Download Kepler`s Laws

Announcements
PHYS 1411 Introduction to Astronomy
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Homework 1 Extended till February 5th.
Homework 2 is assigned on MindTap: Due Feb. 10th
Homework 3 is assigned on MindTap: Due Feb. 14th
Help Session: Every Wednesday from 5-6pm
Exam 1: Wednesday February 15th during class
– Multiple Choice Questions (40 or 50) on whatever we cover by
the exam date
– Bring a Green Scantron Sheet, No. 2 pencil
– Can use a calculator if needed.
– Will provide conversion and constants if needed.
– No cell phones or calculator on cell phone, laptops, index card,
cheat sheet etc. allowed
– Be prepared to present School ID if asked.
– There is no review session: use the help sessions and questions
we do in class and those assigned on homework.
Cycles of Moon
History of Astronomy
Chapter 3
This chapter is not part of this
class syllabus
Chapter 4
Topics in Chapter 4
Chapter 4 talks about the history of
Astronomy and the development of the
model of the solar system. For this class
only the following topics are needed.
• Overview of the model of solar system
• Parallax
• Kepler’s Laws of Planetary Motion
• Please study the rest of the topics on your
own
Model of the Solar System
The early Greek philosophers believed that the Earth was
in the center of the solar system and all the planets and
sun revolved around it.
http://ecsst.blogspot.com/
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First Observational Challenge to Geocentric Model
Attempts to Explain Retrograde Motion
• ~140 BC: Ptolemy perfects the geocentric model of the solar system
– Uses epicycles to explain retrograde motion.
– Note the displacement of Earth from the center o f the circle.
– Each epicycle has a different rate
Ptolemy’s Solar System Model
The Copernican Revolution
The Copernican Universe
The Eye is Inefficient
• The early Greek philosophers believed
that the earth did not moved because their
eyes could not see the motion of stars
• The telescope was not invented yet.
• So they could not decide which model
(heliocentric or geocentric) was correct.
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What is Parallax?
Apparent Motion of Stars
• After the invention of the
telescope it became known that a
foreground star appeared to move
with respect to background stars
during the course of a year.
• This let the acceptance of
heliocentric model
• Parallax can be used to find
distances to nearby stars. We will
look at it in detail in chapter
“Properties of Stars”
Attendance
Johannes Kepler (1571 – 1630)
• Used the precise observational tables of
Tycho Brahe to study planetary motion
mathematically
• Found a consistent description by
abandoning both:
– Circular motion
– Uniform motion
• Planets move around the sun on elliptical
paths, with non-uniform velocities
Campus.kellerisd.net
Kepler’s Laws of Planetary Motion
Kepler’s Laws of Planetary Motion
1. The orbits of the planets are ellipses with the
sun at one focus.
c
Eccentricity e = c/a
Thinglink.com
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Ellipse
How to find Eccentricity
Eccentricities of Ellipses
1)
2)
e = 0.02
3)
e = 0.1
Eccentricities of Planetary Orbits
Orbits of planets are virtually
indistinguishable from circles:
e = 0.2
Earth: e = 0.0167
Most extreme example:
Pluto: e = 0.248
5)
4)
e = 0.4
e = 0.6
Kepler’s First Law of Planetary
Motion
Kepler’s Second Law of Planetary
Motion
• A line from a planet to the Sun sweeps
over equal areas in equal intervals of time
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Keplers Third Law
Keplers Third Law
• A planet’s orbital period (P) squared is
proportional to its average distance from the
sun (a) cubed:
(Py = period in years; aAU =
distance in AU)
Py2 = aAU3
Schools.wiki.com
Kepler’s Third Law of Planetary
Motion
• A planet’s orbital period squared is
proportional to its average distance from
the Sun cubed
ClassAction: Astronomy Education at the University of Nebraska-Lincoln Web Site (http://astro.unl.edu)
Planetary Orbits Worksheet
http://astro.unl.edu/naap/pos/animations/kepler.html
ClassAction: Astronomy Education at the University of Nebraska-Lincoln Web Site (http://astro.unl.edu)
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ClassAction: Astronomy Education at the University of Nebraska-Lincoln Web Site (http://astro.unl.edu)
ClassAction: Astronomy Education at the University of Nebraska-Lincoln Web Site (http://astro.unl.edu)
Acknowledgment
• The slides in this lecture is for Tarleton:
PHYS1411/PHYS1403 class use only
• Images and text material have been
borrowed from various sources with
appropriate citations in the slides,
including PowerPoint slides from
Seeds/Backman text that has been
adopted for class.
ClassAction: Astronomy Education at the University of Nebraska-Lincoln Web Site (http://astro.unl.edu)
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