Law of Universal Gravitation

Chapter 12November 9/10

Objectives

• Analyze how Earth is falling• State Newton’s law of universal gravitation• Evaluate the significance of inverse-square

law

Introduction

• All objects have gravity• Therefore, all objects attract one another

The Falling Apple

• An apple falls to Earth because of gravity• Does Earth’s gravity pull the moon?– YES

• Why doesn’t the moon fall into Earth?– It does but it doesn’t crash because of tangential

speed

The Falling Moon

• Earth’s gravity pulls moon = centripetal force• Moon falls beneath the straight line it would

follow if no force acted on it– Below the tangential speed line

• Figure 9.2• Confirmed with experiment– Figure 9.4

The Falling Earth

• Earth (and other planets) falls around the sun• Why don’t planets crash into sun?– Because of tangential velocities

• What would happen if tangential speeds went away?– Crash into sun– This has happened to asteroids and other matter

without a big enough tangential speed

Check for understanding

• In the picture below use vectors and words to describe how the Earth orbits the sun

EarthSun

Fc = gravity

Tangential speed

Earth stays in orbit as the resultant of the sun’s gravity and Earth’s tangential speed

Newton’s Law of Universal Gravitation

• Newton discovered gravity is universal– Everything pulls on everything else

• Law of Universal Gravitation– “Every object attracts every other object with a force

that for any two objects is directly proportional to the mass of each object”

– Greater masses = greater force of attraction– Greater distance (farther away) = less force of

attraction

Newton’s Law of Universal Gravitation (con’t)

• Law can be expressed as an equationFG = force of gravity (N)

G = universal constant = 6.7 x 10 -11 Nm2

kg2

m1 = mass of one object (kg)

m2 = mass of other object (kg)

r = radius (m)

Class work- Honors

• Use the equation that relates to the law of universal gravitation to solve the problem

Inverse Square Law

• When a quantity varies as the inverse square of its distance from its source

• Figure 9.4 and 9.5– Force of gravity depends on distance from Earth.

Closing

• An apple falls into Earth. Why doesn’t the moon fall and crash into Earth?– It does but it doesn’t crash because of tangential

speedAND– Force of gravity is weaker since moon is farther

from Earth’s surface than apple

Homework

• Next class we will:– Take a quiz on all units and symbols- STUDY!– review for the unit exam

• The following class is the unit exam on:– Newton’s 3 laws– Centripetal force and tangential speed– Law of universal gravitation