Newton, the apple and the Moon

Transcription

http://modellus.fct.unl.pt
This is an activity about the invention of gravitation by Isaac Newton,
during the XVII century.
Newton created a theory of gravitation, based on mathematical
reasoning, that unified all motions, on the earth or on the heavens.
Previous work by Galileo Galilei and Johannes Kepler was essential
for Newton ideas.
In a very short summary, Newton has shown that the motion of any
falling object, like a simple apple falling from a tree, was of the same
nature of the motion of any planet, such as the Moon around the
Earth... Let’s see what was his line or argument.
Geometrical and visual thinking was essential in Newton explanations. The motion of a cannon ball (a projectile!) that can start orbiting
the Earth, if its initial velocity is sufficient high, is a classic of scientific
thinking and imagination (on the background of this text).
Notes and answers by...
Place and date...
http://en.wikipedia.org/wiki/Isaac_newton
Some texts on this document are adapated from
the Wikipedia. Most of the images are also from
the same source.
Teacher/tutor comments...
Newton, the apple
and the Moon
1. Gravitation before Newton: Aristotle
2. Gravitation before Newton: Ptolomey
3. Medieval thought and religious views of the world
“Newton,” by William Blake; here, Newton is depicted as a
“divine geometer”
4. Planets and retrograde motion
5. Explorations of Ptolomey´s Cosmology
16.Grav
6. Gravitation before Newton: Ptolomey
17.Grav
7. Making a model of planetary motion accordingly to
Ptolomey
18.Grav
8. Gravitation before Newton: Galileo, Tycho Brahe and
Johannes Kepler
20.Grav
9. Kepler 1st law: orbits are ellipses with the Sun at a focus
10.Kepler 2nd law: the law of the areas
11.Kepler 3rd law: the law of the periods
12.How fast does the Moon move, assuming it has an uniform circular motion?
13.Gr
14.Grav
15.Grav
19.Grav
21.Grav
22.Grav
23.Grav
1
Gravitation before Newton: Aristotle
1 The Greek philosopher Aristotle (384 BC – 322 BC) developed many theories on the nature of physics that are
completely different from what are now understood as the
laws of physics. These involved what Aristotle described as
the four elements, as well as a variety of principles, most
of which modern science has now disproved, and which
provide no significant roots to any area of modern physics.
2 The Aristotelian theory of gravity was a theory that stated
that all bodies move towards their natural place. For
some objects, Aristotle claimed the natural place to be
the center of the earth, wherefore they fall towards it. For
other objects, the natural place is the heavenly spheres,
wherefore gases, steam for example, move away from the
centre of the earth and towards heaven and to the moon.
Plato (left) and Aristotle (right), a detail of The
School of Athens, a fresco by Raphael. Aristotle
gestures to the earth, representing his belief
in knowledge through empirical observation
and experience, while holding a copy of his
Nicomachean Ethics in his hand, whilst Plato
gestures to the heavens, representing his belief
in The Forms.
3 What were the main ideas of Aristotle about the natural
world?
4 How was Artistotle theory of gravitation modified during
the Middle Age?
Notes, answers and comments...
2
Gravitation before Newton: Ptolomey
1 The
3
Medieval thought and religious views of the world
1 The
Dante
4
Planets and retrograde motion
1 The
5
Explorations of Ptolomey´s Cosmology
1 The tr
Ptolomey’s Cosmology
Ptolomaic System Simulator
6
Gravitation before Newton: Ptolomey
1 The
Alternative Solar Systems
7
Making a model of planetary
motion accordingly to Ptolomey
1 The equant of Mars moves around the
Earth. How long it takes to give a complete
turn? Explain.
2 Mars moves around its equant. How long it
takes to give a complete turn? Explain.
3 The Sun moves around the Earth. How long
it takes to give a complete turn? Explain.
4 Use the animation to find how long it takes
to Mars to be again at the
smallest distance to Earth.
5 Build a model similar to the
one on the right. Don’t forget to attach the origin of
the circular motion of Mars
to the equant.
8
Gravitation before Newton: Galileo, Tycho
Brahe and Johannes Kepler
1 The tr
9
Kepler 1st law: orbits are ellipses with the
Sun at a focus
1 The tr
Comments and answers...
10
Kepler 2nd law: the law of the areas
1 The tr
11
Kepler 3rd law: the law of the periods
1 The tr
12
How fast does the Moon move, assuming
it has an uniform circular motion?
1 The trajectory of the Moon around the Earth is approximately circular, with constant speed.
2 The period of this uniform circular motion is 27.3
days.
3 The radius of the orbit is 384 000 km.
4 How fast is the Moon travelling around the Earth,
in m/s? And in km/h?
Hint...
5 In 1 s, what is the distance travelled by the Moon?
6 Make a model of the Moon travelling around the Earth
for three lunar months (don’t forget to use the AutoScale button and to choose appropriate time step and
time interval...)
Hint...
Click on the image to see the movie...
13
Newton’s law of gravitation
1 The
14
Grav
1 The
15
Grav
1 The
16
Grav
1 The
17
Grav
1 The
18
Grav
1 The
19
Grav
1 The
20
Grav
1 The
21
Grav
1 The
22
Grav
1 The
23
Grav
1 The

Newton, the apple and the Moon

Transcription

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