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Offline Tim Alphabeaver

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Re: Flat Earth Satellites
« Reply #20 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.
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Offline BillO

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Re: Flat Earth Satellites
« Reply #21 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.
Here a quack, there a quack, everywhere a quack quack.

Re: Flat Earth Satellites
« Reply #22 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/

Re: Flat Earth Satellites
« Reply #23 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.

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Offline BillO

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Re: Flat Earth Satellites
« Reply #24 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. 
Here a quack, there a quack, everywhere a quack quack.

Re: Flat Earth Satellites
« Reply #25 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?
« Last Edit: January 25, 2020, 09:21:50 PM by pricelesspearl »

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Offline Tim Alphabeaver

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Re: Flat Earth Satellites
« Reply #26 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.
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Re: Flat Earth Satellites
« Reply #27 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

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Offline Pete Svarrior

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Re: Flat Earth Satellites
« Reply #28 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.
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Re: Flat Earth Satellites
« Reply #29 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. 

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Offline Pete Svarrior

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Re: Flat Earth Satellites
« Reply #30 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):

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.
« Last Edit: January 26, 2020, 10:14:47 AM by Pete Svarrior »
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Re: Flat Earth Satellites
« Reply #31 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):

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?

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Offline Pete Svarrior

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Re: Flat Earth Satellites
« Reply #32 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]
[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.]
« Last Edit: January 27, 2020, 08:49:38 AM by Pete Svarrior »
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Offline Groit

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Re: Flat Earth Satellites
« Reply #33 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]

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

Re: Flat Earth Satellites
« Reply #34 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.



« Last Edit: January 26, 2020, 08:07:20 PM by pricelesspearl »

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Offline Tim Alphabeaver

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Re: Flat Earth Satellites
« Reply #35 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)  ::)
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Re: Flat Earth Satellites
« Reply #36 on: January 27, 2020, 12:33:39 AM »
Quote
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.

Quote
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

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Offline Tim Alphabeaver

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Re: Flat Earth Satellites
« Reply #37 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.
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Offline Pete Svarrior

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Re: Flat Earth Satellites
« Reply #38 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.
« Last Edit: January 27, 2020, 08:51:27 AM by Pete Svarrior »
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Re: Flat Earth Satellites
« Reply #39 on: January 27, 2020, 01:33:07 PM »
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.

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.