newtons law of universal gravitation keplers laws of planetary motion
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Caraga Regional Science High SchoolSan Juan, Surigao City
Newton ‘s Law of Universal Gravitation
&Kepler’s Laws of Planetary Motion
Newton’s Law of Universal Gravitation &&Kepler’s Laws of Planetary Motion
Motion-change ofposition overtime
ISAAC NEWTONEnglish Scientist
1643-1727
Newton’s Law of Universal Gravitation &&Kepler’s Laws of Planetary Motion
~formulated the three laws of motion
1st Law of Motion
Newton’s Law of Universal Gravitation &&Kepler’s Laws of Planetary Motion
ball at rest ball in motion
2nd Law of Motion
Newton’s Law of Universal Gravitation &&Kepler’s Laws of Planetary Motion
great force + less mass
great force +great mass
=great acceleration =less acceleration
3rd Law of Motion
Newton’s Law of Universal Gravitation &&Kepler’s Laws of Planetary Motion
movementreaction force
action force
Newton’s Law of Universal Gravitation &&Kepler’s Laws of Planetary Motion
Why do objects falltoward Earth?
Universal Gravitation
Newton’s Law of Universal Gravitation &&Kepler’s Laws of Planetary Motion
“Every partic le of matter in the universe
attracts every other partic le with a force
that i s d i rect ly proportional to
the square of the d istance
between their centers of mass .”.
•F is the force between the masses,•G is the gravitational constant, G = 6.67 x 10-11 newton-m2/kg2. F means the force of gravitational attraction, m1 the mass of the•m1 is the first mass,•m2 is the second mass, and•r is the distance between the masses. Newton’s Law of Universal Gravitation &&
Kepler’s Laws of Planetary Motion
To help us remember this equation:• For Gravity Makes Masses
Over-React and Reactor• False Gods Make Man Over-
Righteous and Rebellious
Sample problem:• What is the force of gravitational
attraction between the earth (m=5.98 x 1024 kg) and a 70-kg man if he is standing at sea level, a distance of 6.37 x 106m from earth’s center?
• The solution of the problem involves substituting known values of G (6.67 x 10-11 Nm2/kg2), m1 (5.98 x 1024 kg), m2 (70 kg) and d (6.37 x 106 m) into the universal gravitation equation and solving for Fgrav. The
JOHANNES KEPLERGerman Astronomer,
Mathematician, Astrologer
1571- 1630
Newton’s Law of Universal Gravitation &&Kepler’s Laws of Planetary Motion
~ best known forhis three laws of planetary motion
1st law (Law of orbits)“The planets move around the sun in ellipses with the sun at one focus.”2nd law (Law of areas)“The line connecting the sun to a planet
sweeps equal areas at equal time.”3rd law (Law of periods)“The square of the orbital period of a
planet is proportional to the cube of themean distance from the sun.”
Newton’s Law of Universal Gravitation &&Kepler’s Laws of Planetary Motion
Our Laws relate to each other!!
The big question is:
HOW?Newton’s Law of Universal Gravitation &&
Kepler’s Laws of Planetary Motion
• (1) directed toward the Sun from the planet• (2) is proportional to the product
of masses for the Sun and planet• (3) is inversely proportional to
the square of the planet-Sun separation. This is precisely the form
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