Astronomy 104: Lecture 5 (Slide 1)

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Understanding Orbits: Kepler, Galileo, and Newtonian Mechanics
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February 8, 1999

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Astronomy 104: Lecture 5 (Slide 2)

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Announcements

PASS IN HOMEWORK #1

Write your section number at the top of your homework

Start on observing project.

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Astronomy 104: Lecture 5 (Slide 3)

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Johannes Kepler (1571--1630):

Worked with Tycho
Good at Math
Wanted to find simple mathematical relations to explain motions of planets
Tycho didn't like him because he wasn't convinced of Ptolemaic (geocentric) model. Set him to work on Mars, the most confusing planet at the time
Found the solution to the orbits of the planets, doing away with epicycles and the geocentric model. Gave best answers too.
Kepler's Three Laws

Planets orbit Sun in an ellipse with the Sun at one focus
A line joining the planet to the Sun sweeps out equal areas in equal intervals of time
P² = a³ (Period, semi major axis)

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Astronomy 104: Lecture 5 (Slide 4)

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Kepler's 1st Law: Ellipses

To draw an ellipse, tie a loop of string loosely between two tacks
Tacks are at the foci (plural of focus)
Major axis is long dimension
Minor axis is short dimension
Semimajor axis is half of the major axes, this is the average distance between the planet and the Sun
e is eccentricity
Aphelion analogous to apogee (farthest out)
Perihelion analogous to perigee (closest in)

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Astronomy 104: Lecture 5 (Slide 5)

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Kepler's Second Law: Equal Areas in Equal Times

It takes the same amount of time to go from point A to point B as it does to go from point C to point D
The areas of those shapes are the same

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Astronomy 104: Lecture 5 (Slide 6)

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Kepler's 3rd law (Sun/planet form): P²=a³

P = planet's sidereal period (the time it takes to complete one orbit with respect to the stars--use years)
a = planet's semimajor axis (use AU)
Example:

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Astronomy 104: Lecture 5 (Slide 7)

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Galileo Galilei (1564-1642)

Did not invent telescope
First to point it at the sky and write about what he saw:

mountains on the moon
Dim haze of Milky Way is actually LOTS of individual stars
Phases of Venus, important evidence conclusively disproving Ptolemaic system
Moons orbiting around Jupiter (Galiliean moons)

Put under house arrest by Catholic Church for heretical ideas. Recently pardoned.

Phases of venus:

What's really going on:

Ptolemaic model--Would never see Gibbous phase:

Jupiter and the Galilean moons seen with a small telescope:

Jupiter's moons move!

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Astronomy 104: Lecture 5 (Slide 8)

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Isaac Newton (1642--1727):

Primarily a physicist
Dissected every-day phenomena into laws and equations that reflected underlying principles
Newton's laws of motion:

1) A body at rest remains at rest, a body in motion remains in motion with a constant velocity (same direction and speed) unless acted on by a net outside force
2) F = ma
3) For every action (force), there is an equal and opposite reaction

Newton's Universal law of gravitation (the apple thing):

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Astronomy 104: Lecture 5 (Slide 9)

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Newton's 1st Law of Motion

1) A body at rest remains at rest, a body in motion remains in motion with a constant velocity (same direction and speed) unless acted on by a net outside force

Picture a hockey puck on the ice.

Friction, which normally slows things down, can be part of a net outside force

Velocity represents both direction and speed.

Uniform circular motion: speed same but velocity always changing

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Astronomy 104: Lecture 5 (Slide 10)

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Newton's 2nd Law of Motion
F = ma

F = net force

m = mass of object

a = acceleration of object

Mass is different than weight

Your mass is the same anywhere in the universe
Your weight depends on what planet you are on (picture moon walkers)

Acceleration is change in velocity

pushing a car: you provide net force, car starts moving, speed changes
circular orbit: gravity is net force, direction of motion changes

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Astronomy 104: Lecture 5 (Slide 11)

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Newton's 3rd Law of Motion
For every action (force), there is an equal and opposite reaction

When you push your car, it pushes back (otherwise you would not feel)

don't confuse pushing (Force) with acceleration (change in motion)

Sitting in your chair, you exert a force down and the chair pushes back up!

what is the net force on you right now?

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Astronomy 104:Lecture 5 (Slide 14)

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Newton's Universal Law of Gravitation

Gravity is like an invisible string between all objects
Only notice the effects for very large objects

Just recognizing the that Earth, Sun, etc. are "objects" was revolutionary

G = universal constant of gravitation

G = 6.67 x 10^-11 newton m²/kg²

F = force felt by each object is equal but in opposite directions (Newton's 3nd law)
m₁and m₂ are the masses of the objects
r = distance between objects

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Astronomy 104: Lecture 5 (slide 13)

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Newtonian Mechanics

are the combination of Newton's laws of motion and gravity
Explain motion on earth and in the Heavens
F = ma for each object (Newton's 2nd law)

If m is big (Sun) a is small (it doesn't move much)

Can be used to improve Kepler's 3rd law to work with any two body orbiting system

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Astronomy 104:Lecture 5 (Slide 14)

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Predictions based on Newtonian Mechanics

Orbits are not just ellipses but conic sections
The planet Neptune because its gravity was disturbing the orbit of Uranus

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