this post was submitted on 22 Feb 2024
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Astronomy
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Had to read the article to find out that they mean 72 "years worth of orbits" happen in 1 earth day. Although unlikely I was hoping that it was orbiting so fast that 1 earth day there would pass 72 earth years to a stationary observer due to time dilation. Not sure how fast it would need to go for that to happen.
Since time and speed are relative, to have 1 Earth day on the star and see 72 years on Earth, it'd simply be a speed multiplier of 72*365.24= 26,296.28 times faster. Our solar system orbits the galactic center at 250km/s or 0.0008c, so ~26k times that puts it at nearly 22c relative to us. So no.
But quite frankly, there must be a way to be a slower observer. Earth's orbital speed is about 30km/s (0.0001c) so that drops the product way down to 2.6c. And while the Parker Solar Probe holds the record for the fastest man made object at 0.0006c at its closest solar approach, it actually took a lot of energy to slow it down to get it to the sun and stall it's orbit. Otherwise, it'd just orbit it the same as the Earth. It slides out to a Venusian distance from the sun at apogee and drops to 12km/s, halving the differential requirement to +1.2c. But if everything is relative, how do we even determine where 1c is and know it's so definitively impossible to reach? I don't know, I'm starting to have an existential crisis. Maybe time just keeps dilating and simple addition/subtraction doesn't apply for appreciable values of c so you have to start multiplying in decimals.
Relativistic time dilation is nonlinear, so the time dilation "multiplier" approaches infinity as you approach the speed of light. So you will never need more than 1c to pass any finite amount of time for the observer while only passing a smaller amount of time for the moving object. Using a time dilation calculator, it looks like 1 day inside the moving object to 72 years for the stationary observer works out to roughly 99.9999999% the speed of light (9 nines total). Of course if you take into account earths movement as a "stationary" baseline then it'll depend on whether you're moving with or against the fast moving object.
It used to melt my brain too but there's no need to know "absolutely stationary" since you're comparing 2 objects. And due to the time dilation, the 1c limit is different depending on the observer, the time dilation will prevent anyone from observing >1c even if one person is going 0.9c relative to another person who is also going 0.9c relative to a stationary observer.