The Flat Earth Society

Flat Earth Discussion Boards => Flat Earth Theory => Topic started by: MagnusSuperior on January 08, 2020, 05:23:50 PM

Title: Flat Earth Satellites
Post by: MagnusSuperior on January 08, 2020, 05:23:50 PM
If the Earth is flat, how can a G.P.S. satellite stay afloat?  Or the I.S.S., for that matter?
Title: Re: Flat Earth Satellites
Post by: iamcpc on January 08, 2020, 06:32:08 PM
If the Earth is flat, how can a G.P.S. satellite stay afloat?  Or the I.S.S., for that matter?

There are several different FE models so there are many ways to answer this question so i'll just give a few

-there is no such thing as a satellite
-They are attached to the dome
-they are high altitude balloons
-they are orbiting earth in outer space because of gravity
-they are just planes or other high altitude mechanical devices sending out their signals
Title: Re: Flat Earth Satellites
Post by: inquisitive on January 09, 2020, 03:42:44 PM
If the Earth is flat, how can a G.P.S. satellite stay afloat?  Or the I.S.S., for that matter?

There are several different FE models so there are many ways to answer this question so i'll just give a few

-there is no such thing as a satellite
-They are attached to the dome
-they are high altitude balloons
-they are orbiting earth in outer space because of gravity
-they are just planes or other high altitude mechanical devices sending out their signals
Asking the people that build and operate GPS would be a good start.
Title: Re: Flat Earth Satellites
Post by: BillO on January 10, 2020, 01:48:48 AM
Asking the people that build and operate GPS would be a good start.
What if the conspiracy that regards the entire space community being NASA shills is true, or that you truly believe it is true.  What then would be the point of asking the conspirators?
Title: Re: Flat Earth Satellites
Post by: inquisitive on January 10, 2020, 07:44:45 PM
Asking the people that build and operate GPS would be a good start.
What if the conspiracy that regards the entire space community being NASA shills is true, or that you truly believe it is true.  What then would be the point of asking the conspirators?
Bit surprising that GPS works exactly as documented.
Title: Re: Flat Earth Satellites
Post by: BillO on January 10, 2020, 11:48:50 PM
Bit surprising that GPS works exactly as documented.
No, not really ... perhaps you missed my point.
Title: Re: Flat Earth Satellites
Post by: Groit on January 12, 2020, 06:46:37 PM
All satellites are put into orbit using Newton's laws of motion, which only works with a spherical Earth. The orbital period is proportional to radius from the centre of the Earth, and knowing that the Earth's radius is 6,370 km we can determine the altitude of the satellite. GPS satellites orbit the Earth twice a day and are at an altitude of about 20,000 km, geostationary satellites which orbit the Earth every 24 hours and so appear to be stationary, are at an altitude of about 36,000 km.
 
Without Newton's laws of motion/gravity there would be no GPS systems, no Hubble space telescope, no weather satellites, no sky/satellite tv and no internet, therefore this chat forum wouldn't even exist.  ;) 
Title: Re: Flat Earth Satellites
Post by: MagnusSuperior on January 22, 2020, 11:32:20 PM
I'd honestly be interested in seeing/reading explanations how a satellite could work in a flat-earth scenario. Hopefully a scenario with no continuity errors.
Title: Re: Flat Earth Satellites
Post by: ImAnEngineerToo on January 23, 2020, 07:26:03 AM
I’d be curious too. Since there’s no centripetal force to keep them circling...

Curious side note about satellites: I did a project on how they adjust the gps clocks based on the atomic clocks in Colorado taking into account equations for distance from earth and tangential velocity. Apparently they travel so fast, time dilation makes a meaningful difference.
Title: Re: Flat Earth Satellites
Post by: pricelesspearl on January 23, 2020, 01:27:29 PM
Apparently they travel so fast, time dilation makes a meaningful difference.

Which is not something that would be an issue if we were already traveling at close to the speed of light.
Title: Re: Flat Earth Satellites
Post by: Pete Svarrior on January 23, 2020, 02:59:42 PM
Which is not something that would be an issue if we were already traveling at close to the speed of light.
Relative to what?
Title: Re: Flat Earth Satellites
Post by: pricelesspearl on January 23, 2020, 09:49:13 PM
Quote
Relative to what?

That's a really good question. And I really can't answer it because since I don't believe the earth is accelerating at close to light speed. Perhaps you or someone else who does believe that can answer the question...relative to what is the earth accelerating?

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.  If the earth and GPS satellites are accelerating at the same rate, there wouldn't be any time dilation.
Title: Re: Flat Earth Satellites
Post by: Pete Svarrior on January 24, 2020, 08:32:41 AM
That's a really good question. And I really can't answer it because since I don't believe the earth is accelerating at close to light speed.
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.

Perhaps you or someone else who does believe that can answer the question...relative to what is the earth accelerating?
An observer immediately above the Earth, at rest relative to the Earth.

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.

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.
Title: Re: Flat Earth Satellites
Post by: AllAroundTheWorld on January 24, 2020, 11:40:46 AM
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.
I'm genuinely fascinated by what you think GPS satellites are and how they work. As you say, they're not geostationary, they are said to be satellites orbiting the globe earth. Obviously you can't believe that, so what do you think they are and how do they work?
Title: Re: Flat Earth Satellites
Post by: inquisitive on January 24, 2020, 02:57:21 PM
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.
I'm genuinely fascinated by what you think GPS satellites are and how they work. As you say, they're not geostationary, they are said to be satellites orbiting the globe earth. Obviously you can't believe that, so what do you think they are and how do they work?
Worth adding that GPNSS receivers give details of each satellites location and there are 4 separate systems in use.
Title: Re: Flat Earth Satellites
Post by: pricelesspearl on January 24, 2020, 05:53:09 PM
Quote
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

I haven't suggested a frame of reference. The concept of an accelerating earth is an FET one, so it is up to FET to define the frame of reference. I said time dilation wouldn't be an issue if the earth were accelerating.  I don't accept that it is, so there is no reason for me to have to define a frame of reference.  FET believes the earth is accelerating...so I can go whatever frame of reference FET proposes. It's your theory, not mine.

Time dilation wouldn't be an issue if the earth were accelerating relative to whatever reference frame is consistent with FET.  Is that defined enough for you?

Quote
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.


Special relativity only applies to inertial frames of reference…at rest or moving at constant velocity.  If the satellites are accelerating or changing velocity, SR doesn’t even apply, and time dilation wouldn’t be an issue.  GR wouldn’t apply either. There wouldn’t be any time dilation due to gravitational effects, because there is no gravity on FE.

That raises an interesting observation, though.  Currently, effects from both gravity and speed are taken into account to determine the amount of time dilation.  Without taking gravity into account, the FE calculations would be entirely different.
Title: Re: Flat Earth Satellites
Post by: Pete Svarrior on January 24, 2020, 05:59:38 PM
I said time dilation wouldn't be an issue if the earth were accelerating.
Accelerating relative to what and for how long? You can't make this claim without clarifying. It is meaningless.

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).

Special relativity only applies to inertial frames of reference…at rest or moving at constant velocity.  If the satellites are accelerating or changing velocity, SR doesn’t even apply, and time dilation wouldn’t be an issue.
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.
Title: Re: Flat Earth Satellites
Post by: BillO on January 24, 2020, 07:32:45 PM
Accelerating relative to what and for how long?
Acceleration does not have to be relative to anything.  I thought you knew better.
Title: Re: Flat Earth Satellites
Post by: Pete Svarrior on January 24, 2020, 10:16:49 PM
Acceleration does not have to be relative to anything.
Incorrect, given our current set of assumptions in this conversation. If you'd like to explain to pp why his assumptions are silly, by all means, feel free to, but in the future, try to direct your criticisms appropriately.

I thought you knew better.
Given your track record, if you thought something was the case, it can be safely assumed not to be the case. Indeed, if anything, your agreeing with me just now made me doubt my position.
Title: Re: Flat Earth Satellites
Post by: pricelesspearl on January 24, 2020, 10:57:36 PM
Quote
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).

Sorry, I missed that.  An observer immediately above the Earth, at rest relative to the Earth...so how is that definition relevant to my point?

Quote
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.

GPS satellites maintain a constant velocity.  They have to sustain a constant velocity to maintain balance with gravity.  Any faster and the satellite flies off into space and any slower, it crashes to earth.

Global Positioning System (GPS) satellites travel approximately 14,000 km/hour, relative to the Earth as a whole, as opposed to relative to a fixed point on its surface
https://sciencing.com/how-fast-do-gps-satellites-travel-12213923.html
Title: Re: Flat Earth Satellites
Post by: Tim Alphabeaver on January 24, 2020, 11:53:59 PM
GPS satellites maintain a constant velocity.  They have to sustain a constant velocity to maintain balance with gravity.  Any faster and the satellite flies off into space and any slower, it crashes to earth.
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.
Title: Re: Flat Earth Satellites
Post by: BillO on January 25, 2020, 12:03:24 AM
Incorrect, given our current set of assumptions in this conversation. If you'd like to explain to pp why his assumptions are silly, by all means, feel free to, but in the future, try to direct your criticisms appropriately.
It does not depend on your assumptions or anyone else's.   It's simply wrong to refer to acceleration the way you did.  I'm sure the pp got the gist too.  If not, then perhaps there is little to be done about it.

Given your track record, if you thought something was the case, it can be safely assumed not to be the case.
You mean my 'track record' based on your incorrect interpretations and opinion?  When I'm wrong I admit it.  If I have not admitted to being wrong, it is because I was not.  Regardless of your opinion.

Indeed, if anything, your agreeing with me just now made me doubt my position.
I'm not the one that posted something dumb.  That was you, now it seems you are trying to back out of it.

If you find this post inappropriate, then you find yourself so too.  You have used exactly the same language and approach each time we converse.
Title: Re: Flat Earth Satellites
Post by: pricelesspearl on January 25, 2020, 03:00:04 AM
Quote
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.

No, actually the lower the orbit the faster it needs to go.

Quote
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.

https://scijinks.gov/satellites-orbit/
Title: Re: Flat Earth Satellites
Post by: pricelesspearl on January 25, 2020, 03:38:27 AM
Accelerating relative to what and for how long?
Acceleration does not have to be relative to anything.  I thought you knew better.

In a way, I think you are both right.  Acceleration is just motion and motion is a change in position relative to a fixed point.  That fixed point could be an object's previous position.

So yes, acceleration must be relative to "something", but it doesn't have to be another object.
Title: Re: Flat Earth Satellites
Post by: BillO on January 25, 2020, 04:10:52 AM
In a way, I think you are both right.  Acceleration is just motion and motion is a change in position relative to a fixed point.  That fixed point could be an object's previous position.

So yes, acceleration must be relative to "something", but it doesn't have to be another object.
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. 
Title: Re: Flat Earth Satellites
Post by: pricelesspearl on January 25, 2020, 06:04:04 AM
[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.

I think I understand what you are saying (except for the thermodynamics stuff, :))

You can't really tell if you are at rest or moving at constant velocity without a reference point. But you don't need a reference point to know if you are moving at constant velocity or accelerating.  Is that close?
Title: Re: Flat Earth Satellites
Post by: Tim Alphabeaver on January 25, 2020, 07:49:55 PM
Quote
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.

No, actually the lower the orbit the faster it needs to go.

Quote
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.

https://scijinks.gov/satellites-orbit/
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.
Title: Re: Flat Earth Satellites
Post by: pricelesspearl on January 25, 2020, 10:36:58 PM
Quote
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

While its true that constant velocity is only a requirement for a circular orbit...it is still true that even in an elliptical orbit, the higher the orbit, the slower the velocity and the lower the orbit, the faster the velocity.  Its all about having to balance gravity and velocity.  In any event, GPS satellites have a circular orbit and constant velocity and GPS satellites were the topic of discussion.

Quote
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.

http://www.satellites.spacesim.org/english/anatomy/orbit/elliptic.html
Title: Re: Flat Earth Satellites
Post by: Pete Svarrior on January 25, 2020, 11:13:18 PM
GPS satellites maintain a constant velocity.
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.
Title: Re: Flat Earth Satellites
Post by: pricelesspearl on January 26, 2020, 05:09:14 AM
Quote
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.
Quote

The GPS satellites move at 3.874 km/s relative to Earth, a speed that is 0.0013% of the speed of light.
https://www.perimeterinstitute.ca/images/perimeter_inspirations/GPS/gps_relativity_guide.pdf

I hope that is meaningful enough. 
Title: Re: Flat Earth Satellites
Post by: Pete Svarrior on January 26, 2020, 09:55:09 AM
Well, it makes it meaningful, but it also makes it immediately false (and I had warned you this would be the case, so I guess you just wanted to be wrong).

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.

Funnily enough, the document you quoted (but forgot to read) confirms this. The first FAQ in supplementary information reads as follows (emphasis mine):

Quote from: https://www.perimeterinstitute.ca/images/perimeter_inspirations/GPS/gps_relativity_guide.pdf
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.

You also know that, in RET, they orbit the Earth, and are thus subject to acceleration. You'll really struggle to find one without the other...

Your claim that they do not accelerate is amazingly nonsensical, and you'd do well to fix it. The answer above might provide you with a less terrible claim to make. I would strongly suggest reading it before citing it again - it actually has some good ammunition for your position once you've understood it. Plus, it's generally good practice not to quote-mine papers for something you think agrees with you without reading them and checking that it actually does.

Finally, I missed this gem earlier:

It does not depend on your assumptions or anyone else's.
Of course. After all, it's not like these would look differently in different inertial and non-inertial FoR. We can just ignore that. Oh, wait...

BillO, remember my usual advice: if you didn't understand what someone has said, simply ask them to clarify. No need to go on a tirade about how right you think you are.
Title: Re: Flat Earth Satellites
Post by: inquisitive on January 26, 2020, 10:57:59 AM
Well, it makes it meaningful, but it also makes it immediately false (and I had warned you this would be the case, so I guess you just wanted to be wrong).

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.

Funnily enough, the document you quoted (but forgot to read) confirms this. The first FAQ in supplementary information reads as follows (emphasis mine):

Quote from: https://www.perimeterinstitute.ca/images/perimeter_inspirations/GPS/gps_relativity_guide.pdf
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.

You also know that, in RET, they orbit the Earth, and are thus subject to acceleration. You'll really struggle to find one without the other...

Your claim that they do not accelerate is amazingly nonsensical, and you'd do well to fix it. The answer above might provide you with a less terrible claim to make. I would strongly suggest reading it before citing it again - it actually has some good ammunition for your position once you've understood it. Plus, it's generally good practice not to quote-mine papers for something you think agrees with you without reading them and checking that it actually does.

Finally, I missed this gem earlier:

It does not depend on your assumptions or anyone else's.
Of course. After all, it's not like these would look differently in different inertial and non-inertial FoR. We can just ignore that. Oh, wait...

BillO, remember my usual advice: if you didn't understand what someone has said, simply ask them to clarify. No need to go on a tirade about how right you think you are.
What is the value of the acceleration?
Title: Re: Flat Earth Satellites
Post by: Pete Svarrior on January 26, 2020, 02:36:57 PM
What is the value of the acceleration?
%5Cfrac%7BGM%7D%7Br%5E2%7D, where G is the gravitational constant, M is the mass of the round Earth, and r is the distance between the round Earth's and the satellite's centres of gravity. Without wasting too much time doing your physics homework for you, this should be somewhere in the region of 0.56%5Cfrac%7Bm%7D%7Bs%5E2%7D

[EDIT: I originally claimed this would be 0.3%5Cfrac%7Bm%7D%7Bs%5E2%7D, a commonly-used figure for geostationary satellites orbiting around 37,500km. This was silly of me, given how many times I had to explain here that GPS satellites are not geostationary. They are supposed to be in medium Earth orbit, so I revised my calculation using r of 20,200km borrowed from our friends at the US government (https://www.gps.gov/systems/gps/space/)]
[EDIT 2: I'm on a roll. The altitude of 20,200km is measured from the round Earth's surface, and I failed to include the round Earth's radius in my calculation.]
Title: Re: Flat Earth Satellites
Post by: Groit on January 26, 2020, 04:57:06 PM
What is the value of the acceleration?
%5Cfrac%7BGM%7D%7Br%5E2%7D, where G is the gravitational constant, M is the mass of the round Earth, and r is the distance between the round Earth's and the satellite's centres of gravity. Without wasting too much time doing your physics homework for you, this should be somewhere in the region of 0.98%5Cfrac%7Bm%7D%7Bs%5E2%7D

[EDIT: I originally claimed this would be 0.3%5Cfrac%7Bm%7D%7Bs%5E2%7D, a commonly-used figure for geostationary satellites orbiting around 37,500km. This was silly of me, given how many times I had to explain here that GPS satellites are not geostationary. They are supposed to be in medium Earth orbit, so I revised my calculation using r of 20,200km borrowed from our friends at the US government (https://www.gps.gov/systems/gps/space/)]

Pete, you forgot to add the radius of the Earth to r  which gives 26,570 km and thus giving an acceleration of 0.56 m s^-2
Title: Re: Flat Earth Satellites
Post by: pricelesspearl on January 26, 2020, 05:59:10 PM
Quote
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?

That’s because, the velocity is relative to the earth as a whole, not to any fixed point. The earth rotates slower at the poles than at the equator so the exact velocity of the receiver will vary depending on where it is.  Not to mention that more often than not the receiver itself will be moving.  The relative velocity between the receiver and the satellite changes because the velocity of the receiver changes depending on location and/or speed…not because the velocity of the satellite changes.
https://en.wikibooks.org/wiki/Space_Transport_and_Engineering_Methods/Orbital_Mechanics

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.

IOW, the speed of the receiver changes, not the velocity of the satellite.

Quote
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.

The document specifically says it is not average

Quote
At each moment in time, it has an instantaneous velocity of 3874 m/s along its orbit.



Let’s review…

GPS satellites are in a circular orbit
Quote
The current GPS constellation includes 24 satellites, each traveling in a 12-hour, circular orbit.

https://cddis.nasa.gov/Techniques/GNSS/GNSS_Overview.html

Circular orbits maintain a constant velocity.

Quote
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 body
https://en.wikibooks.org/wiki/Space_Transport_and_Engineering_Methods/Orbital_Mechanics

You should be able to put 2 and 2 together.



Title: Re: Flat Earth Satellites
Post by: Tim Alphabeaver on January 26, 2020, 11:35:39 PM
Circular orbits maintain a constant velocity.
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)  ::)
Title: Re: Flat Earth Satellites
Post by: pricelesspearl on January 27, 2020, 12:33:39 AM
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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)

Not according to the Equivalence Principle.  You are forgetting that in GR, straight is defined as a geodesic.

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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

https://en.wikipedia.org/wiki/Equivalence_principle#Development_of_gravitational_theory
Title: Re: Flat Earth Satellites
Post by: Tim Alphabeaver on January 27, 2020, 01:04:33 AM
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
[/quote]
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.
Title: Re: Flat Earth Satellites
Post by: Pete Svarrior on January 27, 2020, 08:48:29 AM
Pete, you forgot to add the radius of the Earth to r  which gives 26,570 km and thus giving an acceleration of 0.56 m s^-2
So I have. Thank you for pointing it out. I'll correct my post.

As for pricelesspearl, I think it's safe to assume that his posts should fall under the "blatant troll" category by now - we shouldn't waste our time with them.
Title: Re: Flat Earth Satellites
Post by: pricelesspearl on January 27, 2020, 01:33:07 PM
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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.

Helpful or not helpful isn't really a valid scientific or logical standard.  Pointing out that a circular orbit could imply acceleration is a valid point.  Frankly, I was expecting Pete to bring it up sooner. But if that is an argument you want to make, be prepared for where it leads and to be intellectually consistent.

Time dilation is concept that results from special relativity.  Special relativity only applies in inertial reference frames, which by definition, are not accelerated.  If a circular orbit is acceleration, it is a non-inertial reference frame, special relativity doesn't apply and there is no time dilation.

You can't have it both ways.

Title: Re: Flat Earth Satellites
Post by: Tim Alphabeaver on January 27, 2020, 09:13:13 PM
Helpful or not helpful isn't really a valid scientific or logical standard.
Well I think I can't argue with that.
Title: Re: Flat Earth Satellites
Post by: Tim Alphabeaver on January 27, 2020, 09:19:14 PM
As for pricelesspearl, I think it's safe to assume that his posts should fall under the "blatant troll" category by now - we shouldn't waste our time with them.
A 'blatant troll' is what you call a valid direct response to your post, with citations?
Title: Re: Flat Earth Satellites
Post by: Groit on January 27, 2020, 10:43:29 PM
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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?

That’s because, the velocity is relative to the earth as a whole, not to any fixed point. The earth rotates slower at the poles than at the equator so the exact velocity of the receiver will vary depending on where it is.  Not to mention that more often than not the receiver itself will be moving.  The relative velocity between the receiver and the satellite changes because the velocity of the receiver changes depending on location and/or speed…not because the velocity of the satellite changes.

Hi Pricelesspearl

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.   
Title: Re: Flat Earth Satellites
Post by: pricelesspearl on January 27, 2020, 11:44:15 PM
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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.


I don’t disagree with that.  I was just responding to Pete’s apparent understanding of the passage below and explaining why a GPS satellite will have differing speeds relative to different GPS receivers…because the receivers are accelerating, not the satellites
The response given makes it clear that although “in principle” the speed of the receiver changes the calculations; the difference is so minor it isn’t relevant.


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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.