**3 Flight Path Analysis**In this you yet again provide numbers with no justification or reference, and no uncertainty.

Looking at the first one you list, Sydney to Johannesburg, this is flown as QF 63.

According to Google Maps, the great circle distance is 11 024.22 km (putting dots roughly in the airport).

According to flight aware, the direct distance is 11036 km.

Doing the math, taking the positions as Sydney as 33.9 degrees south, 151.2 degrees east, and Johannesburg as 26.1 degrees south, 28.2 degrees east.

The formula for great circle distance (from wikipedia, but also verified elsewhere) is:

d=r*acos(sin(lat1)*sin(lat2) + cos(lat1)*cos(lat2)*cos(deltaLong))

That gives a distance of 11035 km.

So your number seems like pure fiction. Where did you get it?

But yes, the flights are longer, as you would expect.

This is for several reasons.

The simplest is that the plane is not taking off in the correct direction, nor do they land in the correct direction.

Some airports have complex approach paths which they need to take.

This means a plane needs to follow a complex route to reach a point where it is free to fly wherever it wants.

Even over large areas, there are some times corridors they are restricted to, so they can't fly directly. This is to avoid planes crashing into other planes.

Another factor is weather, where they may change their route to avoid weather.

And another is wind. Planes don't go for the shortest distance, they go for a short time and economy. So if there are prevailing winds, they will follow them.

A quite well known route for this is Sydney to Perth, with prevailing winds helping the plane go east. So a trip from Sydney to Perth is usually at least 1 hour longer than a trip from Perth to Sydney.

e.g. QF651 v QF 652.

And depending on how significant it is, they can take a longer route which is faster and uses less fuel.

So the real question is how much longer, and is this reasonable.

Looking at past flights from flight aware

https://www.flightaware.com/live/flight/QFA63 (21st through 31st October) we get distances of (in km):

21st - 11119

23rd - 11297

24th - 11321

25th - 11251

26th - 11210

27th - 11451

28th - 11188

30th - 11186

31st - 11132

They average 11239.44 km, or roughly 200 km more.

I would say that is fairly reasonable.

And it is nothing like your almost 2000 km more.

But again, where is the comparison to a flat Earth?

Especially with this great flight.

If we ignore the route it actually takes, and instead pretend it follows a straight line (which would put the passengers over completely different locations) and take the common monopole FE model, we first switch to polar coordinates.

So we leave the longitude the same.

But now the latitude becomes 10000 km * (90-latitude)/90, with latitude in degrees, with north being positive and south being negative.

This gives us a distance from the north pole of 13767. km for Sydney and 12900 km for Johannesburg.

Now converting to cartesian coordinates using x=r*cos(long), y=r*sin(long), we get locations of (-12064, 6632) for Sydney and (11369, 6096) for Johannesburg

Now to get the distance we just find the sqrt of the sum of squares of the differences in x and y.

That gives us 23439 km.

So if Earth was round, we would expect a distance of slightly above 11 038 km.

If Earth was flat, we would expect a distance of slightly above 23 439 km.

We observe a distance of roughly 11240 km.

This is entirely within the plausible range for a RE, and is entirely impossible for the common FE model.

So flight paths, instead of supporting a FE and challenging a RE actually fully support a RE and show a FE is impossible.

**4.1 Star Trails and Celestial Observations**Star trains, and stars and other celestial observations in general, firmly support a RE and entirely refute a FE.

Here you again misrepresent what is expected for a FE and a RE.

For a FE, with the stars circling the north pole, we would expect star trails to appear as a circle directly at the north pole. As you move away from the north pole they should be distorted into ellipses for those near, and even more complex as you get further out. Even stars quite close to the southern rim of the flat Earth should still be circling the north pole.

They should appear to turn to the north. and go off to the north east, still circling the north pole (but we would not view it as a circle due to the distortion).

We can also determine the angle to the north celestial pole, based upon its height and our distance to the north celestial pole.

a=atan(h/d)

Taking the common 5000 km altitude, and the substitution from before, that gives us a=atan(5000/(10000*(90-latitude)/90))

a=atan(45/(90-latitude))

This also means it should still be well above the horizon.

We can even put in values, for example at the equator the north celestial pole should still be 26.6 degrees above the horizon.

Even going all the way out to 90 degrees south, it should be 14 degrees above the horizon.

This distortion should also effect constellations.

This is easily demonstrated by printing out a constellation laying it on a flat surface, and then taking pictures of it from different locations. Then if you try to overlay them, they will appear distorted due to the different perspectives.

For the RE, the situation is vastly different.

Instead the constellations are so far away they will not appear distorted by any significant amount.

Because Earth is rotating about its axis, the stars will have a constant angular velocity in the equatorial plane, which is observed.

They will appear to trace circles around both the north celestial pole and the south celestial pole, with these always being observed 180 degrees apart.

The angle to the north celestial pole is directly based upon your latitude, in fact it is your latitude.

i.e an observer at the equator should see it level due north, at 45 degrees it should appear at 45 degrees.

And because all that is really happening is we are at a different spot on Earth with our reference changing angle, the sky should appear the same, just tilted.

So the star trails should appear as circles, just not circling a point directly above.

And what is observed in reality?

We observe star trails around a point due north and a point due south. These always appear as circles (or circular arcs for those cut off by Earth).

The constellations appear the same. There is no observed distortion.

And the stars, including the north celestial pole, appear to drop below the horizon.

i.e. what is observed in reality is entirely consistent with a RE and firmly refutes a FE.

**4.2 The Horizon Phenomenon**Another compelling refutation of the FE model, which you get entirely incorrect. But that has already been covered above.

We can see the curve if high enough (e.g. satellites in space), the curve you are trying to see is hidden by the horizon, and the horizon is NOT level.

And importantly, the FE has no explanation at all for why the horizon should exist in the first place.

**4.3 The Behavior of Water**Also already discussed.

Yes water remains LEVEL, not flat. This is shown by long distance observations having water block the view of a distant object (or just the bottom of it), where both the object and observer are above the water.

The only way for this to happen is if water is curved (or if light curves to produce the same result).

That significant bulge you are appealing to is evident.

**Conclusions**Your paper is full of simple math mistakes, entirely unjustified claims, made up numbers, baseless claims for observations and outright falsehoods.

An honest analysis of the points you have raised clearly demonstrates that Earth is round, and clearly refutes the FE.

You have nothing which supports the FE perspective as for the most part you entirely ignore it, likely because an honest examination of the FE model would show these to be massive problems for it.

Your paper is in no way scientific and is just taking FE myths as fact.