1.
Newton and the Theory
of Universal Gravitation
Pablo Ginés López-Oliver
Nicolás Lozano Pulido
Rodrigo Rincón Sanz
Francisco Tomás-Valiente Jordá

2.
NEWTON´S BIOGRAPHY
• Sir Isaac Newton was born on the 4th of January 1643 in Woolsthorpe,
Lincolnshire, England. His father was a wealthy and uneducated man. He was a
prosperous farmer, who died three months before Newton was born. Finally he
was raised up by his grandmother after his mother remarried a clergyman from
North Welham. When her second husband died in 1656 Isaac’s mother returned
to Woolsthorpe and Isaac went to live with her again.
• From the age of 12 to 14 Isaac Newton went to Grantham Grammar School. Then
in 1659 he had to leave to help his mother on the familiar farm.
• It is said that he wasn´t excellent at school. He studied law at Trinity College
which was a part of Cambridge University. He worked as a servant to pay his bills.
• He was one of the most influential scientists of the 17th century and his ideas
became the basis of modern physics.
Trinity College

3.
• He studied in Cambridge University where he became interested in mathematics,
optics, physics and astronomy. In October 1665, a plague epidemic forced the university
to close and Newton returned to Woolsthorpe. During the two years he spent there, he
began to think about gravity. He also spent time with optics and mathematics, and
thinking about his ideas about calculus.
• By 1666 he had completed his work on his three laws of motion. Later he got his
master’s degree.
• In 1667, Newton returned to Cambridge, where he became a fellow of Trinity College.
Cambridge University
Newton´s prism Newton´s three laws of motion

4.
• Later on, he was focused on the diffraction of light (he used a prism to discover that
white light is made up of the spectrum of colours), universal gravitation, centrifugal
force, centripetal force, and on the effects and characteristics of bodies in motion.
• He was best known for his work on gravity. He also invented better reflecting lenses
for telescopes. Among his greatest “inventions” was calculus. Maths and algebra
weren´t enough to explain the ideas in his head, so he invented calculus.
• Newton continued studying the notion of gravity and he applied it to the motions of
the Earth, sun and moon.
• He also made many contributions to optics and calculus, whose founder he has been
claimed to.
Diffraction of light
Newton´s calculus manuscripts Law of universal gravitation

5.
• Newton's Principia formulated the laws of motion and universal gravitation. It
dominated scientists' view of the physical universe for the next three centuries. Newton
removed the last doubts about the theory of the heliocentric model of the cosmos. This
theory also demonstrated that the motion of objects on Earth and of celestial bodies
could be described by the same principles.
• Newton also built the first practical reflecting telescope and , as mentioned before, he
developed a theory of colour based on the observation that a prism decomposes white
light into the colours of the visible spectrum. He formulated an empirical law of cooling,
studied the speed of sound, and introduced the notion of a Newtonian fluid.
• In addition to his work on calculus, as a mathematician Newton contributed to the study
of power series, generalised the binomial theorem to non-integer exponents, developed
Newton's method for approximating the roots of a function, and classified most of the
cubic plane curves.
Newton's Principia
theory of the heliocentric model of
the cosmos
Newtonian fluid

6.
 From the mid-1660s, Newton conducted a series of experiments on the composition of light,
and he established the modern study of optics (behaviour of light).
 Newton's reflecting telescope, made in 1668, finally brought him to the attention of the
scientific community and in 1672 he was made a fellow of the Royal Society. In 1669 Isaac
Newton became Lucasian professor of mathematics ( mathematics teacher at Cambridge
University) .
 In 1687, with the support of his friend the astronomer Edmond Halley, Newton published his
greatest work, 'Philosophiae Naturalis Principia Mathematica' ('Mathematical Principles of
Natural Philosophy'). This showed how a universal force, gravity, is applied to all objects in all
parts of the universe. It set out his theory of gravity.
 In 1704, Newton published 'The Opticks' a book about light and colour. He also studied and
published works on history, theology and alchemy.
Newton's reflecting telescope Royal Society The Opticks
Philosophiae Naturalis
Principia Mathematica

7.
• In 1689, Newton was elected Member of Parliament for Cambridge. In 1696, he was
named warden (guard) of the Royal Mint, which was settled in London. He took his duties
at the Mint very seriously and he made campaigns against corruption and inefficiency
within the organisation. In 1703, he was elected president of the Royal Society, a
position he held until his death. Then, he was knighted in 1705.
• He was a devout but unorthodox Christian. Beyond his work on the mathematical
sciences, Newton dedicated a lot of his time to the study of biblical chronology and
alchemy, but most of his work in those areas remained unpublished until long after his
death.
• Newton was a difficult man, he had many depressions and he was often involved in
arguments with other scientists. However, by the early 1700s he was the dominant
figure in British and European science. He died on 31 March 1727 at the age of 84 and
was buried in Westminster Abbey.
Isaac Newton Royal Mint
Astronomer Edmond Halley Isaac Newton buried in
Westminster Abbey

8.
Acceleration of gravity
In physics, we refer to gravitational acceleration as the
acceleration on an object caused by gravitation. Not taking
friction into account (such as air resistance), gravity force
(whose acceleration is acceleration of gravity) is the only
force applied on an object on free fall on a body big enough
to have its own weight. In other words, mass of the object
or composition do not interfere in free fall movements.
Acceleration of gravity changes slightly in relation with
altitude. From 9.78 m/s2 to 9.83 m/s2. But we take as a
conventional standard value: 9.80665 m/s2.
Practically though, we can observe that objects with low
density and big surface fall slower because of air force of
friction and such.

9.
The force of gravity is the force applied by the gravitational
field generally of a massive object on any body within the
range of this field. This force is dependent on three factors:
the mass of the massive object (usually the Earth or another
planet to make it simple), the mass of the smaller body (the
object attracted by the planet), and the separation between
the two (usually not important in leaser problems because
the smaller object is usually within the atmosphere).
Actually, this force is established between any two objects
because, as Newton stated it is universal. However, when we
talk about force of gravity, we usually refer to the force
exerted by a massive object, since the force of gravity
exerted by an object whose mass is very small is extremely
little.

10.
In late XVII century Kepler stated that the planets
revolved around the Sun following elliptical orbits.
However he couldn’t explain why they did, why did
they not alter their orbits or why satellites did not crash
with their planets.
This is when Newton started thinking about it and when
the famous story of the apple is supposed to have
happened. He didn’t invent gravity, it already existed.
But he applied it universally and explained this way why
the moon revolved around the Earth and the Earth
around the Sun.

11.
Newton stated that if you throw a stone with enough force
and in the correct angle it will keep revolving forever. This
theory explains why the Moon revolves around the Earth
without crashing with it.

12.
Inverse square law
 Newton proposed that gravity was universal.
 He proved this by showing that the reason why don’t always
“feel” it is because gravity is diminished as distance increases.
 He discovered this by observing the Moon´s motion. He calculated
the acceleration of the Moon towards the Earth (caused as a
result of a circular motion) and compared it to the acceleration of
gravity on Earth.
 He empirically proved that gravity was is inversely square
proportional to distance.
퐹푔푟푎푣푖푡푦 ∝
1
푑2

13.
Universality of gravity
 He also proposed that all objects attract each other. He
proved this by means of his 3rd Law.
 If the Earth attracts an object, due to action-reaction
principle, the object also attracts the Earth. However,
because of the little mass, this is not noticeable.
 This, added to the fact the distance diminished gravity force,
meant that gravity was universal.

14.
Dependence on mass
 Newton proposed that force of gravity also depended of
mass, because his second law states that F=ma
 He therefore had proved that the force of gravity
between two objects was directly proportional to its
masses.
퐹 = 푚푎 퐹푔푟푎푣푖푡푦 ∝
푚1 푚2
푑2

15.
Theory of universal gravitation
 As a result of this, in 1687 included in his “Principia” he
could propose his theory of universal gravitation.
 It stated that force of gravity is directly proportional to
the masses of the objects and inversely proportional to
the distance squared.
 He called the constant of proportionality G “the
constant of universal gravitation”. Its value was
experimentally determined by Henry Cavendish in 1798.
퐹푔푟푎푣푖푡푦 = 퐺
푚1푚2
푑2
퐺 ≈ 6.674 · 10−11 푁 푚2
푘푔2

16.
Theory of universal gravitation and
acceleration of gravity
 His theory can be applied to calculate the acceleration of
gravity in different planets.
 The acceleration of gravity at the surface must be directly
proportional to the mass of the planet and inversely
proportional to the radius squared.
푊푒푖푔ℎ푡 = 푚푔
푊푒푖푔ℎ푡(푠푢푟푓푎푐푒) = 퐺
푚 · 푀푝푙푎푛푒푡
푅2
푔 =
퐺 · 푀푝푙푎푛푒푡
푅2

17.
Dynamic’s laws

18.
INERTIA
 I. If no force is applied on any body, that body will not
change it’s speed. So, if it is at rest, it will continue
being at rest, and if it is moving, it will continue
moving with a rectilinear and uniform motion (v=cte).
 This is sometimes not so clear because people do not
take into account the forces of friction

19.
F=ma
 If on an object, a force is applied, that object will
modify its velocity, therefore it will have an
acceleration.
 The force applied and the acceleration produced
are proportional.
 The mass is considered a property of bodies that
measures its inertia. So, it is the resistence of
bodies to change their velocity.
 The unit of force is the newton (N). It is defined as
the force you have to apply on an object with 1kg of
mass so that it has an acceleration of 1m/s2.

20.
Action-Reaction law
 If a body applies a force on another body, the
original body will receive from the second
body another force, equal in magnitude but
opposite in direction to the first force.
 These forces of action and reaction are not
cancelled beacuse they are applied in
different bodies.