1. PHYS16 – Lecture 28 Kepler’s Laws and Fluids November 12, 2010

2. Kepler’s Laws

3. Orbits are elliptical Eccentricity = 0, then circular Eccentricity = 1 then linear Most planets have an eccentricity close to 0

4. Equal areas in equal times The area of the triangle swept out by the object is equal for equal amounts of time The further the object is from the sun the lower the speed.

5. Example Question: Earth Speed Where is the speed of the earth the greatest? D AC B

6. Period-squared is proportional to a 3

7. Example Question: Venus’ Period Venus has a semi-major axis that is 0.723 times the Earth’s semi major axis. How long does it take Venus to orbit the Sun? A)204 days B)224 days C)264 days D)294 days

8. Example Question: Seasons If the earth spends two less days in the winter half of the orbit than the summer half of the orbit (for N. hemisphere), what is its speed in winter vs. summer? A)Faster B)Same C)Slower D)Not enough information Supposed to be sweeping out equal areas in equal times. But if times aren’t equal, then either the areas aren’t equal or the Earth’s speed is faster in winter…

9. Main Points Gravitational Force and Potential Satellites – Orbital energy – Escape velocity – Geostationary orbits Kepler’s Laws – Orbits are elliptical – Orbits sweep out equal area in equal time – Orbital period-squared is proportional at a 3

10. Fluids

11. This Week Pressure and Pascal’s Principle Buoyant Force and Archimedes’ Principle Equation of Continuity Bernoulli’s Equation

12. Fluids Fluid = a liquid or a gas, a substance that flows What happens when you apply a force to a fluid? – Gas compresses (change density) – Liquids are incompressible http://www.swe.org/iac/images/liquid-gas2.jpg

13. Pressure Pressure (p) – Force per unit area – Direction of pressure is normal to a surface – Unit is Pa=N/m 2 Air Pressure = 1E5 Pa = 1 atm = 760 mmHg http://www.school-for-champions.com/science/pressure.htm

14. Example: Force due to Air Pressure What is the force on the lid of a pop can due to air pressure ? (radius = r = 0.020 m) So why doesn’t the pop can get crushed?

15. Pascal’s Principle Pressure change in a confined fluid is the same at all points in the fluid Mechanical advantage in hydraulic lift = A big /A small http://www.vectorsite.net/tpecp_08.html m = 1 kg

16. Example: Cracking an Egg If I apply equal force to all sides of an egg, will it crack? No! http://randywakeman.com/TragicEgg.jpg

17. Main Points Pressure = Force/Area Pressure change in a confined fluid is the same at all points