Hi Doug -- you are very close to the correct altitude of ~3167 km (~1.4965 * earth equatorial radius). I'm now working through the math to figure out the latitude on earth where you age the slowest. ;-) --Rob
-----Original Message----- From: MexicoDoug [mailto:[email protected]] Sent: Thursday, July 21, 2016 9:57 AM To: [email protected]; Matson, Rob D. Cc: [email protected] Subject: Re: [meteorite-list] More fun with GR Hi Rob and the other meteoroidal travelers, I'd say a good mean altitude for government work would be about half of Earth's radius, and that ought to smooth out any technicalities to gain an understanding of the magnitudes which is what is interestng about the new question. A shortcut to calculate that is to set the free fall velocity (no atmosphere) equal to the orbital (tangential) velocity; it avoids the calculus by using the velocity derived from the drop in potential from orbit altitude to surface level. v^2 = GM/r' (orbital) v^2 = 2GM/r -2GM/r' (gravitational) If you solve for the altitude simultaneously, r'-r, you get the altitude of half again Earth's diameter easily. Unless there are more Golgafrinchans lurking somewhere in the thread history! That is a Medium Earth Orbit. In a perfect universe, 3189 km altitude. Nothing special orbit wise, unless you are temporally centric in which case it could be called a temporally synchronous orbit, which clearly the universe is notvery concerned about as we are ;-) Kindest wishes Doug -----Original Message----- From: James Beauchamp <[email protected]> To: Matson, Rob D. <[email protected]> Cc: MexicoDoug <[email protected]>; meteorite-list <[email protected]> Sent: Thu, Jul 21, 2016 10:31 am Subject: Re: [meteorite-list] More fun with GR For the satellite, it varies according to the gravity field it flies over. Technically none exists because the gravity field is never constant. It dithers. Sent from my iPhone On Jul 21, 2016, at 2:01 AM, Matson, Rob D. via Meteorite-list <[email protected]> wrote: Hi Doug, I think you would have come up with the correct answer if I had given a more precise value for the clock slow down relative to a stationary clock in deep space: it should be 0.69693 parts per billion relative to a clock at sea-level on the earth's equator, or 60.2 microseconds per day. It is no accident that the distant rock's velocity would need to be 11.19 km/sec for its clock to remain synchronized with one on the earth's equator. That value should be very familiar to meteorite folks. :-) Here's a harder, but related problem: at what altitude must a satellite in a circular orbit fly for its clock to run at the same speed as a clock on the earth's equator? Another interesting GR factoid: the core of the earth is actually 2 1/2 years younger than the crust (ignoring convection in the core, plate tectonics, etc.) If the earth is modeled as having constant density, the calculation works out to about 1 1/2 years younger, but of course earth is much denser at the core, resulting in even greater time dilation there. --Rob ________________________________________ From: MexicoDoug [[email protected]] Sent: Wednesday, July 20, 2016 4:03 PM To: Matson, Rob D.; [email protected] Subject: Re: [meteorite-list] age of meteorites Rob and all, > For instance, even at solar system escape velocity at earth's distance > from the sun (42 km/sec) What is...The ultimate question of life and the answer to everything? > Extra-credit question for the mathematically > inclined: at what velocity relative to the earth would a meteoroid > have to travel to have its clock stay in sync with a clock at the > earth's surface? :-) Given the figure you mention of 0.6 ppb (52 microseconds per day faster) this question asks be nullified, maybe 10 km/s velocity relative to earth? A good relative velocity to hunt a flock of wild space geese coming to roost on Earth, wearing accurate Rolexes ... But should the meteoroid transition to our gravity, the on-board Rolex might abandon its precision for a few spectacular minutes, and have an "error" of a couple of nanoseconds ;-) Kindest wishes Doug -----Original Message----- From: Matson, Rob D. via Meteorite-list <[email protected]> To: meteorite-list <[email protected]> Sent: Mon, Jul 18, 2016 6:43 pm Subject: Re: [meteorite-list] age of meteorites It's not a bad idea, Pete, but unfortunately the time dilation is really minimal unless you get up to a substantial fraction of the speed of light. For instance, even at solar system escape velocity at earth's distance from the sun (42 km/sec), a meteoroid's clock would be running at about 10 parts per billion slower than that of a stationary rock. (Additional note: due to general relativity, a clock on a meteoroid would be running about 0.6 parts per billion *faster* than a clock at the earth's surface, but that is more than made up for by the time dilation due to special relativity.) Extra-credit question for the mathematically inclined: at what velocity relative to the earth would a meteoroid have to travel to have its clock stay in sync with a clock at the earth's surface? :-) --Rob -----Original Message----- From: Meteorite-list [mailto:[email protected]] On Behalf Of Pete Shugar via Meteorite-list Sent: Monday, July 18, 2016 3:12 PM To: The List Subject: [meteorite-list] age of meteorites greetings to all, my background is in electronics. everything deals with either C or C2. Einstein states that nothing goes faster than the speed of light and that as you approach the speed of light, things get older slower. So this meteorite in it's travels is going at a rate that is a subtantual percentage of the speed of light. Has anyone taken this into consideration when placing an age on the meteorite? Just a thought to tickle the old brain cells!! Pete Shugar ______________________________________________ Visit our Facebook page https://www.facebook.com/meteoritecentral and the Archives at http://www.meteorite-list-archives.com Meteorite-list mailing list [email protected] https://pairlist3.pair.net/mailman/listinfo/meteorite-list ______________________________________________ Visit our Facebook page https://www.facebook.com/meteoritecentral and the Archives at http://www.meteorite-list-archives.com Meteorite-list mailing list [email protected] https://pairlist3.pair.net/mailman/listinfo/meteorite-list ______________________________________________ Visit our Facebook page https://www.facebook.com/meteoritecentral and the Archives at http://www.meteorite-list-archives.com Meteorite-list mailing list [email protected] https://pairlist3.pair.net/mailman/listinfo/meteorite-list ______________________________________________ Visit our Facebook page https://www.facebook.com/meteoritecentral and the Archives at http://www.meteorite-list-archives.com Meteorite-list mailing list [email protected] https://pairlist3.pair.net/mailman/listinfo/meteorite-list
