Astronomy 1020-H Stellar Astronomy Spring_2014 Day-8

1. Astronomy 1020-H Stellar Astronomy Spring_2014 Day-8

3. Course Announcements • Smartworks Chapters 3, 4: Due Fri. 2/7 • Exam 1: Friday 2/7 – Chapters 1-4 • 1st Quarter Observing night – Thursday, 2/6 at 7:30pm – Archwood parking lot or Atrium.

4. Newton’sFirstLaw of Motion A body remains at rest or moves in a straight line at a constant speed unless acted upon by an outside (net) force. A rockets will coast in space along a straight line at constant speed. A hockey puck glides across the ice at constant speed until it hits something

5. Newton’sSecondLaw of Motion (net)Force = mass x acceleration or Fnet = m x a Acceleration is the rate of change in velocity – or how quickly your motion is changing. Three accelerators in your car!!

6. Newton’sThirdLaw of Motion Whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body. Don’t need a rocket launch pad! The Bug and the Windshield – who is having the worse day?

8. Newton’s Laws of Motion & Gravitation • All my favorite Projectiles behave like this!!! Velocity Force Acceleration

9. The gravitational force results in an acceleration. • All objects on Earth fall with the same acceleration known as g. • g = 9.8 m/s2

10. Orbits describe one body falling around another. • The less massive object is a satellite of the more massive object. • The two bodies orbit a common center of mass. • For a much smaller satellite, the center of mass is inside the more massive body.

11. An astronaut inside an orbiting space shuttle will experience free fall because he is falling around Earth at the same rate as the shuttle. • He is not weightless.

12. Gravity provides the centripetal force that holds a satellite in its orbit. • Uniform circular motion: moving on a circular pathat constant speed. • Still experiencing an acceleration since the direction is constantly changing.

13. Circles and ellipses are bound orbits. • Objects with higher orbital speeds can escape bound orbits to be in unbound orbits. • Parabolas and hyperbolas are examples.

14. 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. What the ….? I thought I understood gravity?

15. Newton’s Law of Gravitation • To figure out the gravitational force just multiply the mass of the two things together then divide by the distance they are apart (squared). m1 d m2

16. 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? • It would be half as strong. • It would be one-fourth as strong. • It would be twice as strong. • It would be four times as strong. • It would not change.

17. MATH TOOLS 4.1 • 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.

18. Newton’s Law of Gravitation g ~ 10 m/s2 “the acceleration of gravity” & g x m is your weight! • 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.

19. 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: • 600 newtons. • much smaller than 600 newtons because your mass is much less than Earth’s. • exactly zero, since only massive objects have gravity.

20. 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? • The force on the Moon is much larger than that on Earth. • The forces are equal size, even though the masses are different. • The Moon has a larger acceleration than Earth.

21. CONNECTIONS 4.1 • Gravity works on every part of every body. • Therefore, self-gravityexists within a planet. • This produces internal forces, which hold the planet together.

22. CONNECTIONS 4.1 • 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.

23. MATH TOOLS 4.2 • 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:

24. MATH TOOLS 4.3 • 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

25. 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.

27. CONNECTIONS 4.2 • 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 L1.