User talk:Donbenladd
Caption for the Scott & Mark Kelly image at the top of the Twin Paradox article
[edit]One of the sources (ref 1) in the current caption gives a value of 13 milliseconds simply by way of quoting Scott Kelly, who gave no indication of whether that was a GR/SR effect, a biological effect of weightlessness, or some combination of the two. The other source (ref 2) has a non-functioning specific link (OL 20717998W: Bing: "can't reach this page"), so I could find nothing there to corroborate ref 1.
Nor can I find any source on the Net that specifies 13 milliseconds without simply repeating Scott's words as quoted in the article referenced (ref 1 in the caption).
If, as seems apparent, Scott was referring to the combination of his combined GR/SR lesser aging (using 8 milliseconds) and a biological age increase of 5 milliseconds due to orbital weightlessness (that 5-millisecond value we see here and there on the Net, but which actually refers to six months in orbit aboard ISS and is incorrectly used by Mark Kelly in an interview), and then accidentally added instead of subtracting, he would obtain 13 milliseconds. But of course, the Twin Paradox article should not include any aging difference relating to the effect of orbital weightlessness in any case.
A graph accompanying the Wikipedia "Time Dilation" article indicates about 25 microseconds per day (8.5 milliseconds per 340 days) combined SR/GR time-difference for ISS, in keeping with the simple equations for GR and SR time-dilation. And note the smooth lines connecting ISS to all the satellites.
https://en.wikipedia.org/wiki/Time_dilation#Experimental_testing_3
Quartz, a reliable source by Wikipedia standards, states the correct value for the GR/SR combined time difference, which is 8.6 milliseconds.
Quartz is described in a Wikipedia article: https://en.wikipedia.org/wiki/Quartz_(publication)
Quartz article for use as a new source: https://qz.com/370729/astronaut-scott-kelly-will-return-from-a-year-in-space-both-older-and-younger-than-his-twin-brother
(The Wayback Machine is still down -- so can't archive this source until they're up again in a predicted few days. Will reference the archive once the Wayback Machine is back online.)
The article manages (by way of self-canceling slight errors and the correct methodology) to state the correct aging difference of 8.6 milliseconds when combining GR and SR effects. This is the best source I've found.
The article uses 17,000 mph and 342 days (the original planned length for the mission) and then makes rounding errors in the calculations which cancel that slightly incorrect speed and mission-duration; but at least they use the correct methodology.
Their errors in assumptions and their rounding errors are all insignifcant. Without the rounding errors, the 17,000 mph & 342 days would yield 8.23 milliseconds.
Fortunately, when using more accurate numbers (ISS speed of 17,400 mph (that is the most accurate available, based on a 254-mile altitude and an average orbital period of 91.3 minutes) and a 340 day mission), one does in fact arrive at 8.636 milliseconds combined GR & SR less aging for Scott, making for an exact agreement with the above-referenced source.
The mission involved 5440 orbits. Sources that state speeds for ISS of 17,600 mph or more are using 90 minutes as the average orbital period, rather than the more accurate 91.3 minutes.
Earth mass= 5.972 10^24 kg
Earth avg rad = 6,371,000 m
ISS alt = 254 miles = 408,772 m
==>
ISS rad = 6,779,772 m
Using the ISS-speed and mission-duration as used in the article, which is 17,000 mph and 342 days:
GR:
E esc vel = 11,186 m/s ==> time difference of 0.020569 seconds
ISS esc vel = 10,843 m/s ==> time difference of 0.019327 seconds
0.020569 - 0.019327 = 0.001242
==>
0.001242 sec increase of clock time for ISS (Scott) relative to the surface of the earth (Mark)
SR: 0.009494 seconds decrease in clock time for ISS (Scott) relative to center of Earth
Mark (at 45 degrees latitude) has a decrease in clock time relative to center of Earth of 0.00001755 seconds.
==>
Scott has 0.009476 seconds less clock time than Mark per SR effect.
Combined GR and SR:
0.008234 seconds (8.23 milliseconds) decrease in clock time for ISS
That is the value the article would have obtained without their rounding errors.