it's already doing 17.46 km/hour
That doesn't sound right.
"it's already doing 17.46 km/sec"
NASA's announced that Voyager 1's already-amazingly-long mission will probably be extended for an extra two or three years, thanks to a successful attempt to use thrusters that haven't fired up since the year 1980. As NASA announced last Friday, Voyager 1's been using its “attitude control thrusters” (ACMs) for decades, to …
@Geniality "You need to be going very close to the speed of light (299,762 km/sec) for time dilation to become meaningful on a macroscopic scale. "
Tell that to the GPS satellite physicists. They'll set you straight^H^H^H^H^H^H freefall trajectory through curved spacetime.
@Barley registers Satellites have to keep incredibly precise time, down to the picosecond (which isn't macroscopic). Voyager 1 doesn't. As I said, time dilation takes place at any relative velocity but it takes a long time to build up to something meaningful. Even for GPS satellites it takes months to go a few picoseconds out of sync with Earth-based stations.
@Geniality - you didn't read that link did you?
Money quote: "But at 38 microseconds per day, the relativistic offset in the rates of the satellite clocks is so large that, if left uncompensated, it would cause navigational errors that accumulate faster than 10 km per day!"
So - relativistically tiny speeds still causing 10km per day error.
Pretty meaningful in my book. Your mileage may vary. (Ha! see what I did there?)
You need to be going very close to the speed of light (299,762 km/sec) for time dilation to become meaningful on a macroscopic scale. It does happen at any speed though, Voyager's time travel relative to Earth would be a bit less than 2 seconds, accumulated over the last 40 years, if it travelled in empty space. Because of its tour of the outer planets, their gravitational wells actually sped up its relative time. It's hard to calculate how much dilation that caused though, since it depends on altitude and how many bodies (planets, moons and rings) had a meaningful impact.
Well perhaps back in 1980 it was a cylinder and not a golden disk originally.
As Voyager approaches the speed of light, something called the Fitzgerald contraction becomes effective.
There once was a fencer named Fisk,
Whose speed was incredibly brisk.
So fast was his action,
The Fitzgerald contraction,
Foreshortended his foil to a disk.
17.46 km/s is not close enough to light speed for significant time dilation, but the fact that Voyager is so much further out of the Sun's gravity well, the on board clocks of Voyager would certainly be ticking faster than clocks on Earth. Gravitational time dilation even has to be accounted for on GPS satellites and they're much closer to Earth (and the Sun).
"When you're going that fast, doesn't time slow down or something"
yes but the amount is negliglble. you'd probably notice if you're receiving radio signals that are supposed to be xx.xxxx Mhz, but end up being xx.xxxy Mhz [that kind of difference].
As I recall, on one of the Apollo missions, they had an atomic clock or something similar on board the spacecraft, and they actually measured the time difference. Since they were moving at ~50k MPH for the trip to/from the moon, there would be a measurable effect, even though it was pretty tiny. But, the scientists involved in the experiment DID find "that difference" and announced that Einstein WAS right. It was definitely worth doing, yeah.
You can figure out the effect on time when you consider that if you're travellng at 1/2C, then [simplified] from YOUR perspective, light still moves at C, which means that for you, time effectively moves 1/2 as fast as it is for someone who's not moving at all. It's actually more complicated than that, but discussing all of the details in here would be TLDR and *yawn*. NOT mentioning that would invite the anal retentive howler monkey types to nit-pick every word.
anyway, ~18km/sec compared to ~300,000 km/sec is a pretty small change in the flow of time, but it's in the neighborhood of 1/10,000 [unless I made a math error] so radio frequencies would be shifted in a measurable way [as I already mentioned at the top] but that's about it. What's interesting, however, is that the shift would probably be TWICE what doppler alone would cause, because the relative time would affect the RF oscillators, which would put out a lower transmit frequency, which would then be further time-stretched by the doppler effect as the craft moves away from earth.
[gravity wells, as mentioned earlier, notwithstanding]
17.46kps really isn't that fast when compared to light speed at 300,000kps, so any time dilation can safely be ignored. The dilation only becomes meaningful when you get up to higher fractions of light speed.
According to Relativity time will slow down even when you just walk to the corner store. Its all about how fast your moving relative to another point of reference.
That's about Mach 49 (for reference Earth orbital velocity is about M23).
OTOH that's 0.0056% of the speed of light.
However in principal systems can be engineered (no breakthroughs in physics, including fusion, needed) that could get to 5% of the speed of light.
Mach number is relative to local speed of sound so a velocity doesn't correspond to any specific Mach number unless you know what the local speed of sound is. For ideal gas the local speed of sound is a function of temperature (and temperature only). As for the temperature of the so-close-to-vacuum-as-makes-no-difference environment of the Voyager probes (assuming analyzing it as ideal gas even makes sense)... I have no idea.
Possibly why us runners tend to use minutes per mile or for the modern inclined minutes per km. I having grown up in metric NZ and being an SI unit using scientist (I have to think about what an Angstrom is) for some reason which is opaque to me still use minutes per mile. Though for a rough and ready 5min/km = 8min/mile.
I suspect it is because most road distance races are 5miles, 10miles, half marathon (13.1miles) or marathon (26.2miles) etc. 10km's (6.25miles) is an aberration in the system. I bow to the track system of course though I haven't run a track race in several decades. Cross country races tend to be approximate due to the nature of the beast, proper cross country races anyway, with sucking mud patches and fences you have to vault with cow pat hazards. Sheep droppings are a mere inconvenience.
In the last thirty seven years, Voyager 1 has 'lost' almost two whole seconds, compared to us on the earth due to relativistic velocity time dilation.
(not really 'lost time', more, 'experienced time at a rate very slightly slower than us')
(On the other hand, being in a smaller gravitational field, the Voyager probes will have 'gained' some time as well, but less than lost to velocity)
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