How many Earth years does it take for Jupiter to revolve around the Sun if it is approx.

km away from the Sun?

In previous lesson, you have learned how Johannes Kepler used Tycho Brahe’s extensive astronomical data to come up with the three
laws of planetary motion.

While Kepler’s laws have successfully described the distance and period of planet’s orbits, Isaac Newton deepened the laws by
integrating his law of universal gravitation. This is highly evident in his derivation of Kepler’s third law, which, not only describes the
planets discovered during Kepler’s time but predicts the motion of most planets and local bodies orbiting the Sun that were discovered
thereafter.

Key Points
• According to Newton, Kepler’s third law of planetary motion not only describes the planets discovered during Kepler’s time but
predicts the motion of most planets and local bodies orbiting the Sun that were discovered thereafter.
• The farther the body is from the Sun, the longer it will take complete its orbit.

Aristotelian Conceptions: Vertical Motion, Horizontal Motion, and Projectile Motion

Aristotle is one of most influential Greek philosophers whose ideas were the basis for many concepts that time. How
did he view and explain the motion of objects?
Aristotle’s view on motion was based on his observations, which made his ideas acceptable and stood for many years.
Motion is an object’s change in position with respect to time. According to Aristotle, motion can either be a natural motion or a violent
motion.

Natural Motion
An object will move and will eventually return to its natural state depending on the composition that the object is made of. An object
made of material similar to earth will return to earth or an object that is similar to air will return to the air. For example, a ball mostly
resembles the earth so when it is thrown upward its natural tendency is to go back to Earth, its natural state or the smoke mostly
resembles the air so its natural tendency is to go up the atmosphere.

Violent motion
An object will move if an external force such as pushing or pulling is applied to it. No motion will take place unless there is a 'mover' in
contact with an object.

Aristotle’s View on Projectile Motion

Aristotle believed that the motion of an object is parallel to the ground until it is the object's time to fall back into the ground. An impetus
will be kept by the object until such time that the initial force is forgotten, and the object returns to its natural state to stop moving and
fall to the ground.
Example
A cannon is fired which give the cannonball an impetus that will dictate its course until such time that the impetus is forgotten, and the
cannonball will naturally fall to the ground.
Key Points
• According to Aristotle, motion can either be a natural motion or a violent motion.

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 • An object will move and will eventually return to its natural state depending on the composition that the object is made of. This
referred as the natural motion of an object.
• An object will move if an external force such as pushing or pulling is applied to it. This is referred as the violent motion of an
object.
• The motion of an object is parallel to the ground until it is the object's time to fall back into the ground. This is referred as the
projectile motion of an object.

Galilean Conceptions: Vertical Motion, Horizontal Motion, and Projectile Motion Why
do objects move?
Scientists and philosophers alike have been trying to answer this question even before 300 B.C. One of the well-known philosophers
who attempted to do this was Aristotle. His attempt was based on inductive-deductive reasoning and was accepted for centuries.
However, Galileo Galilei challenged the Aristotelian view of motion when he had his actual and thorough experiments. He disagreed
with most of Aristotle’s claims and provided his own description of motion.

Galilean Conceptions vs. Aristotelian Conceptions

According to Aristotle, motion can be either natural or violent motion. In a natural motion, the object will move and will return to its
natural state based on the object's material or composition. In contrast, an object moving in a violent motion requires an external force
(push or pull) for the object to move.

He also had his view on the projectile motion of an object. He believed that an object thrown at a certain angle is given an impetus—
a force or energy that permits an object to move. It will continue to move in such state until the object’s impetus is lost, and the object
returns to its natural state, causing it to stop and fall to the ground.

Galileo disproved Aristotle’s claims and believed that the motion of objects is not simply due to the composition of objects. He
mentioned that motion can be described by mathematics and the changes in some physical variables such as time and distance. Using
his actual and thorough experiments, he was able to prove that:

1. an object in uniform motion will travel a distance that is proportional to the time it will take to travel;
2. a uniformly accelerating object will travel at a speed proportional to some factor of time; and
3. an object in motion, if unimpeded, will continue to be in motion; an external force is not necessary to maintain the motion.

Galileo's Conceptions of Motion

Horizontal motion
An object in motion, if unimpeded, will continue to be in motion, and an external force is not necessary to maintain the motion. If the
Earth’s surface is very flat and extended infinitely, objects that are pushed will not be impeded. Thus, the objects will continue to move.
This kind of motion, however, is not evident in nature. For example, if a ball is pushed on an infinitely flat plane, the ball will continue to
roll if unimpeded.

Vertical motion
In the absence of a resistance, objects would fall not depending on their weight, but in the time of fall. Also, if the object encountered a
resistive force from a fluid equal or greater than its weight, it will slow down and reaches a uniform motion until it reaches the bottom
and stops. For example, without any resistance, a 1-kg object will be as fast as a 10-kg object when falling because they fall with the
same amount of time, given that they are released from the same height. Also, a stone dropped in the ocean will sooner or later travel
at constant speed.

Projectile motion
Galileo believed that a projectile is a combination of uniform motion in the horizontal direction and uniformly accelerated motion in the
vertical direction. If it is not impeded, it will continue to move even without an applied force. For example, when you shoot a ball in a
basketball ring, the ball does not need a force to keep it moving.

Key Points
• Galileo believed that an object in uniform motion will travel a distance that is proportional to the time it took to travel; a
uniformly accelerating object will travel with a speed proportional to some factor of time; and an object in motion, if unimpeded,
will continue to be in motion; an external force is not necessary to maintain the motion.

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 • Galileo believed that a projectile is a combination of uniform motion in the horizontal direction and uniformly accelerated
motion in the vertical direction.

How Galileo Inferred That Objects in Vacuum Fall with Uniform Acceleration
Recall that a body moving with uniform acceleration changes its speed by a constant value per unit of time.

Imagine yourself holding a bowling ball and a ping pong ball. If you drop these balls simultaneously, which ball do you think
would have greater acceleration upon reaching the ground? Why?
Galileo proved with his experiments that when objects are dropped simultaneously, they will reach the ground at the same time
regardless of their masses and air resistance. In another set of experiments, he discovered that objects fall with uniform acceleration.

Galileo was fascinated by the behavior of falling objects. He knew that falling objects increase their speed as they go down. This
change in speed is acceleration. However, he did not have any equipment to measure this change, so he used inclined planes to lessen
the acceleration of the moving bodies. He was then able to investigate the moving bodies carefully.

On his experiment, he had observed the following:

• A ball rolling down an inclined plane increases its speed by the same value after every second. For example, the speed of a
rolling ball was found to increase by 2 m/s every second. This means that the rolling ball would have the following speeds for
every given second

• As the inclined plane becomes steeper, the acceleration of the rolling ball increases.
• The maximum acceleration of the rolling ball was reached when the inclined plane was positioned vertically as if the ball is
simply falling
These observations lead Galileo to conclude that regardless of the mass of objects and air resistance, falling objects would always have
uniform acceleration.

Key Points
• A body with uniform acceleration changes its speed by a constant value.
• Galileo proved that when objects are released simultaneously from a certain height, they reach the ground at the same time,
regardless of their masses and air resistance.
• Galileo discovered that all objects fall with the uniform acceleration in vacuum.

The Position vs. Time and Velocity vs. Time Graphs of Constant Velocity Motion Recall
the following terms of the basic quantities that describe motion.
• Distance is the total length or ground covered by an object.
• Displacement is the change in the position of an object or the shortest distance between the initial and the final position of an
object .
• Speed is how fast the object is moving and can be calculated by dividing the total distance by the total time spent to cover that
distance.
• Velocity is how fast and where the object is moving and can be calculated by dividing the displacement of an object to the
time spent.
• Acceleration is the change in the velocity of an object per unit time. An object accelerates when there is a change in the
object’s speed, direction, or both speed and direction.

An object is said to be in motion when its position changes relative to a reference point, usually the ground. The motion of an object can
be described in different ways; it can be described using distance, displacement, speed, velocity, and acceleration.

Motion can also be presented graphically like the position vs. time and velocity vs. time graphs which show the type of motion an object
undergoes in a unit of time.

Key Points
• The position vs. time graph of a body moving with constant velocity is a straight line that slants to the right and has a
constant slope that corresponds to the body’s constant velocity.
• The velocity vs. time graph of a body moving with constant velocity is a flat line and has a zero slope which means the body
is not accelerating.
• The velocity vs. time graph of a body moving with constant acceleration is a straight line slanting to the right and has a
constant value for its slope which corresponds to the body’s constant acceleration.

Acceleration in Physics
When does an object accelerate? Does the term only refer to fast-moving objects?
Acceleration in everyday usage
In everyday terms, acceleration refers to objects which are moving so fast. This is demonstrated in a speeding race car or a runner who
accelerates to finish a short sprint. On the other hand, a race car that suddenly slows down or a runner who accidentally stumbles is not
accelerating.
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Acceleration in physics
In physics, an object that moves fast may not be accelerating. Also, an object that moves slowly may be accelerating.
Acceleration is the rate at which an object’s velocity changes. Velocity is the rate at which an object changes position. Acceleration
indicates how fast an object changes its velocity. Just like velocity, it is a vector quantity, which means it has both magnitude and
direction. Magnitude refers to the amount or size of a quantity. For example, 3 m/s.
An object accelerates when its velocity changes in magnitude, direction, or both magnitude and direction.
Example
The car in the following situations is accelerating.

A. When the traffic light turned green, the car sped up from 0 km/hr to 20 km/hr.

B. When the driver saw the pedestrian, the car slowed down from 20 km/hr to 0.

C. The driver turned the car to the right while maintaining his speed of 40 km/hr.

In situation A, the car is accelerating because the magnitude of the car’s velocity changed. It increased from 0 km/hr to 20 km/hr.

In situation B, where the car decreased its velocity from 20 km/hr to 0 is accelerating because there is a change in the magnitude of its
velocity. It accelerates even if it went slower and eventually stopped.

An object which maintains a constant magnitude of velocity but changes direction is accelerating. This can be seen in situation
C where the driver was initially going 40 km/hr forward and turned 40 km/hr to the right. The car accelerates because there is a change
in its velocity’s direction.

An object that goes from 40 km/hr eastward to 20 km/hr southward accelerates because there is a change in its velocity’s magnitude
and direction.

Objects that move in uniform circular motion have constant speeds but still accelerate because they constantly change in direction as
they go around the circular path.
Satellites orbiting the Earth maintain a nearly circular orbit and travel very fast at an almost constant speed like the International Space
Station which moves at approximately 27 000 km/hr. Even though these satellites have constant speeds, they are accelerating because
they constantly change direction as they move in a circular path around the Earth.

Key Points

• In everyday usage, acceleration refers to fast moving objects such as a speeding race car.
• In physics, acceleration is the rate of change in an object’s velocity.
• An object accelerates when there is a change in its velocity – which means there could either be a change in its magnitude,
direction, or both magnitude and direction.

The Three Laws of Motion

The systematical study of motion started way back from the ancient civilizations when they started observing and predicting the motion
of stars, planets, and other celestial bodies. Aristotle stated that motion can be classified as ‘natural’ and ‘violent’ motion.
Natural motion can be observed in nature, such as falling of leaves while violent motion is one that is unnatural and instigated by
other factors. For example, it is natural for a rock to roll down the hill, but in order for the rock to move up the hill, someone or
something must push it upward.

After a couple of millennia, several more scientific studies about motion has been made.

Sir Isaac Newton in 1687 published his book entitled Philosophiae Naturalis Principia Mathematica (The Mathematical Principles of
Natural Philosophy) which contains his treatise on motion and the three laws of motion.

The laws of motion are useful ways of thinking about the motion of everyday objects. Though considered as a scientific law, it still has
limitations.

The laws of motion are valid when the objects we are analyzing are not travelling at the speed of light nor the object is too small.

Inertia is the existing state of matter, whether at rest or in uniform motion in a straight line unless a net external force is applied to
change its state. It is the tendency of an object to resist changes in its state of motion.
1st Law: The Law of Inertia
An object at rest or in motion will stay at rest or in motion with constant velocity unless acted upon by a net external force.
According to this law, an object at rest will remain at rest unless you push or pull them with enough net force.
For instance, when a book is at rest on the table several forces act on it: the downward force exerted by gravity and the upward or
normal force exerted by the table on the book. When we say net force, the sum of all the forces acting on the object is equal
to zero thus, it is at rest or there is no change in its speed. In the case of the book, the downward and normal force are of the same
magnitude but opposite in direction that is why they add up to zero.
The same is true for objects that are moving. If no net force acts on a moving object, then it will neither increase nor decrease its speed.
Therefore, it will continue to move with constant speed in a straight line.
For instance, why do we move forward when the driver steps on the brakes after moving at a constant speed in a straight line? When
the car moves, our body moves with it. Based on the first law, in the absence of a net force, an object will move at a constant speed.
When net external force is applied, in this case, when the driver steps on the brakes, then there is a change in the velocity of the car;
however, because of inertia, our body tends to stay in motion that is why our body moves forward involuntarily.

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On the other hand, when we are on a car that is at rest, our body is also at rest. When a net external force is applied to the car that
starts the car moving, our body tends to stay at rest that is why our body moves backwards involuntarily.
Inertia and Mass
An object’s inertia depends on its mass. Mass is the amount of matter in an object. It is a quantity that only depends on the inertia of an
object. This implies that heavier objects are harder to move or when it is already moving, it is hard to stop. Simply put, the greater the
mass, the greater the amount of inertia.

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Key Points
• Sir Isaac Newton in 1687 published his book entitled Philosophiae Naturalis Principia Mathematica which contains his treatise
on motion and the three laws of motion.
• The first law of motion states that an object at rest or in motion will stay at rest or in motion with constant velocity unless
acted upon by a net external force.
• The second law of motion states that the acceleration of an object is directly proportional to the force exerted on the object
and inversely proportional to the mass of the object.
• The third law of motion states that when an object exerts a force on another object, the second object exerts an equal and
opposite force to the first object.

Newton’s Law of Inertia vs. Galileo’s Assertion on Horizontal Motion

Before Isaac Newton came up with his laws of motion, a lot of scientists have laid the foundation for the study of force and motion. One
of these scientists was Galileo Galilei.
Who was Galileo Galilei? What were his contributions to the concept of inertia?

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Is there a difference between Galileo’s assertion and Newton’s first law of motion?

There is a subtle difference. The difference lies in the concept of force. Galileo knew about friction but did not know about the concept of
force. He used the term 'push and pull' to signify forces. It was Sir Isaac Newton who defined the concept of force and its relation to
motion.
Key Points

• The concept of inertia was a result of Galileo’s studies of motion.

• Inertia refers to the tendency of any material to change its state of motion.
• Galileo asserted that if a rolling ball was ‘left alone’ it will continue to move with constant velocity.
• The only difference between Galileo’s assertion and Newton’s first law of motion is the concept of force.
• Galileo did not know yet the concept of force, and it was Newton who finally explains the nature of forces.
Newton’s Second Law of Motion and Newton’s Law of Universal Gravitation: Identica l Acceleration

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Key Points

Newton’s Law and Kepler’s Laws of Planetary Motion

Think about chess and checker
s. If you are familiar with these two games, then you certainly know the rules of these games.
Now think about this:
Do the set of rules of chess applicable to checkers and vice-versa?
If you have answered no, then you are correct. The rules of these games are unique from one another, the same way Newton’s laws
and Kepler’s Laws are unique. So how are they related?

There are many scientific laws that describe movements of objects. Newton’s laws of motion generally describe the motion of bodies
ranging from tiny objects, such as a speck of dust, to very large objects, such as stars. On the other hand, Kepler’s laws of planetary
motion specifically describe the motion of orbiting planets. Both of these laws describe the motion of objects, but how are they related?

Laws, Axioms, and Empirical Laws

Scientific laws, like Newton’s laws and Kepler’s laws, are descriptions of an observed occurrence. Unlike theories, laws do not explain
the cause of the observed phenomenon or why it happens. In science, we can say that laws are the ‘rules of the game’ followed by all
things in our world.
Laws can be considered as axioms or empirical laws. An axiom, in Mathematics, is a well-established statement. Just like in the game
of chess and checkers, the set of rules are already established and we just accept it to be true or the proper way of playing this game
even without proving that they are the ‘proper way’ to play the game. An axiom, although accepted and taken to be true, remains
unprovable.

Empirical laws, on the other hand, are descriptions supported by factual observations and are not derived from existing laws.

Newton’s Laws of Motion and Kepler’s Planetary Motion

Newton’s laws of motion are considered to be axioms. The three laws of motion are actually unproven and unprovable but we accept
them to be true. They provide useful ways of thinking for us to understand the motion of the objects around us.
Let us consider the first law of motion:
An object at rest remains at rest and an object in motion remains in motion remains in motion in with constant velocity unless acted
upon by an external, unbalanced force.
Can you identify any situation in which this ‘law’ holds true?
If you have made assumptions first before giving an example, then that is the first sign that this is an axiom. An axiom holds true only
within the context that they are applied. Therefore, we can say that the Newton’s laws of motion are axioms because they hold true only
when assumptions are established.
On the other hand, Kepler’s laws of planetary motion are empirical laws because they are based on his observation and computation
of planetary movements; it is not derived from any existing law and is evidence-based descriptions.
Let us look at the first law of planetary motion by Johannes Kepler: Each
planet moves on an ellipse with the Sun at one focus.
Do you think you have to make assumptions about this ‘law’ to be true?
If you have answered no, then you are correct. As an empirical law, we can directly observe and gather physical evidence that this law
is true.

Tips
To differentiate between axioms and empirical laws, you need to remember that axioms are accepted truths but they are unproven and
unprovable while empirical laws are based on factual observation and evidence.
Key Points

• Scientific laws describe a certain phenomenon without explaining why they occur or what causes their occurrence.
• An axiom is a statement that is accepted to be true but remains unproven or unprovable.
• Axioms hold true only when assumptions are made.
• An empirical law is based on factual observations and evidence.
• Newton’s laws of motion and Kepler’s laws of planetary motion are both scientific laws that describe motion.
• Newton’s laws are axiom because they are unproven and unprovable and holds true only when assumptions are made.
• Kepler’s laws of planetary motion are empirical laws because they are based on observation and evidence.

The Law of Conservation of Momentum

Mass is the measure of inertia of an object which is at rest. That is, the greater the mass of the object, the greater is its tendency to stay
at rest (or it is harder to get it moving). Whereas, momentum is the measure of inertia of moving objects. That is, the greater the
momentum (or the faster the object moves) the greater is its tendency to stay moving (or it is harder to stop).

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Tips
• If the object is at rest, its momentum is zero.
• To check your answer, add the momentum after and before collision. If they are equal you are most likely correct, if not go
back and check your solution. Key Points

Mass, Momentum, and Energy Conservation

Mass, momentum, and energy are three quantities that can be conserved. In Physics, when we say a quantity is conserved, it means
that after an interaction or a reaction, no part of that quantity is lost.

Law of Conservation of Mass

The law of conservation of mass states that mass in an enclosed system is neither created nor destroyed by a chemical reaction.
Thus, in a chemical reaction, the mass of the reactants must be equal to the mass of the products.

Below are the people who had contributed to the understanding of mass and its conservation.

• Ancient Greek philosophers believed that 'nothing comes from nothing' which implied that everything in the present had
come from an origin.
• Nasir al-Din al-Tusi was a Persian polymath who wrote that a body of matter could not disappear completely. It could only
change its form, condition, and other properties. These changes could turn it into a different form of matter.
• Mikhail Lomonosov was a Russian writer and polymath who disproved the phlogiston theory, which assumed that matter
contained phlogiston— a fire-like substance that existed in combustible materials. He showed in an experiment of burning
metals that the mass of metals remained the same after burning.
• Antoine Lavoisier proposed the law of conservation of mass. This law states that in a chemical reaction, the total mass of the
products is always equal to the total mass of the reactants; and atoms are neither created nor destroyed, but rearranged to
form new substances.

Law of Conservation of Energy

The law of conservation of energy states that energy cannot be created or destroyed. It can only be transformed from one form to
another. Hence, the total energy of an isolated system never change.

Below are some of the scientists who had contributed to the development of the law of conservation of energy.
• Galileo Galilei was an Italian astronomer and physicist who studied an 'interrupted pendulum. His experiment showed that the
energy was conserved in the pendulum causing it to swing to the same height as it was released. If energy was not conserved,

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 it would have stopped and have not completed its swing. In a modern sense, he demonstrated that kinetic energy can be
converted to potential energy and vice versa.
• Christian Huygens was a Dutch mathematician who published his laws of collisions. He noted that the kinetic energies of
colliding objects were the same before and after the collision.
• Gottfried Wilhelm Leibniz was a German polymath and philosopher who used Huygen's work on collision to derive a
mathematical formulation for energy that is related to motion (kinetic energy). It is called vis vivawhich is the Latin word for
'living force' and represented as mv2.
• Émilie du Châtelet performed experiments where she dropped a ball into soft clay at different heights. She learned that the
ball's kinetic energy was proportional to the square of its velocity, and the deformation on the clay was proportional to its initial
potential energy. She then proposed that energy is different from momentum.
• Albert Einstein developed a theory that united the concepts of mass and energy. Einstein’s energy-mass equivalence implies
that neither mass nor energy are separately conserved, but they could be interchanged. The total ‘mass-energy’ of the
universe is conserved.

Law of Conservation of Momentum

Just as mass and energy are conserved, momentum is also conserved. The law of conservation of momentum states that the total
momentum of an object does not change (i.e it remains at rest or in motion with constant velocity) if there are no external forces acting
on it.

Below is a list of scientists who have contributed to the development of the law of conservation of momentum.
• Jean Buridan was a teacher and philosopher who first used the term ‘impetus’ to signify the notion of momentum. According
to his theory, an impetus set an object in motion, and it increases as the object's speed also increases.
• Rene Descartes was a French philosopher and mathematician who proposed that the total 'quantity of motion' of the universe
is conserved and it is equal to the product of the object's size and speed. This is almost the same as the modern concept of
conservation of momentum, however, Descartes had no concept of mass that was different from weight and size of the object.
• John Wallis was an English mathematician who suggested the law of conservation of momentum. This law states that a body
will remain at rest or in motion, unless an external force applied to it is greater than its resistance. This statement is similar with
the first law of motion of Sir Isaac Newton.
• Isaac Newton was an English physicist and mathematician who defined the 'quantity of motion' as a product of velocity and
mass and later identified it as momentum. He implied that when no force acts on the object, the quantity of motion is
conserved. Key Points
• Mass, momentum, and energy are quantities that can be conserved in a physical interaction.
• The law of conservation of mass states that mass in an enclosed system is neither created nor destroyed by a chemical
reaction.
• People who had contributed to the understanding of mass and its conservation include some of the ancient Greek
philosophers, Nasir al-Din al-Tusi, Mikhail Lomonosov, and Antoine Lavoisier.
• The law of conservation of energy states that energy cannot be created or destroyed. It can only be transformed from one
form to another. Hence, the total energy of an isolated system never change.
• Some of the scientists who had contributed to the development of the law of conservation of energy include Galileo Galilei,
Christian Huygens, Gottfried Wilhelm Leibniz, Émilie du Châtelet, and Albert Einstein.
• The law of conservation of momentum states that the total momentum of a system does not change as if there are no
external forces acting on it.
• Some of the scientists who had contributed to the development of the law of conservation of momentum include Jean Buridan,
Rene Descartes, John Wallis, and Isaac Newton.

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