4 ms·
Traveling at 16km/s for 9.5 years would dilate time by almost 300 minutes! Not only is there a 4.5 hr delay because of the speed of light, there's an extra 300
by e0m 11y ago
Traveling at 16km/s for 9.5 years would dilate time by almost 300 minutes! Not only is there a 4.5 hr delay because of the speed of light, there's an extra 300 min of relativity correction.
- rootbear 11y agoWhoa! I hadn't thought about that. The speed of New Horizons hasn't been constant, of course, but the accumulated time difference is probably close to what you calculated. There would also be a correction due to it being farther out of the Sun's gravity well, but that's a much trickery calculation.
- ars 11y ago(Just a note: His math is off.) You also have to account for the dilation caused by the force of launch itself. But then you have to subtract the dilation of Earth. > There would also be a correction due to it being farther out of the Sun's gravity well Because it is in free-fall relative to the Sun there is no Solar gravitational dilation.
- devb 11y agoBut the transmission time delay is still only 4.5 hours, not 9.5. The onboard clock has simply drifted out of sync with one on Earth.
- agildehaus 11y agoIt's been a while since I took a physics course, but: t' = t * (1-v^2/c^2)^(1/2) t' = 9.5 * (1-16000^2/299792458^2)^(1/2) t' = 9.5 * 0.99999999857... (t-t') years = 426.7 milliseconds
- Trombone12 11y agoOk lets see if we can get this to match. I get the gamma factor to be gam = 0.9999999985758079 with this, earth sees any time interval on new horizons t' to be \detla t' = \delta t / gam longer than the time t on earth. Integrating both sides above over time, keeping velocity constant, we get t' = t/ gam = 9.5 yr / 0.9999999985758079 = 9.500000013529824 yr this gives an difference between our observed "new horizons time" and out local time of t' - t = t/gam - t = (1/gam - 1) t = 0.4 s we disagree by about a factor of 45000.