, what slight changes and shrugged shoulders we have substituted for things that other civilizations think of as fundamental.