Last time we introduced the term acceleration of gravity, a physical phenomenon posited by Sir Isaac Newton in his book Philosophia Naturalis Principia Mathematica. Newton’s Law of Gravitation is also presented in this book. It provides the basis for his mathematical formula to calculate the acceleration of gravity, g, for any heavenly body in the universe.
Newton’s formula to compute the acceleration of gravity is,
g = (G × M) ÷ R2
where, g is the acceleration of gravity, M the mass of the heavenly body, R the radius, and G the universal gravitational constant.
As for the values of the variables in his equation, Newton theorized that G would be a constant, holding the same numerical value throughout the universe. This universal gravitational constant would be the glue that bound together M, the mass of the object being measured, and R, its radius, and render Newton’s formula a workable equation. Without these three values, scientists would be unable to determine the acceleration of gravity rate, g, for the heavenly body under study, and Newton’s equation would be useless, relegated to the depths of pure mathematical theory.
In fact, the value for G wasn’t determined until 1796. At that time Henry Cavendish derived its value as an adjunct to calculating the mass of Earth. In the end he was able to arrive at values for Earth’s mass, M, as well as its radius, R. He also came up with the much needed value for G, the universal gravitational constant. He was able to accomplish so much by building upon the work of other scientists before him.
We’ll see who those earlier scientists were and how they contributed to the world’s discoveries concerning gravity next time.
Archive for September, 2014
Last time we watched a video of Astronauts Scott and Irwin simultaneously dropping a hammer and feather to the surface of the Moon and were amazed to find that the objects struck the surface at exactly the same time. It was history in the making, and Galileo’s theory regarding gravity was proven beyond a shadow of a doubt.
If you watched the video of the event very closely, it might have struck you that the hammer was falling more slowly than it would had it been dropped on Earth, and you’d be right. Let’s find out why.
Sir Isaac Newton was a pioneer in this subject matter. According to his book, Philosophia Naturalis Principia Mathematica, first published in 1687, every heavenly body in the universe, whether it be planet, moon, or star, generates gravity, and any object in freefall towards its surface will be subject to that gravity. He posited that the falling object will gain speed at a constant rate as it falls, that constant speed being dictated by the acceleration of gravity factor that’s at play on the heavenly body it’s falling toward.
For example, if the acceleration due to gravity on a small planet is, say, 2 feet per second per second, after one second of falling, an object’s velocity will be 2 feet per second. After two seconds of falling, the object will have accelerated to a velocity of 4 feet per second. After three seconds, the object’s velocity will have accelerated to 6 feet per second, and so on.
In other words, the speed, or velocity, of the object’s descent will increase for every second it falls closer to the surface of the planet, a phenomenon which is measured in units of feet per second (ft/sec). The acceleration of gravity of a falling object is the linear increase in its velocity that takes place during each succeeding second of its fall, a phenomenon which is measured in feet per second per second (ft/sec2).
Next time we’ll discuss the formula which enables us to calculate gravitational acceleration. We have Sir Isaac to thank for that one, too.
Last time we discussed how Galileo proved Aristotle’s theory regarding the physics of falling objects to be wrong, although his experiment, which took place on the infamous Leaning Tower of Pisa, did not actually prove his own theory to be correct. So why didn’t Galileo go the extra mile and prove his theory? Because he couldn’t.
Galileo, of course, resided on Earth, which was also the arena in which his experiment took place. As such, both he and his experiment were subject to the physical constraints presented by the Earth lab, the single most influential factor being the impact of the planet’s atmosphere upon his falling objects.
Put another way, contrary to popular belief at the time, air is not an empty, innocuous space devoid of physical properties. It’s actually a gaseous soup of molecules. Nitrogen, oxygen, carbon, hydrogen, and other elements are in the mix, and they all have mass, that is, weight within a gravitational field. As Galileo’s balls fell, they continuously bumped against these molecules, which slowed their descent. This air friction will be discussed later in our blog series.
But in order to prove Galileo’s theory correct beyond a shadow of a doubt, the testing arena would need to be one free from the interference of atmosphere. The Moon fits this criterion and provided the perfect environment to prove, once and for all, that Galileo’s theory was correct. So when astronauts Scott and Irwin simultaneously dropped a hammer and feather to the Moon’s surface, both objects hit at precisely the same moment. Watch this captured live footage of the event to see for yourself:
One thing you may have noticed while watching the astronauts’ experiment is that the hammer fell more slowly than it would have on Earth. This has nothing to do with the absence of atmosphere on the Moon, but it has everything to do with gravity. We’ll discuss gravity’s influence in detail next time.
Picture yourself holding a feather in one hand, a hammer in the other. Your buddy has bet you that if you simultaneously drop them, the hammer will hit the ground first, and he’s got a beer riding on it.
This exact experiment was performed in 1971 by Apollo 15 Astronauts David Scott and Jim Irwin when they landed on the moon. We’ll tell you how it turned out later, but first let’s review the history behind the study of falling objects.
Aristotle, the ancient Greek philosopher, would have bet with your buddy. Back in the 4th Century BC he developed a theory of gravity to explain the physics behind falling objects. He asserted that the heavier the object, the faster it will fall. His theory seems intuitively obvious on its face, but although Aristotle was a great philosopher, he was a lousy scientist. He never ran tests to actually prove his theory. Nevertheless, it was accepted by academics of his time, and it remained the theory of choice until Galileo came along in the 16th Century.
Galileo was a scientist, and he came up with his own theory concerning falling objects. He believed that all falling objects continue to accelerate, picking up speed as they fall, and that this rate of acceleration is the same for all objects, regardless of their weight or density.
The story goes that in 1589, at the age of 25, young Galileo attempted to prove his theory by climbing to the top of the Leaning Tower of Pisa with two balls in hand, one large and heavy, the other small and light. He dropped them at the same time, and guess what happened?
Both balls hit the ground at almost the same time. They would have hit the ground at precisely the same moment had there been no air resistance, a subject which will be discussed at length later in this blog series.
Because Galileo’s experiment was subject to the dense atmosphere of Earth, the influence of air resistance prevented him from proving his theory correct, however he did manage to prove Aristotle’s theory wrong because the balls did not strike the ground at significantly different times.
We’ll see how the astronauts’ experiment turned out next time.