The Motions of Celestial Bodies, and Newton s Laws of Motion

Transcription

1 The Motions of Celestial Bodies, and Newton s Laws of Motion

2 Announcements The results of Quiz 1 are posted in OWL Looking ahead: Homework 1 is on-going, and is due on Thu, Sept. 29 th ; Homework 2 will be available through SPARK/ OWL starting on Thu. Sept 29 th ; it is due on Thu, Oct. 6th The second in-class quiz will take place on Tue, Oct 4 th The First in-class Exam will take place on Thu, Oct 6 th

3 Units 13 and 14. Assigned Reading

4 Section 2: Tools of Astronomy

5 Section 2: Tools of Astronomy They include: Ø Understanding the Motions of Astronomical Bodies (gravity, inertia, mass, force, velocity, acceleration, etc.) Ø Understanding matter, light, and their interactions Ø Understanding the structure of the smallest of particles: atoms, and how they determine the appearance of some of the biggest of objects (stars, galaxies, etc.)

6 Today s goals Review the Laws of Planetary Motion Understand the concept of Inertia Introduce the concept of momentum Newton s First Law of Motion

7 Kepler s Laws of Planetary Motion 1 The orbits of the planets are ellipses, with the Sun at one focus of the ellipse. 2 Planets move proportionally faster in their orbits when they are nearer the Sun (cover equal areas in equal time. 3 More distant planets take proportionally longer to orbit the Sun

8 Kepler s Second Law of Orbits 2. As a planet moves around it s orbit, it sweeps out equal areas in equal times. 1 month

9 Calculations Using Kepler's Third Law The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semimajor axes. R 3 =P 2 (R in AU; P in years) As an example, the "radius" of the orbit of Mars (the length of the semimajor axis of the orbit) is: R=P 2/3 =(1.88) 2/3 =1.52 AU

10 Survey Question A planet that is farther away from the Sun than the Earth, takes: an equal amount of time to orbit the Sun a smaller amount of time to orbit the Sun a larger amount of time to orbit the Sun

11 Survey Question A planet that is farther away from the Sun than the Earth, takes: an equal amount of time to orbit the Sun a smaller amount of time to orbit the Sun a larger amount of time to orbit the Sun P 2 = R 3

12 The Motions of Astronomical Bodies Speed, velocity, acceleration, force Mass, momentum and inertia Newton s three laws of motion The Force of Gravity

13 `Common sense : Survey Question If the Earth spins on an axis, why don t objects fly off the spinning Earth? If the Earth revolves around the Sun, why aren t birds `left behind? 1. Because of `superglue 2. Because of the pressure of the atmosphere 3. Because of gravity 4. Because we are at the center of the Universe

14 `Common sense : Survey Question If the Earth spins on an axis, why don t objects fly off the spinning Earth? If the Earth revolves around the Sun, why aren t birds `left behind? 1. Because of `superglue 2. Because of the pressure of the atmosphere 3. Because of gravity 4. Because we are at the center of the Universe

15 Describing Motion Motion is when the position of an object changes in time If position does not change, the object is at rest To describe motions we need to monitor position and time The rate at which an objects covers a given amount of space in a given amount of time is called speed Ø v = s/t

16 Inertia Inertia is the tendency of any physical objects to resist change in its state of motion (including rest)

17 Galileo and the Concept of Inertia Aristotle held that objects at rest remained at rest unless a force acted on them, but that objects in motion did not remain in motion unless a force acted constantly on them: F = v (Incorrect). Galileo concluded that an object in a state of motion possesses an ``inertia'' that causes it to remain in that state of motion unless an external force acts on it (Correct).

18 Inertia and Friction: think of Teflon Teflon (polytetrafluoroethylene) : the most `slippery solid substance currently known What would happen if our planet were suddenly to change to teflon?

19 Inertia and Mass We measure Inertia by an object s Mass, which is the amount of material in the object. Weight is the force exerted on the object by the gravity of another object, e.g. The force exerted by the planet Earth on you. Thus, for an object, weight depends on the location of the object. Your mass is the same on the moon, but your weight on the surface of the moon is smaller

20 Survey Question The mass of an astronaut on the Moon is: smaller than his/her mass on the Earth the same as his/her mass on the Earth larger than his/her mass on the Earth

21 Survey Question The mass of an astronaut on the Moon is: smaller than his/her mass on the Earth the same as his/her mass on the Earth larger than his/her mass on the Earth

22 Survey Question The weight of an astronaut on the Moon is smaller than his/her weight on the Earth. True False

23 Survey Question The weight of an astronaut on the Moon is smaller than his/her weight on the Earth. True False The mass of the Moon is 100 times smaller than that of the Earth, thus its gravitational pull is smaller (smaller weights)

24 Sir Isaac Newton and the Unification of Physics & Astronomy Newton was by many standards the most important figure in the development of modern science. He demonstrated that the laws that govern the heavens are the same laws that govern the motion on the surface of the Earth. Newton's Three Laws of Motion. Theory of Universal Gravitation ( )

25 Vectors, or things with a direction There are physical quantities in nature for which only one number, their intensity, tells the whole story: e.g. mass, temperature, luminosity, color Other quantities need both an intensity and a direction to be fully described: e.g. velocity (speed with a direction), force, acceleration. These quantities with a direction are called VECTORS

26 Law of Inertia (Newton s First Law) In the absence of a net force, an object moves with constant velocity, or it conserves its momentum (quantity of motion). (paraphrased) If nothing acts on an object, the object will keep moving in a straight line and at a constant speed. If it was at rest (zero velocity), it will try to remain at rest. Objects `resist change. Only a force can change the quantity of motion (momentum) of an object, either by changing its speed, or by changing its direction of motion, or both

27 Momentum Momentum is a quantitative way to describe an object s tendency to continue to do whatever it was previously doing. An object s momentum is simply its mass times its velocity. P = m v Don t forget that velocity is a vector, so momentum is a vector: the direction of motion is very important!

28 Survey Question You are driving your car and suddenly you brake. What happens to the grocery bag on the passenger s seat? It stays where it is It tends to continue moving forward It tends to fall backward

29 Survey Question You are driving your car and suddenly you brake. What happens to the grocery bag on the passenger s seat? It stays where it is It tends to continue moving forward It tends to fall backward The grocery bag tends to keep its momentum constant.

30 Momentum is Conserved P = m v P 1 = m 1 v 1 P 2 = m 2 v 2 If two objects collide and stick together, the final momentum must be the same as the initial momentum. P final = P 1 + P 2

31 Linebacks and Fullbacks P = m v; m in kg; and v in m/s

32 Momentum Conservation