Special relativity is relevant when it comes to steady-state motion, where observers are in an inertial frame of reference. Next, we will learn about gravity and come to understand the effects accelerated motion and gravity have on time and space. We will come to see that special relativity, as the name implies, is just a specific point encompassed within a broader, “general” theory of relativity.
In a gravitational field, objects dropped from the same height will accelerate to the ground at the same rate. What makes understanding this problematic is contending with air resistance. This is why a hammer falls directly to the earth whereas a feather takes more time to float down. When air resistance is excluded, however, as in the case of the Apollo 15 astronauts, the feather and the hammer arrived at the ground simultaneously. Of course, Galileo had already established the simultaneity of free fall. Russell Stannard summarizes this thus: “If an object is placed at a given point in space and given an initial velocity there, its subsequent motion is independent of its internal structure or composition, provided it is subject only to gravitational forces.”
Mathematically, this can be represented F = mGg here mG refers to a body’s gravitational mass. Keep in mind that in the Newtonian approximation, force is defined as mIa, where a is the acceleration and mI refers to the inertial mass of the object. This is a measure of the inertia of an object insoar as it responds to forces. Getting rid of F from both equations leaves us with mGg = mIa.
Suppose you drop a hammer and a feather in a lift. This lift is a reference frame that can be accelerated vertically. Right when you drop the objects, the lift’s cable is severed so that it begins to fall. Their relative positions would not change. The observer in the lift would perceive the feather and the hammer remaining where they were relative to himself. They would not hit the floor. Gravity would appear to have been turned off and the contents would appear to be weightless.
Most people associate weightlessness with space. They tend to believe that they are weightless because they are beyond the pull of gravity of the earth and sun. This is not true. The astronauts can experience weightlessness even as the ship orbits around the earth. This weightlessness obtains because the craft is in a state of free fall thanks to earth’s gravity. Russell Stannard elaborates:
“The reason the craft does not crash down on the surface of the earth is because the earth’s gravitational attraction is all being used up simply converting normal straight line motion into the orbital motion we observe; there is none left over, so to speak, to pull the astronaut down on to the earth’s surface. Hence the astronaut appears to ‘float weightless’ around the orbit.”