Is Inertial Motion a Necessary Concept?
All motion in space is potentially orbital - The length of an orbit is absolute - The geometry of matter's structure is kinematic - Displacement by force adds to the orbit
It is such a common experience that thrown objects continue to move after they are released that we tend to forget that neither Newton nor Einstein were able to explain it. Why, for instance, is a batter able to strike a baseball and send it sailing out into center field. On close examination we discover that current physics simply does not account for this phenomenon in real terms.
Modern physics looks upon the law of inertial motion as its basic and fundamental law. The principle is simple: a body left to itself remains at rest, or if it is put into motion it will continue to move in a straight line indefinitely unless interfered with in its movement. To us the concept is perfectly clear, plausible, and even self-evident. It seems obvious that this is the natural behavior of matter. But less than four hundred years ago to nearly everyone the idea seemed not only false, it seemed even absurd. The reason is that pure inertial motion does not occur in nature. It is utterly and absolutely impossible.
The concept of inertial motion dates from the seventeenth century. Until then it was believed that force was necessary for sustained motion. In his studies of trajectories and falling objects Galileo concluded that motion was a state like being at rest, and it was the change of motion that has to be accounted for. Newton then used inertial motion and gravity as a force of attraction to describe the orbital motions of the moon and planets. Einstein in his general theory dispensed with gravity as a force and curved space-time, but he kept Newton's inertial motion.
Newton's worldview consisted of a cosmic image and objects falling due to gravity. What Newton saw in the orchard, therefore, was an apple being pulled to the earth by the attraction of the greater mass. If, however, we think of the earth as a point mass, as Newton had to do for his calculations, the apple would have behaved quite differently.
When the apple dropped from the tree it would not have been stopped in its fall. It would have continued to fall at an ever increasing rate, zoomed past the earth-point at an enormous velocity, continued in its flight on the other side, decelerating as it goes, then stopping momentarily only to fall back again to complete an extremely elongated orbit and return to the tree with no net gain or loss in energy. What Newton saw was only a small slit of this much larger action. The reason the apple fell to the earth was simply because the earth bulged out and got in the way. When an object is thrown, therefore, it does not take on a continuous endless inertial motion. Any object released in space goes into an orbit, or what can be described as potentially an orbit. Any dropped object begins an orbit, and any motion added to it becomes a part of the orbit length. A thrown object adds the length of forced motion across its elongated elliptical fall and widens it on one end. To us it looks like a continuous motion that could go straight if thrown hard enough, but that is a misimpression. No more motion is created or continued than the forced displacement and the spontaneous motion of the fall.
When a batter hits the baseball the ball is propelled against its inertia only for the instant of the hit and the distance it is accelerated. That equation is d = vt, or for the average velocity during acceleration: d = 1/2v2t. To translate this distance to the length it would add to an orbit it is the fraction of the orbital velocity of a circular orbit at that position in the gravitational field: d = v2t/2vo. That is the distance of absolute motion given to the ball.
If that short distance is all that is added to the ball's orbit why then does a slugged baseball take off for center field?
The baseball is propelled against its inertia only for an instant by the bat and then goes into what potentially would be an orbit. Normally, because of geometry being static, we think of distance as metrical and independent of velocity and time. But in kinematic geometry distance is interrelated with velocity and time by the classic equation, d = vt.
Kepler's second law states that for orbiting planets a line connecting the sun and planet sweeps out equal areas in equal times. In other words, in the kinematics of orbits where distances are related to the velocity and time, distances for equal areas are equivalent. Arcs of an orbit are comparable because the distance covered is dependent on the velocity and time.
When the baseball is hit it gains a high velocity in a very short time and distance. That span becomes an arc of the ball's potential orbit. The ball then continues on its orbit, slowing down and taking longer. The distance it covers is considerably greater than when it was accelerated by the hit. Both distances, however, are equivalent by the equation d = vt. Our problem is that we think of the distance to center field in terms of static geometry, when in fact it is an arc that is equal in area swept to that when it was being propelled. As far as the ball is concerned, it is in orbit and nothing more is changing.