Q:

The question of a fired vs a falling bullet is an interesting thought experiment. It would seem to me that a bullet fired with significant velocity at a perfectly horizontal angle to the immediate plane of the earth (in other words perfectly perpendicular to the earth's gravitational force) would hit the ground after the other bullet, being of identical size and mass, which is dropped from the same exact height above ground. this even assumes that the test is conducted over a topological flat ground. Bullets falling to the ground, whether by dropping or firing, are set into motion on a linear path toward the gravitational center of the earth. In this example we can ignore the slight gravitational variations the fired bullet would travel since the increase of gravitational force would be too small to appreciably affect the result. The main issue here is that by firing the bullet we have applied energy to the bullet that has acted on it in contradiction to its original linear path; we have set it on a new linear path. The two will begin to average out, forming a parabola (or bullet drop) over distance, as the two forces work against each other. But, since we have applied energy to the mass in a linear direction different than that of the linear direction of the gravitational energy, we have acted on it, which as Newton so aptly pointed out, will affect its tendency to "stay in motion". The problem with the thought experiment is that of scale. If you step back and look at it from a larger scale, like that of the bullet's relationship to the entire planet (and the spherical curvature of space-time surrounding our planet's gravitational center) it makes more sense. When you fire that bullet, you've essentially set that bullet in motion against that curvature. Satellites are a good example. Ignoring the concepts of "geostationary" as that is not relevant here, this should make sense. The way that a satellite stays in orbit is by getting it up to the desired height and applying a linear momentum to the satellite perpendicular to the earth's gravitational field. In this way, the satellite will want to travel in a straight line, conserving linear momentum, but the earth's gravity will "tether" the satellite as it exerts energy to pull the satellite along its linear path. The result is the two forces fighting each other: The satellite can't fly off into deep space because of the gravitational "tether", and the satellite won't just fall straight to the earth due to its desire to travel in a linear path perpendicular to this other force. If you balance these forces, the satellite maintains orbit. If, however, you launch the same satellite up to the same height and fail to give it any linear momentum contradicting the gravitational attraction of the two bodies, the satellite will simply fall back to earth, following its linear path along the curvature of space-time towards the gravitational center. The bullets are the same way, only on a much smaller scale. Theoretically, if you fired the bullet with sufficient energy as to have equal energy in both perpendicular paths, take out obstacles and drag coefficient, and could theoretically maintain the linear energy by adding additional energy to the fired bullet as it travels, it would essentially orbit the earth at 3 feet from the ground. It's a matter of energy, of which mass is only a portion of the equation. Velocity is the other portion of that equation. I can imagine that if the test were conducted with the use of a 50 caliber bullet or a large rail gun then the time differences would be such that it would be easier to see the differences between a dropping a bullet with no energy or momentum in the perpendicular linear path or dropping a bullet with vast quantities of energy and high velocities in the perpendicular linear path. I'm by no means a physics expert or professor so if my terminology is off then I apologize, but the concept is evident. Perhaps this angle (pun partially intended) is the one that has been overlooked in the thought experiment because it's hard to imagine a tiny bullet in scale to the entire earth and the space-time in which the earth sits and is traveling.

- Michael (age 38)

Greer SC