Kepler’s Laws, Newton’s Laws, and Their Equations – Hello Sinaumed’s ! Have you ever sat outside your house, balcony, or rooftop at night while looking at the night sky? Especially when you are in an area with minimal light pollution and that night, the weather is very bright and not cloudy. surely you will see full of stars scattered, twinkling, and shining beautifully
Apart from being refreshing , looking at the night sky also has many benefits, you know. One of them is for the development of science. An example is Kepler’s 1st law, whose initial discovery came from observing the night sky. For further explanation, let’s look at the following article
KEPLER’S LAW
Kepler’s 1, 2, 3 laws are used to calculate the motions of the planets orbiting the sun and are a supporter of the heliocentric theory. Kepler’s laws emerged after the collapse of the geocentric theory which assumed that planet Earth was the center of the solar system. After that, Nicolaus Copernicus put forward the heliocentric theory which stated that the sun was the main center of the solar system. Earth is just one of the planets that moves around the sun in its orbit. The heliocentric theory became a science that updated the previously developed theory of the motion of the planets.
Actually, the science of astrology or what is often called astronomy has been known to humans since thousands of years ago. The movement of stars and planets is often of concern to sky watchers. Over time and science, models of the universe also developed. There were two theories that were quite popular at that time, namely the geocentric theory and the heliocentric theory.
1. Geocentric Theory (Ptolemaic Theory)
The geocentric theory is a universe theory which states that planet Earth is the center of the universe. As the center of the universe; the sun, stars and other planets move around the earth. This theory was coined by a Greek astrologer, Claudius Ptolemaeus, around 140 AD. This theory is based on direct observation of the motion of the sun, stars and other planets relative to planet Earth.
2. Heliocentric Theory (Copernicus Theory)
The heliocentric theory is considered one of the most important discoveries in the history of astrology. This theory states that the sun is the center of the solar system. This theory, of course, contradicts the previously existing theory, namely the geocentric theory, which states that the earth is the center of the solar system, which means that all objects in the sky move around the earth.
Meanwhile, the heliocentric theory states otherwise. The sun is the center of the solar system and the objects in the sky surround it, including the planet Earth. They circle the sun in a circular orbit. This theory was coined by Copernicus and supported by Galileo Galilei. However, the heliocentric theory was rejected by the church because it contradicted the geocentric theory which had received support from Aristotle.
Also based on this theory, according to the Ministry of Education and Culture’s Learning Resources page, a scientist named Johannes Kepler (1571 – 1639) gave his opinion that the orbit of the planets around the sun is not perfectly spherical. Even so, said Kepler, these orbits tend to have an elliptical or oval shape.
Kepler’s Laws
Kepler’s research on the motion of all the planets around the sun gave rise to the theory of Kepler’s Laws. Kepler has divided the theory into three theories, and also created a formula for them. Here are Kepler’s Laws:
1. Kepler’s First Law
Kepler’s first law states that, “All the planets move in elliptical paths when they revolve around the sun, where the sun is located at one of the foci of the ellipse.”
2. Kepler’s Second Law
The sound of Kepler’s II law states that, “A planet’s orbit around the sun reaches an area of the same triangular area, and with the same period of time.” Based on this law, when the distance of the planet to the sun is getting closer, the motion of the planet’s orbit is also faster. The area of the orbit and the travel time are the same as when the planet is farther from the sun.
3. Kepler’s III Law
The sound of Kepler’s III law states that, “The ratio of the square at the time of the planet’s period to the cube of the planet’s distance to the sun is the same for all planets.”
From this law, the equation formula is also determined, namely:
T1 squared / T2 squared = R1 to the power of 3 / R2 to the power of 3
T1: period of revolution of planet 1
T2: the period of revolution of planet 2 R1: the average distance of planet 1 to the sun
R2: planet 2’s average distance to the sun
Kepler’s laws in modern life are used to estimate the paths of planets or other space objects orbiting the sun. Examples are asteroids and other planets that have not appeared in Kepler’s lifetime. Kepler’s laws can also be applied to calculate the motion of the moon orbiting planet Earth, or other new objects that orbit planet Earth besides the moon.
NEWTON’S LAW OF GRAVITY
Newton’s Law of Gravity is one of the important materials studied in physics. The law of gravity has a scope of discussion in the form of gravitational interactions between two objects at a certain distance.
Gravity doesn’t just have a role to keep every object on earth from being thrown into outer space even though planet earth is rotating on its axis of rotation.
Gravity is also what makes planet Earth and all objects in our solar system move very beautifully and regularly according to their orbit in orbiting the sun.
The force of gravity is also the guardian of the position of the earth and other objects so they don’t fall to the surface of the sun. The laws of gravity govern the movement and circulation of space objects in the solar system so that one object does not collide with another.
Understanding Newton’s Law of Gravity
Newton’s Law of Gravity is a law in physics that discusses the interaction of attraction between two objects that have mass. Two objects that have mass will experience a force of mutual attraction between the two.
The force of attraction between the two objects with mass is what will later be known as the gravitational force between the two objects.
When Sinaumed’s has two apples that are separated by a certain distance, in fact they will also experience a gravitational force that attracts each other between the two.
If the two apples have a gravitational force between one another, why don’t the two fruits stick together for a long time? The answer is simple, because the gravitational attraction between the two apples tends to be so small that the effect is not significant at all.
A more complete explanation will be discussed in the discussion section regarding the following Law of Gravity Formula. In fact, Newton’s Law of Gravity can not only be applied to understand a number of phenomena that exist on planet Earth.
The Law of Gravity can also be used to understand the interaction between two space objects that have mass. For example, to determine the circulation of planets and satellites. For example, like the moon which is a natural satellite of the earth and so on.
History of the Discovery of Newton’s Laws
The discussion on Newton’s Law of Gravity has quite an interesting historical story. According to a number of sources, Newton did not immediately derive or discover the law of gravity which is phenomenal as well as enduring long enough in the study of physics.
Sir Issac Newton, who is a physicist, mathematician, theologian and philosopher, got the inspiration for this theory of gravity when he accidentally fell an apple while sitting under an apple tree.
Driven by curiosity and curiosity, Newton also developed a number of questions and made efforts to find answers to the questions that arose from himself.
He also believes that there is something on earth that not many people know about. It is this thing that makes the apple, which at first is still hanging from the tree, moves and falls to the ground.
Not only that, Newton also developed his realm of thought into a wider scope. Then, he realized that this something should also make the moon in its current position and not move to fall to the earth.
Newton’s Law of Gravity
As with the laws in other physics, Newton’s Law of Gravity also has a sound formula that is important to understand. Newton’s Law of Gravity can be expressed as follows:
Each object that has mass, attracts each other’s masses with inline force and connects the two cores of objects with mass to each other with the magnitude of the attractive force that occurs. The attractive force will be directly proportional to the product of the two masses and inversely proportional to the square of the distance from the two point masses.
So, apart from depending on the masses of the two objects that interact with each other, the magnitude of the gravitational force also depends on the distance that separates the two objects.
That is, the closer the distance between the two objects that have mass, the greater the gravitational force acting on them. The gravitational force is a vector quantity.
In simple terms, a vector quantity is a quantity in physics that has both magnitude and direction. Mathematically, the equation of Newton’s law of gravity on two objects with mass and which are separated by a distance of equal is:
With information in the form of:
F : gravitational force.
G : The magnitude of Newton’s Gravity Constant
M 1 : the mass of the first object.
M 2 : the mass of the second object.
r: the distance between the two objects.
The negative sign (-) in Newton’s law of gravity equation that has been described indicates that the gravitational force that occurs is a force that attracts each other. For two objects that are in a straight line, the direction of action of the gravitational force is along the straight line that connects the two mass points.
Newton’s Law Formulas
Based on Newton’s Law of Gravity formula, we can calculate the gravitational force between two objects that have a known mass and the total distance between them.
F = G x (m1.m2/r sq.)
Newton’s Law of Gravity is very important material to understand because this law of gravity can be expanded and applied to the realm of space, for example to predict the circulation and or period of revolution of a celestial body about the sun.
Newton’s Law of Gravity Equations and Kepler’s Laws
Newton’s Law of Gravity and Kepler’s Laws are very important parts of physics. Kepler’s laws were discovered first, namely in 1571 – 1630 by Johannes Kepler. Johannes Kepler wrote an astronomical work describing the motion of various planets around the sun. Kepler’s discovery is also based on data collected by Tycho Brahe.
Then, Isac Newton researched the gravity of planets based on Kepler’s Laws. To understand these two laws along with the equations of Newton’s Law of Gravity and Kepler’s Law, let’s look at the explanation below.
Before learning more about the equations of Kepler’s Law and Newton’s Law of Gravity, it is better if Sinaumed’s looks back at the two laws. Kepler’s laws discuss the circulation of planets around the sun.
The essence of Kepler’s First Law is that every planetary trajectory around the sun has an eclipse or oval shape and the sun is the focal point. Kepler’s II law states that the area of the line connecting the planets and the sun in the same major difference has the same time as well. Meanwhile, Kepler’s III Law states that the square ratio of a planet’s period around the sun is proportional to the cube of the planet’s distance to the sun.
Meanwhile, Newton’s Law of Gravity is a law that studies the gravitational force between 2 objects. The sound of Newton’s Law of Gravity is as follows: The gravitational force between 2 objects is an attractive force whose magnitude is directly proportional to the mass of the object and inversely proportional to the square of the distance from the two objects.
Newton issued a statement that Kepler’s Laws can be derived from natural laws. Based on Newton’s second law, Kepler’s law can be substituted using centripetal acceleration.
Relationship of Newton’s Law of Gravity and Kepler’s Laws
According to Isaac Newton, mathematically Kepler’s III Law can be related to Newton’s Law regarding universal gravitational forces and also centripetal movement. The formula of Kepler’s III Law is as follows
If Newton’s Law II and the law of centripetal motion are used, then the formula F = mxa is used, where F means the magnitude of the attractive force of attraction of the two objects in units of N and m is the mass of the object in units of kg. Then, it is reduced to the following formula for the universal gravitational force equation.
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Information :
m1 = planetary time
r1 = the average distance between the planet and the sun
v1 = average speed of the planet’s orbit
M = mass of the sun
Final Equation Formula
When the above two equations are combined, it will produce the equation of Kepler’s Law III which sounds like this
Information :
T1 = period (time needed for planet A for one orbit)
T2 = period (time needed for planet B for one orbit)
r1 = distance of planet A from the sun
r2 = distance of planet B from the sun
That’s a summary of Newton’s Law of Gravity equations and Kepler’s Laws. Kepler’s III law can indeed be equated with the force of gravity and the concept of centripetal motion discovered by Sir Isaac Newton. This equation has been proven systematically. Hopefully this review can help Sinaumed’s in understanding the world of physics. Thank you for visiting and hopefully useful.