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So what forces are impacting both the air and skydiver to cause movement?UA is pushing the Earth, which is pushing the atmolayer, which is pushing the skydiver, but only a little bit.And how would the relative velocity be determined?The same way any other velocity would be determined. Pick your favourite method.
Yes, that is a necessary consequence of the skydiver moving relative to the air.QuoteHe is, relative to the air.
Is the air moving relative to the skydiver?
Me too. It’s really hard, isn’t it?QuoteHave you ever heard of indoor sky diving?
Think about how that works...
I have heard of it...and I’ve done it. I was stationary as long as the airflow was constant and the distance between me and the floor never changed.
What if the airflow wasn’t constant?
What would happen if the speed of the air kept increasing?
Have you ever heard of indoor sky diving?
Think about how that works...
He is, relative to the air.
The skydiver's velocity never changing would imply that the force imposed by drag does not lead to a change in velocity.
Sorry, you're right, that's obviously not a major factor. The important change is that in drag - as the skydiver's velocity relative to the air changes so does the drag coefficient.
This error aside, my comment on pp's confusion stands. The discussion on what is "actually" moving is only likely to distract (and is arguably meaningless). It's the relative motion between the two that matters. I should have kept my response to just that, given TomIA already gave a perfectly good answer to the core question.
I think the effects of time dilation are the same for all receivers on the surface of the Earth (at sea level), as all clocks at sea level tick at the same rate regardless of their rotational speeds. For example an observer at the north pole will feel stronger gravity than an observer at the equator, so the north pole observers clock should tick slightly more slowly. However, the observer at the equator has a faster rotational speed which cancels the effects and thus both observers clocks tick at the same rate.
Obviously not everyone lives at sea level and not everyone travels in a vehicle at the same speed, but i think the effects of time dilation due to this is very, very small.
Q - At different positions in its orbit, a GPS satellite will have differing speeds relative to different GPS receivers. Given this, do we need to adjust the speed used in the equation for time dilation to account for this variation?
A - In principle, we do need to use a different value for v in Equation 1 depending on the precise speed of a given satellite relative to a particular receiver. However, the speed of the satellites (3874 m/s) is much larger than the speed of a GPS receiver as it moves with Earth’s rotation (465 m/s at the equator). Differences in the values of the relative speed between a satellite and a receiver result in variations in the amount of time dilation of just 1% at most and so are insignificant for the current accuracy of the GPS.
Then equally if I jump off a building and we ignore air resistance, I'm not being accelerated towards the ground, I'm just following a geodesic. These are both technically true, but I think not very helpful.
Circular motion requires velocity to be always changing. The thing that's constant in a circular orbit is speed, not velocity. (and yes, I'm aware I made this mistake myself only 1 post ago)
From this principle, Einstein deduced that free-fall is inertial motion. Objects in free-fall do not experience being accelerated downward (e.g. toward the earth or other massive body) but rather weightlessness and no acceleration. In an inertial frame of reference bodies (and photons, or light) obey Newton's first law, moving at constant velocity in straight lines. Analogously, in a curved spacetime the world line of an inertial particle or pulse of light is as straight as possible (in space and time).[4] Such a world line is called a geodesic and from the point of view of the inertial frame is a straight line. This is why an accelerometer in free-fall doesn't register any acceleration; there isn't any.
As an example: an inertial body moving along a geodesic through space can be trapped into an orbit around a large gravitational mass without ever experiencing acceleration. This is possible because spacetime is radically curved in close vicinity to a large gravitational mass
At different positions in its orbit, a GPS satellite will have differing speeds relative to different GPS receivers. Given this, do we need to adjust the speed used in the equation for time dilation to account for this variation?
You already know that the satellites are not geostationary, and that therefore this velocity cannot be constant - the figure you provided is likely an average or estimate. You should have been able to put 2 and 2 together there, really.
At each moment in time, it has an instantaneous velocity of 3874 m/s along its orbit.
The current GPS constellation includes 24 satellites, each traveling in a 12-hour, circular orbit.
First let's consider the ideal case of a single uniform massive object being orbited. Circular orbits have a constant velocity and distance from the center of mass of the bodyhttps://en.wikibooks.org/wiki/Space_Transport_and_Engineering_Methods/Orbital_Mechanics
Constant velocity relative to what? We already know they're not geostationary, so clearly not the Earth. Please render your thought complete and meaningful so we can assess whether it is correct.
https://www.perimeterinstitute.ca/images/perimeter_inspirations/GPS/gps_relativity_guide.pdf
The GPS satellites move at 3.874 km/s relative to Earth, a speed that is 0.0013% of the speed of light.
It looks to me like BillO clarified his position quite well.In thermodynamics, calling the Universe an isolated system is meaningless. It cannot be true nor false, because it does not have an assigned meaning within physics. The danger of accepting undefined terms in a discussion like this is that it will bring unknown consequences later on. BillO was offered plenty of opportunities to replace that term with a meaningful one, but chose not to. Thus, the conversation can't proceed.
Yes and no. If I accelerate in the direction of my velocity vector, (i.e. 'fowards'), then I will both speed up and be in a higher orbit.
This isn't at odds with a higher circular orbit being at a lower velocity.
Maintaining a constant velocity is only a requirement of a perfectly circular orbit, many satellites have stable elliptical orbits and don't have a constant velocity
An elliptical orbit, also called an eccentric orbit, is in the shape of an ellipse. In an elliptical orbit, the satellite's velocity changes depending on where it is in its orbital path. When the satellite is in the part of its orbit closest to the Earth, it moves faster because the Earth's gravitational pull is stronger. The satellite is moving the fastest at the low point of an elliptical orbit. The low point of the orbit is called the perigee. The high point of the orbit, when the satellite is moving the slowest, is called the apogee.
[quote author=pricelesspearl link=topic=15722.msg203549#msg203549 date=1579923507
No. Acceleration is not just 'motion'. Motion, or at least the common understanding of motion is change of position or velocity/movement. Acceleration is change of velocity. Acceleration is not relative to place or position. If you are undergoing acceleration you are in what is called a non-inertial frame of reference. Non-inertial frames of reference are not relative to any position or initial velocity. You can undergo acceleration at any time, place or initial velocity and the magnitude of that acceleration is not dependent on or relative to the time, place or initial velocity.
Now, undiscussed so far is what is implied by acceleration. Acceleration implies a transfer of energy. Depending on the definition of the system under discussion this could mean a relative change in energy - but almost universally not so as in the (RE) universe as we know it, the sources and sinks of energy are usually readily identified.
This hearkens back to the failed discussion Pete and I had about the thermodynamic validity of UA.
) Accelerating relative to what and for how long?Acceleration does not have to be relative to anything. I thought you knew better.
Erm... that's not true? If a satellite sped up it would just go into a higher orbit, and if it slowed down if would go into a lower orbit.Erm... that's not true? If a satellite sped up it would just go into a higher orbit, and if it slowed down if would go into a lower orbit.
When a satellite is in orbit, it has a perfect balance between its momentum and Earth’s gravity. But finding this balance is sort of tricky.
Gravity is stronger the closer you are to Earth. And satellites that orbit close to Earth must travel at very high speeds to stay in orbit.
For example, the satellite NOAA-20 orbits just a few hundred miles above Earth. It has to travel at 17,000 miles per hour to stay in orbit.
On the other hand, NOAA’s GOES-East satellite orbits 22,000 miles above Earth. It only has to travel about 6,700 miles per hour to overcome gravity and stay in orbit.
I already provided you with the FET frame. Your scenario does not apply to it in any meaningful way. Therefore, you clearly must have a different FoR in mind, or you simply presented an argument so incomplete that it does not have a defined meaning (let alone a truth value).
In RET, GPS satellites are accelerating or changing velocity (why did you feel the need to say the same thing twice?) relative to the Earth. And yet, according to RE'ers, the effects of time dilation are clearly observable. I dare suggest that your statement is therefore nonsense.
You're the one who made the assertion. It certainly should be your job to make it complete, or to rescind it.
I would suggest that the frame of reference you've implied (yet can't identify) does not exist outside of a hypothetical thought experiment. I'd be curious to see if you, the claimant, actually put any thought into your claim, or if you just rapid-fired it with its glaring holes
My point is that if the earth is accelerating at c (or really at any rate at all), any satellites would have to be accelerating at the same rate to keep pace. Any faster or slower, eventually it would be out of functional range.
This, too, is incomplete. In order to fulfil your requirement of the satellite not escaping or crashing into the Earth, it has to be accelerating upward together with UA. However, this does not mean that it can't be moving (or accelerating) perpendicular to UA for periods of time, or even oscillating up and down irrespective of UA. As long as this motion remains cyclical, your conditions can easily be met.
Quote from: pricelesspearl on January 23, 2020, 09:49:13 PM
If the earth and GPS satellites are accelerating at the same rate, there wouldn't be any time dilation.
And this, too, is incomplete. The multiple relativistic effects experienced by GPS are (primarily) due to relative velocity and a difference in gravitational potential. Your argument might hold some water if the satellites were geostationary, but they're not.
Relative to what?