1. Astronomy 1020-H Stellar Astronomy Spring_2015 Day-9

2. Course Announcements Smartworks Chapter 2: Start on – Grades will be downloaded sometime this coming weekend. SW Chapter 3 … will be downloaded on Friday 2/13 during the exam. SW Chapters 13-23 are posted now Exam 1: Friday, Feb. 13 1 st set of Dark Sky observing nights: Wed. Feb. 11 & Tues. Feb. 17

3. Lab This Week Hydrogen Energy Levels What you need to know: You get to explore the possible energy transitions for Hydrogen. Reading ahead in Chapter 5 will help.

5. Tutorial: Newton’s Law and Gravity – pg.29 Work with a partner Read the instructions and questions carefully Talk to each other and discuss your answers with each another Come to a consensus answer you both agree on If you get stuck or are not sure of your answer ask another group If you get really stuck or don’t understand what the Lecture Tutorial is asking as one of us for help

6. Concept Quiz—Earth’s Position Assume Earth were moved to a distance from the Sun twice that of what it is now. How would that change the gravitational force it would experience from the Sun? A.It would be half as strong. B.It would be one-fourth as strong. C.It would be twice as strong. D.It would be four times as strong. E.It would not change.

7.  The gravitational acceleration at the surface of Earth, g, can be solved for by using the formula for the gravitational force and Newton’s second law.  The m cancels.  g is the same for all objects at the same R. MATH TOOLS 4.1

8. Newton’s Law of Gravitation Newton’s law of gravitation states: Two bodies attract each other with a force that is directly proportional the product of their masses and is inversely proportional to the square of the distance between them. g ~ 10 m/s 2 “the acceleration of gravity” & g x m is your weight!

9. Concept Quiz—Gravity and Weight Your weight equals the force between you and Earth. Suppose you weigh 600 newtons. The force you exert on Earth is: A.600 newtons. B.much smaller than 600 newtons because your mass is much less than Earth’s. C.exactly zero, since only massive objects have gravity.

10. Concept Quiz—Earth and Moon Earth and the Moon have a gravitational force between them. The mass of the Moon is 1.2 percent of that of the Earth. Which statement is incorrect? A.The force on the Moon is much larger than that on Earth. B.The forces are equal size, even though the masses are different. C.The Moon has a larger acceleration than Earth.

11.  Gravity works on every part of every body.  Therefore, self-gravity exists within a planet.  This produces internal forces, which hold the planet together. CONNECTIONS 4.1

12.  There’s a special case: spherically symmetric bodies.  Force from a spherically symmetric body is the same as from a point mass at the center. CONNECTIONS 4.1

13.  The velocity of an object traveling in a circular orbit can be found by equating the gravitational force and the resulting centripetal force.  This yields:  You can solve for the period by noting that  This yields Kepler’s third law: MATH TOOLS 4.2

14.  In order to leave a planet’s surface, an object must achieve a velocity greater than the planet’s escape velocity.  Therefore, Earth’s escape velocity is MATH TOOLS 4.3

15.  Newton derived Kepler’s laws from his law of gravity.  Physical laws explain Kepler’s empirical results:  Distant planets orbit more slowly; the harmonic law and the law of equal areas result.  Newton’s laws were tested by Kepler’s observations.

17.  The gravitational interaction of three bodies leads to Lagrangian equilibrium points.  These are special orbital resonances where the object at that point orbits in lockstep.  SOHO is near L 1. CONNECTIONS 4.2