I made a little video to clarify my point.
Thanks for the video.
This is definitely perplexing to me since I did the math and it doesn't support what you show in the video. So, there are one of two options: 1) either I messed up the math (which is totally possible) or 2) whatever tool you're using in that program isn't displaying what you think its displaying. I'll leave the math here, if you can figure out what I did wrong then I'll have learned something.
Initial assumptionsInitial velocity is due east (velocity only in the west-east direction)
No change in altitude (R remains constant)
Math sourceshttps://en.wikipedia.org/wiki/Circle_of_a_spherehttps://en.wikipedia.org/wiki/Arc_(geometry)
https://en.wikipedia.org/wiki/Chord_(geometry)
(I also used some basic calculus so if you don't know how to do calculus I can walk you through it)
VariablesR = distance from us to center of the earth
d = radius of the circle that bisects the earth at our given latitude
Theta = longitude degrees
Phi = latitude degrees
WE = west-east distance
NS = north-south distance
dWE/dt = west-east velocity
dNS/dt = north-south velocity
Okay, so the first thing we need to do is figure out the radius of the circle that bisects the earth at our latitude. From the first link we have the radius of a circle that bisects a sphere as:
BC^2 = AB^2 + AC^2
BC = R and AB = d in our example. We can figure out that AC = R^2*sin(Phi) based on trigonometry. Plugging in each of our variables we get:
R^2 = d^2 + R^2*sin(Phi)
Now solve for d
d^2 = R^2 - R^2*sin(Phi)
d^2 = R^2(1 - sin(Phi))
d = R*SQRT(1 - sin(Phi))
Ok, from here we can calculate distance traveled in the west-east direction and distance traveled in the north-south direction in terms of our spherical coordinates. For both directions we'll use the equation for an arc.
WE = d*Theta (theta in radians)
WE = R*SQRT(1 - sin(Phi))*Theta
NS = R*Phi (phi in radians)
Lets look at the north south direction first. Our initial condition is that our initial velocity is in the west east direction only. Therefore, dNS/dt = 0. We also know that R is constant (and non-zero.) If we take the derivative of our NS equation we get:
dNS/dt = R*dPhi/dt
Since dNS/dt equals zero and R does not equal zero then dPhi/dt equals zero. Since dPhi/dt equals zero then integrating will give us that Phi is a constant.
Now going back to our west east direction if phi is a constant than SQRT(1-sin(Phi)) is also a constant. We'll call this constant C. This simplifies our equation to:
WE = R*C*Theta (theta in radians)
therefore, our velocity in the west east direction is:
dWE/dt = R*C*dTheta/dt
Since spherical coordinates defines Theta and Phi as being orthogonal to each other we know that our initial velocity, which only has an west-east component, will result only in a change in Theta and not a change in Phi. This results in only longitude changing but latitude remaining constant.
Like I said, maybe my math is off. Alternatively, maybe you're using the computer program incorrectly or you have a concept error somewhere. I'll try to figure stuff out in the program and you figure out if I messed up in the math.
And if we do find out my math is wrong I'd love to calculate how much change in latitude you see for every one degree of longitude. That would be a fantastic experiment that people could test to give evidence for flat/round earth (of course you'd have to account for things like wind.)