Your mobile phone proves that the earth is round. Every mobile phone now has a GPS receiver in it. As a career electrical engineer, let me explain, in layman's terms, how your GPS can determine your location, including altitude, down to a resolution of a few feet, and how this is technologically impossible without a system of GPS satellites orbiting the earth.
But first, let me dismiss the only objection I have ever heard by flat-earthers to what I am about to describe. They say that your "GPS" location is actually determined by the cell towers. It is true that, using trilateration (three cell towers), it is possible to determine the approximate location of a cell phone (on a geographic plane), if you are within range of three cell towers. If you are within range of three cell towers, each cell tower can ping the cell phone and the differences between time it takes for the response to arrive will, in theory, determine the approximate location, along with consideration of the signal strength and which directional antenna on the tower has the strongest signals.
The cellphone system needs to determine your approximate distance to cell towers anyway, at least in terms of signal strength, so that it can seamlessly hand off your connection from tower to tower as you drive along the road, without dropping your active phone call as you drive beyond range of your last cell tower radio signal connection. However, cell phone trilateration is accurate to only about a quarter of a mile at best, often closer to the better part of a mile or more. See https://transition.fcc.gov/pshs/911/Apps%20Wrkshp%202015/911_Help_SMS_WhitePaper0515.pdf, which discusses how emergency ("E911") services can use this to help locate a person, where they cite accuracy to an area of "3/4 square mile." As a career electrical engineer with an understanding of the technology, I can attest to the fact that this is a very inaccurate and unreliable way to determine location, for many technical reasons. Also, a signal from a cell tower can only reach a couple of miles, more or less, depending on conditions (terrain, obstructions, etc.). This brings us to the next point: It also is of no use if you are out of service range due to being in a very remote location and you cannot reach even one cell tower, and you really need to be within range of three cell towers to do the trilateration. That's what the "tri-" in trilateration means: "Three." Note also that this kind of trilateration only determines your position on a plane, and cannot determine altitude. More on that later.
Also, the telecomms companies are not in the habit of trying to figure out to any greater accuracy where you are than what is needed to determine what the closest cell tower is that you should be connected to, which happens automatically, and is mainly a function of just monitoring your cell phone's received signal strength to determine which cell tower should service you. Other than that, they don't care and don't have any motive to know exactly where you are. They are just providing you telecommunications service. To do more would cost them more, and they, the different telecomms companies, are in competition with each other to give you service at a competitive price. It takes an act of law enforcement authorities and a court order to try to find out exactly where you are, and personnel at the telecomms company have to be summoned and engaged to try to do this; it does not happen automatically or routinely as part of their system. Believe me, they have better things to do than try to figure out whether you are taking a walk to the local post office to mail a letter, or taking your dog to do his thing behind a park bench, even if they could locate you to that resolution, and they can't.
I remember a publicized parental rights case of a young woman, Alyssa Gilderhus, whom parents (counter-)kidnapped out of a hospital. The hospital reported it to the authorities as a "patient abduction," law enforcement got involved, and using cell tower trilateration they came close to apprehending them: It pointed to an Applebee's restaurant in Mankato, MN, so they searched the Applebee's and the Five Guys next to it, but the family was actually in a Walmart down the street, about a half a mile away. Use Google Maps yourself and see. Type "Mankato, MN Applebee's." Click "Directions." Type "Walmart." "0.6 miles" to get there from the Applebee's. I should hope that your phone or car GPS navigator gives you better accuracy than that! This underscores the inaccuracy of using cell towers to locate a cell phone in circumstances where the authorities get involved and the need to find someone is considered dire. Here is an article detailing that story: https://www.cnn.com/2018/08/13/health/mayo-clinic-escape-2-eprise/index.html. Note again that at this point the authorities were treating this as a "patient abduction," a kidnapping in progress. Time was also of essence to them, since it was represented to them by the hospital that the patient was medically at risk, removed from hospital care. Yet they could not locate them even in cooperation with the telecomm operators.
Another way of approximately locating a mobile phone is by the location of a WiFi hotspot, if connected to one. There are databases that have been collected, even by private industries, of where all the WiFi hotspots are, everywhere. Any industry in the private sector can just accumulate these, even by driving down the road and pinging WiFi hotspots without logging into them. A WiFi hotspot advertises it's presence, necessarily before you can even log into it, and each WiFi hotspot has a unique numerical identifier (a MAC address) to distinguish it from all other hotspots in the world. That's how your mobile phone sees a hotspot and recognizes a hotspot you have previously authenticated yourself into. But, of course, the location is only as accurate as the street address of the hotspot. And hotspots are not able to trilaterate like cell towers, since they are on different and private networks. And determining location by WiFi hotspot is of no use if you are not near one.
So now, I have documented two ways of determining the location of a mobile phone that do not depend on GPS: Cell tower trilateration and WiFi hotspots. If you are out of range of both, your location must depend on GPS.
GPS works as follows: There are systems of two to three dozen satellites orbiting the globe of the earth in space. No matter where you are on the globe, you will be in line-of-sight range of at least three or four or more of them. Each GPS satellite has an atomic clock in it, making the time extremely accurate. Atomic clocks are very, very expensive, far beyond what you could put on a cell tower or in a home WiFi hotspot. Each satellite simply transmits its exact position in three-dimensional space, and the exact time. The GPS receiver on a mobile phone looks for the signals of at least three or four satellites. In theory, you only need three or four, but the more the better and more accurate the result. Each GPS satellite repeatedly broadcasts its exact location and the time of day. Because the radio signal travels at the speed of light, about one and a half nanoseconds per foot, the mobile phone receives the location of the satellite and the time of day as was represented by each satellite when it transmitted it, so the mobile phone can calculate from that exactly where the mobile phone is, down to an accuracy of about fifteen feet or so, if it has a clear view of the open sky (worse if it doesn't, due to the signal bouncing off of obstructions to get there, or atmospheric/weather conditions). To visualize this, imagine if there was only one satellite, defining a sphere around it, the radius of the sphere being the distance to the satellite, such that you only knew where the satellite was and how far you were from the satellite. You could be anywhere on the surface of that sphere. With two satellites, the intersection of two spheres would be a circle. Now you could be anywhere on that circle. With three satellites, the intersection of three spheres would be two points, one of which may perhaps not be on the sphere of the surface of the earth and could be discarded. With four satellites, the intersection of four spheres would be only one point. More satellites in view serve to help the mobile phone average the final value.
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Again, both the accuracy of GPS, and the fact that it is the only way for your mobile phone to know where it is if you are out of cell phone service range and not near a WiFi hotspot, proves that the earth is a sphere, since it requires satellites orbiting the globe to work.
At this point a flat-earther's only escape from my conclusions about GPS is to accuse me of being part of the conspiracy, an actual conspirator, since my career knowledge and experience in electrical engineering and my career employment capacity in computer/datacomms hardware design/development qualifies me as an expert in this kind of technology. In this situation I cannot be accused of being ignorant or duped; I must be accused of intentionally deceiving you at this point, if what I am saying is not true. Do you think this is reasonable?
Now in the twenty-first century, the number of reliable witnesses of a round earth from many sectors of knowledge, science, engineering, industry, arctic/antarctic exploration, meteorology (weather), aviation, space exploration, and documented history, people you can talk to, are more than millions upon millions of people with no round-earth motive or reason for a conspiracy agenda. Now we have billionaires taking joy-rides into space, people viewing the International Space Station with their telescopes in their backyards (one time recently observing astronauts doing an actual space walk), Elon Musk's growing constellation of Starlink internet satellites providing internet service where there are no cell towers (and astronomers and others complaining about it), concern about satellites and "space junk" collisions, concern about Russia (and formerly the Soviets) and China -- political enemies, not co-conspirators -- using space and satellites to gain military advantage over the West/NATO, and vice versa. How is it that you consider that the majority of information we receive via textbooks and libraries, news and internet, from both the ideological left and right, communist and free, Christian and non, is deception, such that you can't believe anything you watch or read anymore, yet the few, obscure sources you do read about flat earth are supposedly the truthful, rare exception? And I have touched upon only one proof, that of GPS, among countless ways to show that the earth is round, not flat.
If you consider yourself a Christian, you know that you have made a choice from three possibilities: The authors of the Bible are either intentional liars (conspirators, since there are multiple witnesses in collaboration), duped as a group, or accurate witnesses of the prophecies, life, and death/burial/resurrection of Jesus. According to 1 Cor 15:6, the witnesses of the resurrection of Jesus numbered on the order of only five hundred, and the historical accounts are just a few in the New Testament, written almost two thousand years ago by only Christians with a known Christian motive and agenda. Why is that not a conspiracy? How is it that you believe that Jesus rose from the dead but do not believe that the earth is a sphere, given millions upon millions of witnesses alive today? I've heard some people claim that flat earth is by confirmation by the witness of the Holy Spirit. But that could be your own imagination and mental/emotional delusion, without the historical accounts of the Bible. I've heard that you can proof-text flat-earth from the Bible itself. But that is just frame of reference. The Bible does not talk about the geometric shape of the earth anywhere in any literal way. Isaiah 40:22 talks about the "circle of the earth," yet Isaiah 11:12 and Rev 7:1 talk about the "four corners of the earth," as usually translated (and most flat-earthers believe that the earth is a disk). Even I say things like, "The sun rises in the east and sets in the west," "sunrise/sunset" not "earth-dawn-spin" or "earth-dusk-spin," use flat maps, and speak as though the curvature of the earth is negligible, which it mostly is on any scale we walk, drive, or look with our eyes in our daily lives.
One thing that history has noted Christians for has been their wisdom, presence of mind, critical thinking skills, and education, which has contributed to the betterment of society worldwide, whereas Islam, Hinduism, and other religions, including atheism, have resulted in the reverse, capitalizing on captivating people with fanciful story-tales that Christians can easily rebut with wisdom, presence of mind, critical thinking skills, and education, even aside from their spiritual authority and supernatural indwelling power. Let's not tarnish this image. Flat earth is a case of superstition, lack of education, lack of critical thinking skills, and fear-mongering, and it is the flat-earther who is duped and easily deceived. Christians should be the source of reliable information and truth.
I grant this work to the public domain.