Is this calculation correct?

Question

The International Space Station orbits the Earth at an altitude of 200 miles and its forward speed is 17240 MPH. At this altitude the acceleration of g is 14.7 ft. per second. In one second the station moves forward 4.78 miles. Will it drop 14.7 for each second in orbit , or will it drop at some other rate?

Renaisence Man. The station is in orbit, it always remains the same distance above the Earth's surface, the 14.7 feet it falls in one second is a distance.
Dam Dave. I agree with every word in your answer but you did not answer the question, I understand the conditions required to stay in orbit.

skeptic, It has to drop or it will not maintain its altitude above the surface of the Earth as it moves forward, the surface of the curves down, the station must follow this curvature.
Dennis H. The 1/2d is already factored in, the pull of g at 200 miles altitude is 29.4 ft.,the Earth should curve down by that much in 4.78 miles.

Answer 1

When an object is in orbit there are two things happening at once. The Object's momentum is carrying it forward, in a straight line, that would carry it away from the larger body(earth). The gravitational pull is pulling the object off it's straight trajectory toward the earth. Orbit is sustained because the forward momentum combined with the gravitational pull move the orbiting object in an arc that keeps it at a stable distance from the earth. So the object is always falling toward earth, but never getting any closer.

That is why achieving orbit requires precision. Too slow and you plunge to earth. Too fast, and you leave orbit.

Answer 2

The distance dropped is independent of forward motion. So

d=1/2at^2
d=7.35ft in one second.
From what I understand this is actually the distance that the earth falls away in 4.78 miles which keeps the ISS at a relatively constant height over the earth, although there is a significant amount of atmospheric drag at that height that slowly erodes the orbit.

Answer 3

It will not drop at all - it is in a stable orbit.

Assuming your numbers are correct - It will be deflected from the straight line its inertia would dictate by 14.7 ft. Which is exactly the amount needed to keep it at 200 miles.

Answer 4

You have things a bit twisted, my friend.I think you meant that the acceleration of g is 14.7 ft per second per second. That means that the velocity changes by 14.7 feet per second every second.That additional velocity is directed downward. 14.7 is a velocity, not a distance.