Maybe we could use a couple of more real life thought experiments.
You are on the top of a mountain and you setup your Muon detector. and will be able to count the mouns before they decay because,
1) In the frame of reference for the Muon lengths are contracted.
2) In the frame of reference for the Muon lengths are expanded.
3) Neither of the above.
Or instead of a train we use the LHC and particle beams instead of lasers.
The new collider is turned on and you press the button to fire two particle beams at each other at .9999c. When a few million revolutions have completed you trip the switch for them to collide.
When you look at the screen for the results.
1) You as the observer would see nothing as the beams are in a different frame of reference and for the particles in the beams time is passing slower and they haven't collided yet.
2) You as the observer would see the collision as the beams are in a different frame of reference and for the particles in the beams time is passing slower so they haven't collided yet (Added bonus we just created a time machine).
3) You as the observer would see the collision as time dilation didn't occur.
Yes, but all you need to calculate is the acceleration caused by the Earth and the acceleration caused by the moon. I would guess, based on the respective masses of said Earth and moon, coupled with the proximity to the Earth, that the effect due to the moon is negligible...however, I would also bet that it's been taken into account.
Not quite as simple as you suggest. you would need to take into account the orbits of the whole constellation (triangulation) in different angular positions and orbits with respect to the moon so that it worked for everyone. At any point in time there would always be a percentage of satellites on the other side of the earth completely devoid of lunar grabitational influence. "Back of a napkin calculations" suggest it is more than negligable center of gravity moves very roughly 25%. As I said it all boils down to physical evidence, show me the proof that they do this (No Wikis or Term papers), Dont you think the GPS center would be proud of the fact and publish it?
Yes, it is. Simply look at the effect of the differing gravitational potential on the far side of the satellite orbit compared to the nearside, assuming worst case of the satellite, Earth, and Moon in alignment. A quick calc shows the gravitational time dilation between far sides of the orbit, owing to the Moon, is about 34,000 times smaller than the difference between orbit and the Earth's surface. I leave verification of this as an exercise.
So, negligible. Anything else? Shall we check the effect of the Sun next?
1) it's not MY essay, it was merely one of the first I found discussing the subject
2) The action of the moon on GPS satellites is quite probably small enough that it doesn't affect the calculations - at some point you have to give up and say "margin of error". It's what you call "diminishing returns" - the payoff from taking it into account is either so small, or the difference so negligible, that it simply isn't worth it. The moon? How about the SUN? How about the four gas giants in our solar system? How about globular cluster M1? Why stop there? Perhaps you'd like the author to take into account all of the matter of the known universe?
When you've reached your quota of 10 posts, can we assume you'll leave, or stick around and attempt to learn something?
At any point in time there would always be a percentage of satellites on the other side of the earth completely devoid of lunar grabitational influence.
Just because I think you're somebody who is self-impressed with their own smarts but could one day make a difference to the world, I intend to give you a gentle nudge towards REAL math and science rather than homeschooled fail or religulous technobabble.
I'm sorry to break it to you, kid, but mass does NOT shield from the effects of gravity.
If you want proof, then you'd have to get a really big rock to stand on. If you don't float away, the mass of the Earth is still pulling on you.
You can measure this if you want - try to weigh yourself close to the earth's surface, then get on your mobile really big rock and weigh yourself again - you'll be the same weight.
The only reason this would change (as discussed) is if you are far enough OUT of the gravity well of the planet Earth that it's cumulative effect on you is diminished.
Gravity reduces according to the inverse square law - hence we probably don't need to take into account the moon and the sun.
And yes, I'm lazy, I'll leave that as an exercise for YOU since you're not happy with the theory and I am.
You know, I was going to write a response to Guiri about time dilation and how the math works, but I'm not sure if it would be worth it.
It doesn't matter how good the bullshit
The problem is that many people don't think it is bullshit. They believe it and that's a tremendous problem. I don't know how it is in the UK and the leaders across the pond, but in the US, people are still pushing for Creationism in Science, and some of those people are in charge.
10% of Americans STILL believe the sun revolves around the earth! In the health-care debate, many Americans believe that under a government run health care system, the government will form "death panels" to determine who lives and who dies.
You hear about JFK and his challenge to Americans to put a man on the moon and in eight years we landed a man on the moon. Now, in eight years, we can't even build a building to memorialize those who lost their lives due to the attacks of 9/11.
Sorry, just had to get that off my chest.
For you Guiri, welcome, and I hope the light of knowledge will drive away the darkness of ignorance.
Our observations of the real world support the mathematical models of Relativity and the idea that gravity and velocity have an effect on the passage of time. I had a whole post laid out to explain it to you in rudimentary mathematics, but I'm not sure if you would consider it. If you are willing to, I'd be happy to share it with you.
I know what you mean about the conspiracy theorists here in the U.S. and those 10% of americans are probably valley girls (L.A. quip). The 911 memorial I agree with you wholeheartedly they should get it built.
Thank you for your offer, but I tend towards Essens view, he was a pretty smart guy and knew a thing or two about time.