Download Senior Science topics Programme

Senior Secondary Science Programme
Gravitation
Teachers' Notes
Subject
Physics
Level
S4-S6
Duration:
15 minutes
Key Points
1. Newton’s law of gravitation
2. Kepler’s Laws
Content:
1.
Newton’s law of gravitation
Scientists before Newton had already discovered and put forward the concept of gravitation,
but only Newton employed mathematical principles to prove that gravitation exists in all
objects.
In 1687, Newton explained the law of universal gravitation in his book, Philosophiae Naturalis
Principia Mathematica: “Every point mass attracts every single other mass by a force pointing
along the line intersecting both points. The force is proportional to the product of the two
masses and inversely proportional to the square of the distance between them.”
If the spatial extent of the objects is limited, we can assume that all the mass is concentrated at
the center of the objects. It is called the point mass. Gravitational force refers to the attraction
between objects. It is a kind of action-and-reaction forces. In simple terms, the gravitational
force acting on two point masses is directly proportional to the product of the masses and is
inversely proportional to the square of the distance between them.
Newton law of gravitation is applied to explain the motion of the moon revolving around the
Earth.
2.
Kepler’s laws
Astronomers in the past believed that the planets in the sky moved in circular motions. Kepler
thought the same initially, but after examining the information of the motions of Mars obtained
by Brahe as well as making calculations based on the assumptions of circular orbits, he found
that the orbit of Mars was an ellipse rather than a circle. This finding was later known as
Kepler’s First Law.
Kepler’s First Law states that “the orbit of a planet is an ellipse, with the Sun at one of the two
foci of the ellipse.”
Kepler’s Second Law states that “a line segment joining a planet and the Sun sweeps out equal
areas during equal intervals of time.”
Kepler’s Third Law states that “the square of the orbital period of a planet is directly
proportional to the cube of the semi-major axis of its orbit.”
Kepler derived his laws from his experiences in astronomical observations. Although Kepler
tried hard to find out why these laws could be established, e.g. why planets would sometimes
move faster and at other times slower when orbiting the Sun, he was never able to draw a
correct conclusion. Newton, however, was different from the scientists before him. While the
past scientists relied on observations and data, Newton believed it was the most important to
identify the relationship between interacting objects. From his very own Newtonian Mechanics
and Law of Gravitation, Newton deduced Kepler’s Third Law mathematically. Kepler’s Third
Law is also an important basis for Newton’s Law of Gravitation.
Suggested Learning Activities
Preparation before viewing the programme
1.
Teacher may discuss with students to what extent do they know about the motions of planets in
the solar system.
Activities after viewing the programme
1.
Student may, under the guidance of teacher, review the physical concepts presented in the
programme.
2.
Teacher may lead students to discuss how Kepler’s law posed great challenges to Aristotle and
Ptolemy’s schools of thoughts in the areas of astronomy and physics.