
Mark H. answered 10/31/20
Tutoring in Math and Science at all levels
Answers follow.....
1.The biggest issue is ignoring the laws worked out by Newton and Kepler. From Newton, we have the law of gravity, which tells us that rocks flying around in space will tend to gather into spherical shapes. Kepler used Newton's laws to work out th motions of objects in fre space---------------or in orbits around other larger objects.. These laws have verified by many observations of planetary motion---and the orbit of the moon around the earth.
Another issue is the known properties of the earth, including plate tectonics and the magnetic field. These would be very hard to explain if the earth were not a sphere
All of this is taught in high school and early college science classes, and there are lots of resources on the web----eg Wikipedia
2, (added 11/1)
One argument I found (here at Wyzant): Suppose you are travelling along the surface of a large ball. ...It is apparent that you will get closer to the surface on which the ball is resting . From Geometry, we know that the circumference of the ball is the radius multiplied by "pi", which is approximately 3.142. From this, we can "do the math', and find the "drop" associated with the motion along the surface. Since we know that traveling along the earth's surface does not directly cause us to lose altitude, the argument was made that we should conclude that the earth is not in fact round.
The fallacy: On a body such as the earth, "down' is defined as movement towards the center---which is the direction of the force of gravity. (If you drop something, it will head towards the center of the earth.) Clearly, walking along the Earth' s surface does not cause one to get closer to the center. What DOES happen is that the motion has 2 components---one along a north-south line, and the other along an east -west line. Neither of these is "down"---as defined above.