ASTRONOMY 161Introduction to Solar System Astronomy

Class 7

Newton’s LawsMonday, January 22

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Newton’s Laws: Key ConceptsThree Laws of Motion:

(1) An object remains at rest, or moves in a straight line atconstant speed, unless acted on by an outside force.

(2) The acceleration of an object is directly proportional toforce, and inversely proportional to mass.

(3) For every action, there is an equal and opposite reaction.Law of Gravity:

(4) The gravitational force between masses M and m,separated by distance r, is

Discovered:three laws of motion,one law of universal

gravitation.

Isaac Newton (1643-1727): English

Newton’s laws areuniversal in scope,and mathematical inform.

Newton’s great book:

(1) Newton’s First Law of Motion:An object remains at rest, or moves in a

straight line at constant speed, unless actedon by an outside force.

Precise mathematical laws require precise definitions ofterms:

SPEED = rate at which an object changes its position.Example: 65 miles/hour.

VELOCITY = speed plus direction of travel.Example: 65 miles/hour to the north.

= rate at which an object changes its velocity.

Acceleration can involve:(1) increase in speed(2) decrease in speedOR(3) change in direction.

Acceleration

= a push or pull acting on an object.

Examples:gravity = pullelectrostatic attraction = pullelectrostatic repulsion = push

Force

(2) Newton’s Second Law of Motion:

The acceleration of an object is directlyproportional to the force acting on it, and

inversely proportional to its mass.

In mathematical form:

Or alternatively: amF !=

m

Fa =

Example of Newton’s Second Law:A package of cookies has mass

m = 0.454 kilograms,And experiences gravitational acceleration

g = 9.8 meters/second2

How large is the force acting on the cookies?

pound) 1 Newtons (4.4

Newtons 4.4m/sec kg 4.4

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(3) Newton’s Third Law of Motion:

For every action, there isan equal and opposite reaction.

Whenever A exerts a force on B, B exerts a forceon A that’s equal in size and opposite indirection.

All forces come in pairs.

Example of Newton’s Third Law:Cookies push on hand: F = 1 pound, downward.Hand pushes on cookies: F = 1 pound, upward.

Remove hand!

Earth pulls on cookies: F = 1 pound, downward.Cookies pull on earth: F = 1 pound, upward.

THIRD Law states:force on Earth = force on cookies

SECOND Law states:acceleration = force divided by mass

Mass of Earth = 1025 x mass of cookies

Therefore, acceleration of cookies =1025 x acceleration of Earth.

(Cookies reach a high speed while the Earth hardlybudges.)

But…why do the cookies and the Earth exert aforce on each other?

Newton’s Law of Gravity states that gravity is anattractive force acting between ALL pairs ofmassive objects.

Gravity depends on:

(1) MASSES of the two objects,

(2) DISTANCES between the objects.

(4) Newton’s Law of Gravity:

The gravitational force between two objects

F = gravitational forceM = mass of one objectm = mass of the second objectr = distance between centers of objectsG = “universal constant of gravitation”

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Gravitational force variesdirectly with mass and

inversely with square of distance.

Double the distance between objects:Force 1/4 as large.

Triple the distance between objects:Force 1/9 as large.

)small!(very /m Newtons 107.6 2211 kgG !"=

Example: What is gravitational forcebetween Earth and cookies?

pound 1 Newtons 4.4F

kg/m Newtons 107.6

m 106.4Earth of radius

kg 454.0 cookies of mass

kg100.6 Earth of mass

:in numbers theplug sLet'

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Example Encore: What isacceleration of cookies?

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..Therefore.

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Newton’s question: canGRAVITY be theforce keeping theMoon in its orbit?

Newton’s approximation:Moon is on a circularorbit.

Even if its orbit wereperfectly circular, theMoon would still beaccelerated.

The Moon’s orbital speed:

radius of orbit: r = 3.8 x 108 mcircumference of orbit: 2πr = 2.4 x 109 morbital period: P = 27.3 days = 2.4 x 106 sec

orbital speed:v = (2πr)/P = 103 m/sec = 1 km/sec!

Acceleration required tokeep Moon on a circular orbit

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Acceleration provided by gravity

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Bottom Line

If gravity goes as one over the square of thedistance,

Then it provides the right acceleration to keepthe Moon on its orbit (“to keep it falling”).

Triumph for Newton!!