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

Describing Motion: Examples from Daily Life Structure your notes—these are the goals: Distinguish between speed, velocity, and acceleration. What is the acceleration of gravity? How does the acceleration of gravity depend on the mass of a falling object?

Objects in Motion Objects in motion can be described as possessing… speed – rate at which an object moves i.e., the distance traveled per unit time [m/s; mi/hr] velocity – an object’s speed in a certain direction, e.g., “10 m/s moving east” acceleration – a change in an object’s velocity, e.g., a change in either speed or direction is an acceleration [m/s2]

The Acceleration due to Gravity As objects fall, they accelerate. The acceleration due to Earth’s gravity is 10 m/s* each second, or g = 10 m/s2. The higher you drop the ball, the greater its velocity will be at impact. *ok, it’s really 9.8 m/s, we’ll use 10 and note the lower- case g

The Acceleration of Gravity (g) Galileo demonstrated that g is the same for all objects, regardless of their mass! This was confirmed by the Apollo astronauts on the Moon, where there is no air resistance. Apollo 15 landed and performed the experiment Galileo could only do in his mind.

Forces acceleration Forces - change the motion of objects. momentum – the (mass x velocity) of an object force – anything that can cause a change in an object’s momentum As long as the object’s mass does not change, the force causes a change in velocity, or an… acceleration

a brief note about force(s)… Whenever you see this f-word used in a scientific context, you should toggle the same mental switch you would for the word theory. That is, a force is anything that causes a push or a pull on objects. This action results in a change of motion and a change in position. Let’s also take the opportunity to introduce the scientific symbol for change. It is the Greek letter, delta or Δ. Thus, a change in velocity would be written as Δv.

Is Mass the Same Thing as Weight? mass – the amount of matter in an object weight – a measurement of the force which acts upon an object

Recall Kepler's Laws: p2 = r3 Kepler's First Law: Each planet’s orbit around the Sun is an ellipse, with the Sun at one focus. Kepler's Second Law: Line joining planet and the Sun sweeps out equal areas in equal times 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 Motion Our goals for learning: What are Newton’s three laws of motion? Why does a spinning skater spin faster as she pulls in her arms?

Sir Isaac Newton (1642-1727) Perhaps the greatest genius of all time Invented the reflecting telescope Invented calculus* Connected gravity and planetary forces Philosophiæ Naturalis Principia Mathematica

*ok, ok, here you go…

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

Newton’s Laws of Motion The change in a body’s velocity due to an applied force is in the same direction as the force and proportional to it, but is inversely proportional to the body’s mass. F/ m = a F = m a

Newton’s Laws of Motion 3 For every applied force, a force of equal size but opposite direction arises.

Newton’s Laws of Motion © 2004 Pearson Education Inc., publishing as Addison-Wesley

Angular Momentum angular momentum – the momentum involved in spinning /circling = mass x velocity x radius torque – anything that can cause a change in an object’s angular momentum (twisting force)

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

The Force of Gravity Our goals for learning: What is the universal law of gravitation? What types of orbits are possible according to the law of gravitation? How can we determine the mass of distant objects?

Newton’s Universal Law of Gravitation Isaac Newton discovered that it is gravity which plays the vital role of determining the motion of the planets - concept of action at a distance. …and seriously freaked some people out.

So, what was gravity? For Newton’s contemporaries, it seemed a very troubling prospect, almost like a form of “magick”. How could the action of one physical body affect another without them ever touching? Still, it became a law. Scientific laws tell us what nature will do given certain variables. A law also implies that you will get the same answer every single time you run the experiment or conduct the observation. Every. Single. Time.

What about the theory of gravity? Theories tell us why something happened. A theory will explain the essential nature of the phenomena being investigated. Laws are the rules by which theories operate. "Two objects always attract in direct proportion of their masses and in inverse proportion of the square of the distance between them."

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

Newton’s Universal Law of Gravitation G=6.67 x 10-11 m3/(kg s2) this is the value of G, the gravitational constant. We call it “Big G.” Little g is for the pull of gravity on a particular planet or mass. On Earth, g = 9.8 m/s2 On the Moon, g = 1.6 m/s2 On Jupiter, if there were a solid surface you could stand on, you would experience g as 21.9 m/s2. This extra force would turn your 100 lbs into 236 lbs.

Why is there a need for G? Short answer, no one knows but it is found in physical science where there is a constant of proportionality (such as here, inverse-square) between phenomena. It makes each side of the equation equal. The actual value would be determined by Cavendish some 80 yrs after Newton’s death. Physicists are still 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

To summarize, 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

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