We are not ignoring the fact that we have no idea what the sun is really doing. We are asserting that the sun appears to orbit the earth at 15 degrees per hour as observed since the beginning of recorded observations. This is not in dispute. Your next-door neighbors can corroborate it. This is not a NASA trick. Take the time to make your own sundial and record your observations.
Why is this so hard for you? Why do you keep asking about my maths and physics when you struggle with plain English?
The sun does not cross the sky uniformly at 15 degrees per hour. Let that sink in. Now fully understand that before you try to wrap your head around the incredibly difficult proof of that assertation.
The sun's speed changes through out the day from the perspective of the individual observer. Wait for it. Wait for it. You can verify this by looking at sunrise and sunset times and the times it takes the sun each day to travel through 6 degrees.
http://www.ukweathercams.co.uk/sunrise_sunset_times.phpso in the case of London today ...
Sunset: 15:52:34
Dusk - civil twilight ends 16:32:42
Nautical twilight ends 17:15:52
Astronomical twilight ends 17:56:40
Please note, the sun doesn't do each 6 degrees in the same time period. It isn't linear. Ergo, the sun isn't doing 15 degrees per minute. In fact it took almost 1 hour and 43 minutes for the sun to do 15 degrees over London at sunset today. It took, two hours, 4 minutes and 6 seconds to pass 18 degrees.
This is just simple addition and subtraction. I'm not trying to bamboozle you with numbers here.