Sir Isaac Newton Sir Isaac Newton and Astronomyand Astronomy

Newton, as he Newton, as he appeared on the appeared on the last day of his life, last day of his life, in 1727. He was in 1727. He was born the year born the year Galileo died (but Galileo died (but no, not the same no, not the same day).day).

Describing Motion: Describing Motion: Examples from Daily LifeExamples from Daily Life

• Distinguish between speed, velocity, and Distinguish between speed, velocity, and acceleration.acceleration.

• What is the acceleration of gravity?What is the acceleration of gravity?

• How does the acceleration of gravity How does the acceleration of gravity depend on the mass of a falling object?depend on the mass of a falling object?

Structure your notes—these are the goals:

Objects in MotionObjects in Motion

• speedspeed – – raterate at which an object moves i.e., at which an object moves i.e., the distance traveled per unit time [m/s; the distance traveled per unit time [m/s; mi/hr]mi/hr]

• velocityvelocity – – an objectan object’’s s speedspeed in a certain in a certain directiondirection, e.g., , e.g., ““10 m/s moving east10 m/s moving east””

• accelerationacceleration – a change in an object – a change in an object’’s s velocityvelocity, e.g., a , e.g., a change in either speed or change in either speed or direction direction is an acceleration [m/sis an acceleration [m/s22]]

Objects in motion can be described as possessing…

The Acceleration due to The Acceleration due to GravityGravity

As objects fall, As objects fall, they accelerate.they accelerate.

The acceleration The acceleration due to Earthdue to Earth’’s s gravity is 10 gravity is 10 m/s* each m/s* each second, or second, or

gg = 10 m/s = 10 m/s22..

The higher you The higher you drop the ball, the drop the ball, the greater its greater its velocity will be at velocity will be at impact.impact.*ok, it*ok, it’’s really 9.8 m/s, s really 9.8 m/s, we’ll use 10 and note the we’ll use 10 and note the lower-case lower-case gg

The Acceleration of Gravity The Acceleration of Gravity ((gg))

Galileo demonstrated that Galileo demonstrated that gg is the same for all is the same for all objects, regardless of their mass!objects, regardless of their mass!

This was confirmed by the Apollo astronauts on This was confirmed by the Apollo astronauts on the Moon, where there is no air resistance.the Moon, where there is no air resistance.

Apollo 15 landed and performed the experiment Galileo could only do in his mind.

ForcesForcesForcesForces - change the motion of objects. - change the motion of objects.

momentummomentum – the (mass x velocity) of an object – the (mass x velocity) of an object

forceforce – anything that can cause a change in an object – anything that can cause a change in an object’’s s momentummomentum

As long as the objectAs long as the object’’s mass does not change, the force s mass does not change, the force causes a change in velocity, or an…causes a change in velocity, or an…

accelerationacceleration

a brief note about a brief note about force(s)force(s)……

Whenever you see this f-word used in a scientific Whenever you see this f-word used in a scientific context, you should toggle the same mental switch context, you should toggle the same mental switch you would for the word theory. That is, a force is you would for the word theory. That is, a force is anything that causes a push or a pull on objects. anything that causes a push or a pull on objects. This action results in a change of motion and a This action results in a change of motion and a change in position.change in position.

Let’s also take the opportunity to introduce the Let’s also take the opportunity to introduce the scientific symbol for change. It is the Greek letter, scientific symbol for change. It is the Greek letter, delta or delta or ΔΔ. . Thus, a change in velocity would be Thus, a change in velocity would be written as Δv.written as Δv.

Is Mass the Same Thing Is Mass the Same Thing as Weight?as Weight?

massmass – the amount of matter in an object – the amount of matter in an object

weightweight – a measurement of the – a measurement of the forceforce which acts upon an objectwhich acts upon an object

Recall Kepler's Laws:Kepler's Second Law: Line joining planet and the Sun sweeps out equal areas in equal times

Kepler's First Law:

Each planet’s orbit around the Sun is an ellipse, with the Sun at one focus.

Kepler's Third Law: The squares of the periods of the planets are proportional to the cubes of their semi-major axes:

p2 = r3

Newton’s Laws of Newton’s Laws of MotionMotion

• What are NewtonWhat are Newton’’s three laws of s three laws of motion?motion?

• Why does a spinning skater spin Why does a spinning skater spin faster as she pulls in her arms?faster as she pulls in her arms?

Our goals for learning:

Sir Isaac Newton (1642-Sir Isaac Newton (1642-1727)1727)

Perhaps the greatest Perhaps the greatest genius of all timegenius of all time

Invented the reflecting Invented the reflecting telescopetelescope

Invented calculus*Invented calculus*

Connected gravity and Connected gravity and planetary forcesplanetary forces

Philosophiæ Philosophiæ Naturalis Principia Naturalis Principia MathematicaMathematica

*ok, ok, here you *ok, ok, here you go…go…

Newton: Laws of Newton: Laws of MotionMotion

1 A body at rest or in motion at a A body at rest or in motion at a constant speed along a straight constant speed along a straight line remains in that state of rest line remains in that state of rest or motion unless acted upon by or motion unless acted upon by an outside force.an outside force.

NewtonNewton’’s s LawsLaws of of MotionMotion

2 The change in a bodyThe change in a body’’s velocity s velocity due to an applied force is in the due to an applied force is in the same direction as the force and same direction as the force and proportional to it, but is inversely proportional to it, but is inversely proportional to the bodyproportional to the body’’s mass.s mass.

F = m a

F/ m = a

NewtonNewton’’s Laws of s Laws of MotionMotion

33 For every applied For every applied force, a force of equal force, a force of equal size but opposite size but opposite direction arises.direction arises.

NewtonNewton’’s Laws of Motions Laws of Motion

© 2004 Pearson Education Inc., © 2004 Pearson Education Inc., publishing as Addison-Wesleypublishing as Addison-Wesley

Angular MomentumAngular Momentumangular momentumangular momentum – the momentum involved – the momentum involved in spinning /circling = in spinning /circling = mass x velocity x radiusmass x velocity x radius

torquetorque – anything that can cause a change in an – anything that can cause a change in an objectobject’’s angular momentum (s angular momentum (twisting forcetwisting force) )

Conservation of Angular Conservation of Angular MomentumMomentum

In the In the absence of absence of a net a net torque, the torque, the total total angular angular momentum momentum of a system of a system remains remains constant.constant.

The Force of GravityThe Force of Gravity

• What is the What is the universal law of universal law of gravitationgravitation??

• What types of orbits are possible What types of orbits are possible according to the law of gravitation?according to the law of gravitation?

• How can we determine the mass of How can we determine the mass of distant objects?distant objects?

Our goals for learning:

NewtonNewton’’s s UniversalUniversal LawLaw of Gravitation of Gravitation

Isaac Newton discovered that it isIsaac Newton discovered that it is gravitygravity which plays the vital role of determining the motion of the planets - concept of action at a distance.action at a distance.

……and seriously freaked some people out.and seriously freaked some people out.

So, what So, what was was gravity?gravity?For Newton’s contemporaries, it seemed a very For Newton’s contemporaries, it seemed a very troubling prospect, almost like a form of “troubling prospect, almost like a form of “magickmagick”. ”. How could the action of one physical body affect How could the action of one physical body affect another without them ever touching?another without them ever touching?

Still, it became a law. Scientific laws tell us what Still, it became a law. Scientific laws tell us what nature will do given certain variables. A law also nature will do given certain variables. A law also implies that you will get the same answer every implies that you will get the same answer every single time you run the experiment or conduct the single time you run the experiment or conduct the observation. observation.

Every. Single. Time.Every. Single. Time.

What about the theory What about the theory of gravity?of gravity?

Theories tell us Theories tell us whywhy something happened. A something happened. A theorytheory will will explain the essential nature of the phenomena being explain the essential nature of the phenomena being investigated.investigated.

Laws are the rules by which theories operate.Laws are the rules by which theories operate.

"Two objects always attract in direct proportion of "Two objects always attract in direct proportion of their masses and in inverse proportion of the square their masses and in inverse proportion of the square of the distance between them."of the distance between them."

NewtonNewton’’s Universal Law of s Universal Law of GravitationGravitation

Between every two objects there is an attractive Between every two objects there is an attractive force, the magnitude of which is directly force, the magnitude of which is directly proportional to the mass of each object and proportional to the mass of each object and inversely proportional to the square of the distance inversely proportional to the square of the distance between the centers of the objects.between the centers of the objects.

NewtonNewton’’s Universal Law of s Universal Law of GravitationGravitation

G=6.67 x 10G=6.67 x 10-11-11 m m33/(kg s/(kg s22) this is the ) this is the value of Gvalue of G, the , the gravitational constant. We call it “Big G.” Little g is for the gravitational constant. We call it “Big G.” Little g is for the pull of gravity on a particular planet or mass. pull of gravity on a particular planet or mass.

On Earth, g = 9.8 m/sOn Earth, g = 9.8 m/s22 On the Moon, g = 1.6 m/s On the Moon, g = 1.6 m/s22 On Jupiter, On Jupiter, if there were a solid surface you could stand on, you would if there were a solid surface you could stand on, you would experience g as 21.9 m/sexperience g as 21.9 m/s22. This extra force would turn your . This extra force would turn your 100 lbs into 236 lbs.100 lbs into 236 lbs.

Why is there a need for Why is there a need for G?G?

Short answer, no one knows but it is found in physical Short answer, no one knows but it is found in physical science where there is a constant of proportionality (such science where there is a constant of proportionality (such as here, inverse-square) between phenomena. as here, inverse-square) between phenomena.

It makes each side of the equation equal. It makes each side of the equation equal.

The actual value would be determined by Cavendish The actual value would be determined by Cavendish some 80 yrs after Newton’s death. Physicists are still some 80 yrs after Newton’s death. Physicists are still fine-tuning their understanding still today.fine-tuning their understanding still today.

•How does the acceleration of gravity depend on the mass of a falling object?

•It does not. All falling objects fall with the same acceleration (on a particular planet).•Now see why… •F = ma and on Earth acceleration due to gravity denoted “g” so F=mg or g=F/m•If mass of earth is ME then Fg=GMEm/d2 •mg=GMEm/d2 g=GME/d2

•Every mass attracts every other mass through the force called gravity•The strength of the gravitational force attracting any two objects is proportional to the product of their masses•The strength of gravity between two objects decreases with the square of the distance between their centers

To summarize,

So, what’s the deeply So, what’s the deeply meaningful takeaway meaningful takeaway

here?here?Take ten minutes and think about it. In Take ten minutes and think about it. In your Astronomy notebook, write down your Astronomy notebook, write down your thoughts as to how Newton used your thoughts as to how Newton used the ideas and discoveries of his the ideas and discoveries of his predecessors combined with his own predecessors combined with his own insights to create a new Universe. insights to create a new Universe. How is Newton’s Universe different How is Newton’s Universe different from those before?from those before?