Exploring Astronomy and Physics: Orbits, Matter Phases, and Newton's Laws

1. aphelion perihelion FF’ a b 2a • e = FF’ =aphelion - perihelion 2a 2a

2. Homework #3 An asteroids closest approach to the Sun (perihelion) is 2 AU, and farthest distance from the Sun (aphelion) is 4 AU. • What is the semi major axis of its orbit? • What is the period of its orbit? • What is it’s ellipticity?

3. Phases of Matter • the phases • solid • liquid • gas • plasma depend on how tightly bound the atoms and/or molecules are • As temperature increases, these bonds are loosened:

4. Electron Energy • Electrons that are bound in atoms can gain or lose energy. • When electrons have the lowest energy possible, we say the atom is in the ground state. • When electrons have more energy than this, the atom is in an excited state. • When electrons gain enough energy to escape the nucleus, the atom is ionized.

5. Electron Energy Levels • Electrons can not have just any energy while orbiting the nucleus. • Only certain energy values are allowed. • Electrons may only gain or lose specific amounts of energy. • Each element (atom and ion) has its own distinctive set or pattern of energy levels. • This diagram depicts the energy levels of Hydrogen. 0.0 eV -0.85 eV -1.51 eV -3.40 eV -13.60 eV

6. n En (eV) 1 -13.60 2 -3.40 3 -1.51 4 -0.85 5 -0.38 … … Hydrogen Ground state 1st excited state 2nd 3rd 4th n=1 n=3 n=4 n=2 … En = -13.6 / n2

7. n=2 n=3 Photons are created when an electron jumps from one energy level to a lower one

9. n En (eV) 1 -13.60 2 -3.40 3 -1.51 4 -0.85 5 -0.38 … … En = -13.6 / n2 (eV) (Rydbergs formula) DE(3g 2) = E3-E2 =-1.51-(-3.40) = 1.89 eV

10. Important years for astronomy

11. Objects in Motion • 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, i.e. a change in either speed or direction is an acceleration [m/s2]

12. 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.

13. t=0s; v=0m/s t=1s; v=10 m/s t=2s; v=20m/s You may remember my experiment…

14. 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. Galileo was right!

15. Universal Laws of Motion “If I have seen farther than others, it is because I have stood on the shoulders of giants.” Sir Isaac Newton (1642 – 1727) Physicist

16. Sir Isaac Newton (1642-1727) • Perhaps the greatest genius of all time • Invented the reflecting telescope • Invented calculus • Connected gravity and planetary forces Philosophiae naturalis principia mathematica

17. Forces • Forces change the motion of objects. • As long as the object’s mass does not change, the force causes a change in velocity, or an… acceleration

18. Newton’s Laws of Motion # 1 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.

19. F a a Newton’s Laws of Motion # 2 The change in a body’s velocity due to an applied force is in the same direction as the force and proportional to it. The proportionality constant is mass: F = m a

20. Gravity: F = mg g is the gravitational acceleration (10 m/s2)

21. m g h Gravitational Potential Energy E = F n h = mg nh

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

23. Newton’s Laws of Motion