The general formula is simple as all already written. I simply want you to do some job, instead offering people to explain your ... let say fantasies. And there was nothing but elementary algebra in my calculations. So, do not play a cheap game, start a work we expect from you...
Since Yuriy chooses to over complicate the issue and post his typical 1/2 page, in essence (unless you are looking for exceptional accuracy) the distance of a geosynchronous orbit is 35,786 km, that is 35,786,000 m. At the speed of light the information delay is approximately 119.3 milli-seconds. (0.11928,,, seconds). Not counting any proclaimed SRT time dilation affects, etc. Which at that velocity are negligable. The geosynchronous orbit has a velocity of 3,064.8 m/s, divided c = 1.022E-5. Squared = 1.044E-10. The tick rate reference the earths pole (rest)would be (1 - 1.044E-10)<sup>1/2</sup>; which is to small for my calculator to even resolve. The differential to a surface clock would depend on the latitude but deducting the dilation of the surface clock or setting O/E makes the accumulated time due to Gamma adjustment even less than the above. Point being lack of simultaneity is predominately one of information delay. During the 119 ms delay the satellite would be 365.57 m further around its orbit than you see it. In essence the information delay is approximately 1 billion times greater than any velocity affects. Velocity would displace the satellite location by less than 4 millionths of a milli-meter in comparision. I think this is more in line with the type of answer you were seeking.
Unfortunately I think that this issue about simultaneousness for SRT cut's deeper than just info delay. It is more a fundamental regards the abolishment of absolute time. I do see I might add, how information delay could be contrued as non-simultaneousness.......and if this is tha case then dilated time will not cause the effect of an ever increasing time lag between frames..... which would answer my question. However if the issue is not one of information delay and has a deeper reason then the question about accumulating the effects of dilation on the lag in time between frames still stands. Maybe someone has a yes/no answer for it.
if it is just info delay then the two clocks thread you ran MacM would have yeilded totally different results I would think.
What do you mean by velocity would displace the satelite location? If it means what I think it means you are referring to the effects of non-simultaneousness due to rel. velocity meaning that the location is relative to the degree of non-simultaneousness.....and not information delay.....?
The issue is indeed deeper if you increase velocity. But you asked specifically about geosynchronous orbit. In that case the lack of simultaneity is predominanatly simply information delay.
if we take the SRT possition then i assume that time dilation is accumulating for our clock from earths perpective....yes? And my question is: If this is the case then does the degree of non-simultaneousness increase accordingly? If we take the SRT position.
QQ, Do you appreciate your life time or not? Why you are asking MacM about some facts, knowing for sure (what was proven in our Forum dozen times!) that he can not perform … elementary Algebra? You want to know what Lorentz dilation of the clocks on the geostationary orbit is and by some reason can not do calculations by formulas that already were provided here? Well, let’s calculate it together and compare with MacM’s “Math”. As I told you already, the geostationary orbit has a radius R = 6.66 Re = 42,620km Therefore, the satellite on it moves with velocity V=2piR/T = 3.1km/s relatively to the axis of Earth! As you know, the linear speed of points the surface of Earth due to Earth day-night rotation is Ve = 465.4m/s Therefore the relative velocity of geostationary satellite in respect to points of Earth surface is approximately Vrel =2.66km/s. For V the Lorentz-factor is G[V]=1/(1 – V^2/c^2)^1/2 = 1/(1 – 1.068*10^-10)^1/2 = 1 + 5.34*10^-11 During 1 day-night dilation of the orbiting clock the Lorentz time dilation in respect to the clock that are rested on the Earth axis will be equal to Delta T = 24*3600* 0.534*10^-10 = 4.614 microsec (Remember MacM’s “Divided by c = 1.2915E-5. Gamma therefore = 1/(1-1.66797E-10)1/2 Now my calculator, nor computer will resolve these figures, so what follows is an estimation for comparision”. He simply has not even a clue that such values are calculable without any computer, just in mind: (1- x)^1/2 = 1-x/2 ) In respect to the clocks on the surface we will have accordingly: G[V]=1/(1 – V^2/c^2)^1/2 = 1/(1 – 7.862*10^-11)^1/2 = = 1 + 3.461*10^-11 and Delta T = 24*3600* 3.461*10^-11 = 2.99 microsec Now you can use these values in formulas I gave you for measures of “non-synchronization” for your needs…
Lets see what we have here. 1 - Up yours. 2 - Have I made errors certainly. 3 - Have you? Most definately. Starting with just this thread. Wrong. It is 42,164.15km. That is 35,786 Km above the surface and results in: 42,164.15km * 1,000 * 2 * Pi = 264,925,167.8 m circumference. Wrong. Orbit period is 24 hours (close enough) 264,925,167.8 m/(24 * 3,600) = 3,066.26 m/s; NOT 3,100 m/s. I simply used figures from my head and posted 3,064 m/s. So I was 2 m/s off and you are 34 m/s off. I guess that makes your error 17 times larger than mine. Oh really? Wrong. As I mentioned (and you don't) the surface velocity varies by latitude. The diameter of earth is 12,756.3 Km, times 1,000 * pi = 40,075,000 m. Divided by 24/3,600 = 463.8 m/s but only at the equator. It is zero at the poles. Wrong. 3.064km/s - 0.4638 km /s = 2.6 km/s NOT 2.66 km/s. WOW. I'm impressed after two full pages of precise math and tons of false innuendo about my capabilities, you come up with an orbit shift of 9 mm ( check my math to make sure I didn't screw up) and I guessed under 4 mm without lifting a pencil. You have really proven you superior knowledge and capabilities on this one don't you think. TWIT.
awwww shit guys all I wanna know is whether the lag between the nows of each frame increases with the passage of dilated time......yes or no......sheeshh!!!!
QQ, By the definition NOW for any observer is the set of all events that are happening simultaneously at given moment of time by the observer’s clock. So, you are asking literally the following: “Whether the lag between sets of all events that are happening simultaneously at given moment of time by the observer’s clock of each frame increases with the passage of dilated time” What is lag between sets of events? Why you operate with set of event like it is a number? How any logical one can even understand what you want to know? When you will check out your statements for the semantics? Sheeesh!!!!
Inspite of Yuriy's apparent convenient attack of cognition failure, your question is a valid one. Your question, correct me if I am wrong, is "Does the dilated tick rate accumulate so as to cause a diverging reality between observer "Nows" which are in relative motion. Also just to note above my embarrising error pointed out by Yuriy. A differance of 5 mm in a geosynchronous orbit. That equal an error of 1 part in 8 billion or 1.25E-10th Oh my how can I ever recover my credability? Please Register or Log in to view the hidden image! Of course his error of 34 m/s or 1/9th should be ignored as due to rounding error I would think don't you. Or perhaps the fact that he doesn'tinclude approxamately 120 milli-seconds simultantiey shift due to information delay but wants to argue about 3 microseconds velocity affect, really makes sense to me. Affects that are only 1/40,000 or 2.5E-5 of the affects I mentioned. Good show Yuriy you've really put me in my place this time.
I have a question about time dilation due to relative velocity. As MacM pointed out, the Earth has different velocities at the equator than it does at the poles ( 0 at the poles due to rotation). I know that clocks tick at the same rate at sealevel at the poles as they do at sealevel at the equator. Relativist explain this by saying the clock at the pole is in a deeper gravity well than the clock at the equator, and the gravitational effect 'exactly' offsets the relative velocity time dilation effect. But now consider the geostationary satellite. According to SR's time dilation effects, the clocks on the poles and the equator would tick at slightly different beats compared to the clock on the geostationary satellite. I mean there would be slightly more time dilation between the pole-clock and satellite wrt the equator-clock and satellite. Over several years time, it should be recordable. How can the Earth clocks each have their own tick rates wrt the geostationary satellite clock when the Earth clocks tick at the identical rate between themselves? Isn't the gravity well the satellite clock is in calculated from the center of the Earth, so wouldn't be a factor in the difference in tick rates between the two Earth clocks?
Dear 2inquisitive, No matter how you feel about me, please, let me include your question in my book about SRT, which I'm writing right now. For that I need your actual name, please e-mail it to me. I'll very appreciate your kindness and understanding. Guys, this is a moment in sake of which I am in this Forum: 2inquisitive just formulated a best question on SRT, I ever heard! Indeed, How clocks, rested on the surface of geoid (Earth) and having a full compensation of their mutual Lorentz time dilation by the gravitational time outstripping due to shape of geoid, and due to that fact being synchronic with each other, can have the same rate of asynchronism (dilation or outstripping) with clocks of any satellite? This is a question that should excite any of GPS' apologists. Let me emphasize, that even if 2inquisitive is wrong, and there is no natural synchronization of the clocks, rested on the surface of geoid, and we have actually the reliable watches only because of daily synchronization of them with the standard clocks somewhere (let us say - in Greenwich), it does not affect the 2inquisitive’s question. Because I am intuitively sure that there exist a shape of a rotating planet (theoretically) which is satisfying to the condition of synchronization of clocks rested on its surface. Lethe, I thing we got a beautiful mathematical problem: “Find the shape of a rotated planet on the surface of which all rested clocks will be synchronized due to effects of the Lorentz time dilation and Einstein’s gravitational time outstripping.” JamesR, I hope we have a life example, showing that we should not erase posts on the public Forums.
I am pleased to see you begin to participate. I am hopeful that we can go forward without the unwarranted personal assaults. But that clearly is up to you. When you think I am wrong on some issue I do not take offense to being corrected. I do take offense to being called ignorant and a liar. If it is your wish to continnue this pissing contest then I will be forced to oblige but I am hopeful that you can now see that these issues do raise questions and should be considered in the most open light possible to find proper resolutions. I'm going to make one more post regarding your above post and the mathematics but I will do so in a polite manner (that had not been my plan). I had planned to bash you on the issue but I will now post it in the form of a question and allow you and others to address this important consideration.
I'll not attempt to answer your question. It is a good one and I'll let those more atune to the purported theory dynamics attempt to resolve it. I only want to point out that my contribution thus far was considering SR only and GR was being ignored.
