Perceptual acceleration: Galilean dynamics

Kepler's three laws of planetary motion not only supported Copernicus' heliocentric theory, but also inspired Newton to discover the law of gravity decades later.

However, for Newton to discover gravity, it was not enough to have Kepler's three laws, but he also needed his own three laws. Newton's three laws were due in part to his own ingenuity and in part to Galileo's discoveries.

So, what did Galileo actually discover? We usually say that he invented the telescope and then used it to discover the craters on the moon and the black seeds in the sun, and also the four moons of Jupiter and the rings of Saturn, which are his discoveries in astronomy. More importantly, Galileo started the experimental tradition of modern science, and used experiments to initially establish the modern mechanics system.

Newton's first law was actually discovered by Galileo. This law holds that any object in a state of no force remains at rest or in uniform motion. This discovery was so important that Newton listed it as the first law of mechanics, also known as the law of inertia, the origin of the name is obviously related to the inertia of an object remaining at rest or at uniform speed without force.

Why is this law important?

First, it overturns Aristotle's understanding. Aristotle believed that for an object to maintain uniform motion, it must be constantly propelled by forces. Of course, we have to forgive Aristotle, after all, the resistance of air could not be excluded in the time he lived. An object moving in the air will be subject to resistance, so in order to keep the object moving, we have to use another force to counteract the air resistance. Similarly, when we ride a bike or drive a car, we need to constantly counteract the resistance from the ground and the air, so we need to apply force to the bike and car.

Galileo's law of inertia is usually demonstrated in the laboratory: in a very long smooth plate on a ball of iron, the plate downward slope, the ball began to roll under the action of gravity; when we keep the smooth plate lengthening, the slope becomes smaller, the ball remains in motion. And modern technology helps us to do a better experimental demonstration: let an object move in a vacuum tube, it will be able to perfectly demonstrate the law of inertia.

Galileo's law of inertia experiment

Perceptual acceleration: Galilean dynamics

Second, the law of inertia helped Galileo to establish the concept of inertial system. The inertial system is a reference system in which the law of inertia holds. Obviously, the ground is a good inertial system, because we can do experiments on the ground to verify the law of inertia. Likewise, a high speed train, airplane or ship in uniform motion is an inertial system. Galileo added one more principle to the law of inertia - the principle of inertia, that is, all inertial systems look the same, there is no difference. The principle of inertia is very important. For example, if someone moves your bedroom to a huge flying machine, no matter how fast this vehicle, as long as it is uniform speed, you in the bedroom can not feel whether the vehicle is flying.

Look at another situation, when the car brakes, the speed of the car is getting smaller, at this time sitting in the car you will feel a forward pushing force. This shows that if a reference system is not in uniform motion, we will soon feel the force on ourselves.

Experiment on the law of inertia in non-uniform motion

Perceptual acceleration: Galilean dynamics

Newton was able to discover the law of gravity, in addition to the help of Kepler's three laws, but also the help of Galileo, what is this help? Is Galileo's research on gravity. About this research, many people have heard of the Leaning Tower of Pisa experiment.

Perceptual acceleration: Galilean dynamics

Regarding the Leaning Tower of Pisa experiment, the popular version is this: Galileo believed that the object falls faster or slower under the action of the Earth's gravity independent of its mass. In order to convince all opponents, one day in 1589, Galileo, a young mathematics lecturer at the University of Pisa, aged 25, went to the Leaning Tower of Pisa together with his debate opponents and many others. Galileo climbed to the top of the tower and threw an iron ball weighing 100 pounds and one pound at the same time. In full view of the public, the two iron balls unexpectedly fell to the ground almost simultaneously. Faced with the results of this experiment, the people watching the audience were dumbfounded and overwhelmed. The story sounded perfect, but later the story was questioned by many people. Some people went to the Leaning Tower of Pisa to do the same experiment, the results found that the mass of the iron ball fell to the ground first. Is the famous law that the acceleration of gravity is independent of the mass of an object wrong? Of course not. Very simple, the heavy iron ball first, because in the air, the heavy iron ball and light iron ball in addition to gravity is also subject to air resistance, and the iron ball by the air resistance is not proportional to the mass, so the heavy iron ball first to the ground.

A more modern and better understood gravity experiment is to put a small iron ball and a feather in a vacuum glass tube, and then invert the glass tube, we will see the feather and the iron ball fall from the top of the glass tube to the bottom at the same time.

So, is the story of the Leaning Tower of Pisa experiment true or false? In fact, the story was told by Galileo's student Viviani. Viviani mentioned in his book "Galileo" that he had heard that Galileo had done several similar experiments from the highest level of the Leaning Tower of Pisa in the presence of other professors, philosophers and all students. Thus, it seems that Viviani also heard from others, which shows that the story is more of a blackmail.

In any case, Galileo discovered that the acceleration of gravity downward is the same for all objects under the action of the Earth's gravity. Today we know that this acceleration of gravity is about 9.8 m / s 2. That is, after 1 second, the speed of a falling object will increase by 9.8 m / s.

This discovery, together with the law of inertia, allowed Galileo to discover that the trajectory of a thrown object is parabolic. It should be noted that although the ancient Greeks studied the parabola, the original word "parabola" parabolè does not mean "throw", but "to intercept with a plane". because the parabola, like the ellipse, is also one of the conic curves. After Galileo discovered that the trajectory of the thrown object is a parabola, the translation term "parabola" appeared in Chinese.

How did Galileo discover that the trajectory of a thrown object is parabolic? A thrown object has a constant velocity in the horizontal direction because the object is not subject to force in the horizontal direction (in the case of neglecting air resistance). Since this is the case, the distance the bullet flies is proportional to its flight time. However, the bullet is subject to gravity in the direction perpendicular to the ground and will accelerate to fall to the ground, so the distance the bullet falls in the vertical direction is proportional to the square of time. In this way, Galileo discovered the parabola.

When we talked about Kepler, we mentioned that Galileo was a contemporary of Kepler. In fact, Galileo was seven years older than Kepler, who was born in 1571 and Galileo in 1564. Kepler published the first two laws of the planets in 1609, when Galileo had just built his telescope and discovered the moon craters and many other astronomical phenomena the following year.

Before the manufacture of the telescope, Galileo discovered the law of inertia and the principle of inertia long before. Before the age of 30, Galileo also studied free-fall motion, parabolic motion, as well as statics and some architectural aspects.

In addition to mechanics and astronomy, Galileo made many other discoveries, for example, he believed that the speed of light was finite and also tried to measure the speed of light. However, the speed of light was so fast that his measurements ended in failure. He invented the thermometer, and used the principle of buoyancy to invent a buoyancy balance to measure the proportion of gold and silver in jewelry. He also discovered the principle of single pendulum (this principle is related to gravity), and later this principle became one of the principles for making mechanical clocks.

Galileo laid the methodological foundation of modern science, and at the same time, his important discoveries laid the foundation of modern mechanics. It can be said that Galileo is the progenitor of modern science.

When modern science rose to prominence, it was inevitably in conflict with religion because discoveries such as heliocentrism, sunspots, and lunar craters were contrary to the theories of the traditional church. The Holy See had imprisoned Galileo for his belief in and propagation of heliocentrism.

Nikkei says

Perceptual acceleration: Galilean dynamics

The conflict between the founder of modern science and the Church was reconciled more than 300 years after his death: in 1979, Pope Paul II of the Vatican, on behalf of the Holy See, publicly vindicated Galileo, considering that the persecution of him by the Holy See more than 300 years ago was a grave error