As Galileo had discovered, heavy objects and light objects fall to the ground at the same rate, provided there is little air resistance. Near the surface of the earth, free-falling objects accelerate at a nearly constant rate of approximately 9.8m/s2. In other words, the velocity of a free-falling object increases by 9.8 m/s every second. This gravitational acceleration is often denoted with the lowercase letter “g”: g = 9.8m/s2
However, this value only holds for free-falling objects near the surface of the earth. Gravitational acceleration near the surface of the moon is much slower: about 1.6 m/s2, because the moon’s gravity is weaker than the earth’s gravity.
Recall from the previous page that mass and weight are not the same thing. Weight is the force of gravity exerted on an object, and it varies depending on the object’s location. If we know the gravitational acceleration near the surface of a planet or moon, we can calculate the weight of an object at that location using Newton’s second law of motion:
So, a 10 kg rock weighs 98 newtons when located near the earth’s surface. Near the surface of the moon, however, the pull of gravity is only strong enough to accelerate objects at 1.6m/s2. So, a 10 kg rock weighs only 16 newtons near the moon’s surface:
In this video, a feather and a bowling ball fall side-by-side in a huge vacuum chamber used for testing spaceships.
Above, I mentioned that free-falling objects accelerate at a nearly constant rate close to the earth’s surface. However, acceleration due to gravity isn’t perfectly constant, for two reasons. First, the strength of gravity weakens with distance, as we’ll see on the next page. This means gravitational acceleration is slower at high altitudes than it is near Earth’s surface. Second, and more obviously, air resistance produces an upward force that opposes the downward force of gravity. This upward force is usually negligible for dense objects (like rocks) falling short distances, but it makes a noticeable difference for low-density objects (like feathers). Moreover, even dense objects like rocks will experience significant air resistance when falling long distances.
As an object falls through the air, the force of air resistance increases as the velocity increases, reducing the rate of acceleration until eventually the downward force of gravity is exactly matched by the upward force of air resistance. At that point, the object continues to fall at a constant velocity called its terminal velocity. That’s why a feather falls more slowly than a rock: it quickly reaches terminal velocity, because it has a large surface area relative to its weight. In a vacuum (with no air resistance), a rock and a feather would fall at the same rate, as demonstrated in the video above.
What would happen if raindrops fell with no air resistance? Cumulonimbus clouds—storm clouds—typically form between 2,000 and 16,000 meters, sometimes much higher. So, how fast would a raindrop be moving if it fell from (say) 10,000 meters without air resistance? First, let’s figure out how long it takes for the raindrop to reach the ground:
Thanks to air resistance, fortunately, the terminal velocity of raindrops is in fact much lower—about 9 m/s (20 miles per hour) for the largest and fastest raindrops. Large hailstones fall slightly faster, with a terminal velocity of about 20 m/s (44 miles per hour).
But why do heavy objects and light ones fall at the same rate? Why do they fall at all? As we saw in the previous chapter, Galileo effectively refuted Aristotle’s theory of gravity, but he proposed no alternative in its stead. In what follows, we’ll see how Newton was able to explain Galileo’s observations.