PHYS16 – Lecture 28

Kepler’s Laws and Fluids November 12, 2010

Kepler’s Laws

Orbits are elliptical

• Eccentricity = 0, then circular

• Eccentricity = 1 then linear

• Most planets have an eccentricity close to 0

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.

constantdtdA

Example Question: Earth Speed

• Where is the speed of the earth the greatest?

D

A C

B

Period-squared is proportional to a3

constant

4

v

3

2

32

2

22

2

aT

rGM

T

rGMr

rGM

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 daysB) 224 daysC) 264 daysD) 294 days

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) FasterB) SameC) SlowerD) 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 orthe Earth’s speed is faster in winter…

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 a3

Fluids

This Week

• Pressure and Pascal’s Principle• Buoyant Force and Archimedes’ Principle• Equation of Continuity• Bernoulli’s Equation

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

Pressure

• Pressure (p) – Force per unit area– Direction of pressure is normal to a surface– Unit is Pa=N/m2

• Air Pressure = 1E5 Pa = 1 atm = 760 mmHg

AFP

http://www.school-for-champions.com/science/pressure.htm

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)

N 130m) )(0.02Pa)( 5E1()( 22

FrPPAF

So why doesn’t the pop can get crushed?

Pascal’s Principle

• Pressure change in a confined fluid is the same at all points in the fluid

• Mechanical advantage in hydraulic lift = Abig/Asmall

http://www.vectorsite.net/tpecp_08.html

m = 1 kg

Example: Cracking an Egg

• If I apply equal force to all sides of an egg, will it crack?

No!

http://randywakeman.com/TragicEgg.jpg

Main Points

• Pressure = Force/Area• Pressure change in a confined fluid is the same

at all points