Gravity & The Distances to Stars. Lecture 8. Homework 2 open Exam on Tuesday in class bring ID and #2 pencil

Transcription

1 1 Gravity & The Distances to Stars Lecture 8 Homework 2 open Exam on Tuesday in class bring ID and #2 pencil

2 2 Preparing for the Exam 1 Exams in this class are multiple choice, but the questions can be tricky. Sample questions and opportunities to test yourself are found on the textbook website. I often use these questions as starting points for questions on our exam Be careful! I often change the question just slightly so the answer is different! Review the PRS questions too.

3 3 Preparing for the Exam 2 Be sure to review the key terms in all of the Units we have covered. Play Jeopardy by inventing a question that would use each key term as an answer. For any areas where you are uncertain of the answers, review the reading material and lecture notes. Come to Monday s Q&A session or visit the Help Desk with your questions.

4 4 PRS: Rocket Wagon Where is the force being applied that causes the wagon to accelerate forward? The gas coming out of the tank pushes on (1) the air behind the cart. (2) the sides of the nozzle. (3) the sides of the wagon. (4) the U of the hose. Answer: 4 (and a little of 2)

5 PRS: Orb on a String 5 (3) (2) (1) A ball is being swung in a circle. If the string breaks at the position shown, which way will the ball go? (4) Answer: 3

6 6 Circular Motion When an object changes direction, a force must be applied. Motion in a circle requires the constant application of a centripetal force to change its velocity. The bigger the velocity and the larger the mass of the orbiting body, the larger the centripetal force required.

7 7 Newton realized that, depending on its initial velocity, a projectile might fall to Earth fall at a rate that curved less than Earth s surface curves away an orbit! Newton s Cannon See book interactive

8 8 Why Kepler s 3 rd Law? P 2 = a 3 Orbital speed is V = 2π a/ P From this, Newton could deduce how Sun s force must decline with distance

9 Newton and Gravity An apple and the Moon are falling toward the Earth but the Moon doesn t hit the Earth because of its sideways motion! Newton realized that larger mass objects must produce a bigger pull. (force proportional to mass) A distant massive object has less pull than a nearer smaller mass (force somehow inversely proportional to distance) His 3 rd law requires that small masses pull on large masses as well as large on small (proportional to both masses) 9

10 10 Universal Gravitation Force is inversely proportional to the square of the distance ( inverse-square law ). Double the distance, get ¼ the force. 1/3 the distance, get 9 times the force. F r 2

11 11 PRS: Gravitation The gravitational force that two 1 kg objects exert on each other is weaker when they are 1) made of low density materials. 2) separated by great distances. 3) distant from any star. 4) spinning more slowly. 5) All of the above. Answer: 2

12 12 Weight vs. Mass The mass of an object does not change. The forces it experiences depend on - Gravitational Pull - Motion of Surroundings Astronauts feel weightless in spaceship because they are falling at same rate as ship

13 13 Escape Velocity What goes up does not always come down. If an object is moving fast enough (has enough kinetic energy) it can travel away forever.

14 The Moon and Tides 14 The Moon s mass is small, but it has a strong effect on tides because of its distance.

15 The Sun s 15 Effect on Tides Neap Tides The Sun can partially cancel or add to the Moon s tidal effect. Spring Tides

16 16 Tidal Friction The Earth spinning under the bulge causes friction. Earth s rotation slows down (1 sec every 50,000 yrs.) As a result, the Moon also moves farther away from Earth by about 4 centimeters each year.

17 The Near Side of the Moon 17 The same effect is why the same side of the moon always faces the Earth.

18 PRS: Force of Gravity 18 The Earth s radius is 6400 km. The acceleration caused by the force of gravity at the Earth s surface is 10 m/s 2. What is the acceleration of gravity at 6400 km above the ground? 1) 2.5 m/s 2 Answer: 2) 5 m/s 2 3) 10 m/s 2 4) 20 m/s 2 Acceleration α Force Force α 1 / distance 2 Double distance acceleration/4 answer is #1.

19 19 Are the brightest stars necessarily the nearest? How can we find their distances?

20 Brightness: 20 Another Inverse Square Law Light is spread out over the surface of each successive sphere, so the same number of watts spread over a larger and larger surface area, which grows as the square of the distance: Brightness = Luminosity / (4 π d 2 ) Therefore: Luminosity = Brightness 4 π d 2

21 21 Proportionality Calculations: Brightness B = L 4Πd 2 1 d B d B is inversely proportional to the square of distance Ex. 1: B gets 9x bigger Ex. 2: d is halved Before After Before After B 9B d ½ d d 2 1/9 d 2 d 2 ¼ d 2 d 1/3 d B 4B 2 2

22 PRS: Brightness and distance 22 An astronomer measures the light from two stars known to be very similar. Star A is 16 times dimmer than Star B. Therefore, we expect that Star A is times farther away than Star B. 1) 256 4) 1/256 2) 16 5) 1/16 3) 4 6) 1/4 Answer: 3

23 23 PRS Review: Retrograde Motion A planet in retrograde motion 1. rises in the west and sets in the east 2. moves randomly with respect to the stars 3. occasionally shifts direction with respect to the stars 4. cannot be explained by Ptolemy s model of the solar system Answer: 3

24 24 PRS Review: Net Force If the net force on an object doubles, then its also doubles. 1) mass 2) acceleration 3) velocity 4) speed Answer: 2