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