Astronomy
Chapter 2
Gravitational Waltz of the Planets
I.
Essential Questions


II.
How do the planets orbit the Sun?
How did the heliocentric model replace the geocentric model?
Learning Targets (I can…)
1. Describe the shapes of the orbits of the planets around the Sun.
2. Explain the difference between direct motion and retrograde
motion.
3. Explain the difference between synodic and sidereal motion.
4. State Kepler’s three laws of planetary motion.
5. State and identify examples of Newton’s three laws of motion.
6. Explain why the planets continue to orbit the Sun.
7. Describe Galileo’s important contributions to the heliocentric
model.
8. Compare and contrast the Ptolemaic and Copernican
cosmologies using evidence for each.
III.
Key Terms
Angular momentum
Configuration
Ellipse
focus of an ellipse
cosmology
Hyperbola
Kepler’s laws
Law of inertia
Newton’s laws of motion
Opposition
Parallax
retrograde motion
Semimajor axis
Superior conjunction
Aphelion
Conjunction
Elongation
Gravity
heliocentric
inferior conjunction
law of equal areas
law of universal gravitation
Occam’s razor
parabola
Perihelion
direct motion
sidereal period
synodic period
IV.
General Questions
A.
Motion of the Planets
1.
2.
3.
4.
5.
6.
7.
8.
What are the planetary configurations and to which location
does each refer?
Explain the phases of Venus and change in its angular diameter
as seen from Earth.
What is the shape of the Earth’s orbit around the Sun?
Do planets orbit the Sun at constant speeds?
Do planets orbit the Sun at the same speed?
How much force does it take to keep an object moving in a
straight line at a constant speed?
What are Kepler’s three laws of planetary motion? What was so
significant about his findings? What is an ellipse?
Newton’s three laws of motion, and Newton’s Universal law of
gravitation, explain how and why the planets orbit the Sun.
Look at the following table and answer the following questions.
9.
10.
For which planet is the sidereal year the longest? The shortest?
Explain why.
What is the sidereal orbit for Venus and what is its synodic
period? Explain why is there a difference. Why is the synodic
period for Neptune very close to the length of the Earth year?
Sidereal
Period (year)
Mercury 0.241
Venus 0.615
Earth
1
0.0748
Moon
1.881
Mars
1 Ceres 4.600
Jupiter 11.87
Saturn 29.45
Uranus 84.07
Neptune 164.9
248.1
Pluto
Synodic Period
(year)
0.317
1.599
—
0.0809
2.135
1.278
1.092
1.035
1.012
1.006
1.004
Synodic
Period (days)
115.9
583.9
—
29.5306
780.0
466.7
398.9
378.1
369.7
367.5
366.7
"orbital period." The Columbia Electronic Encyclopedia, Sixth Edition. Columbia University Press., 2003.
Answers.com 24 Oct. 2005. http://www.answers.com/topic/orbital-period
B.
Geocentric vs. Heliocentric Models
11.
Explain the contribution to astronomy that each of the following
made:
Aristarchus
Ptolemy
Brahe
Kepler
12.
13.
Aristotle
Copernicus
Galileo
Newton
Compare and contrast the geocentric and heliocentric models.
Why is the heliocentric model accepted today? What
prevented the acceptance of the heliocentric model in the
past?
What is parallax and why is it important to the heliocentric
model?
Astronomy
Chapter 2 Questions
1.
Explain the contribution to astronomy that each of the following
made:
Pythagoras: He was the first to use mathematics to describe natural
phenomena.
Aristarchus: He was the first person noted to promote the heliocentric
model of the universe.
Aristotle: Major proponent of the geocentric model, thought the stars
were fixed in a crystal sphere.
Ptolemy: Wrote the Almagast, where he set forth the geocentric model
in print. He used deferents and epicycles to explain the direct and
retrograde motion of the planets as they orbited the Earth.
Copernicus: Wrote the De Revolutionibus Orbium Coelestium, where he
set forth the heliocentric model, indicating that Mercury and Venus are
inside the Earth’s orbit of the Sun and that Mars, Jupiter and Saturn are
outside the Earth’s orbit.
Brahe: Amassed a huge collection of data regarding the position and
motion of planets at his observatory Uranaborg.
Galileo: First practical use of the telescope. Galileo’s observations added
support to the heliocentric model. Galileo observed phases of Venus, four
Moons orbiting Jupiter (not the Earth), sunspots and irregular surface of the
Moon. These observations dispelled the notions of celestial perfection
and that all planets and satellites orbit the Earth.
Kepler: Using Brahe’s data, he correctly proved that planetary orbits are
elliptical and not perfectly circular. He developed three laws to explain
how the planets move, but not why.
Newton: Wrote Principia and Optiks. Explained why the planets move by
developing the universal law of gravitation (a force of attraction exists
between all objects with mass) and three laws of motion (law of inertia, F
= ma and for every action force there is an equal and opposite reaction
force). Newton also explained that white light is composed of a series of
colors, most easily recognized as roy g biv).
2.
Compare and contrast the geocentric and heliocentric models.
Why is the heliocentric model accepted today? What prevented the
acceptance of the heliocentric model in the past?
These models are only similar in that they attempt to explain the motion of
the universe.
Geocentric Model
vs.
Heliocentric Model
All planets orbit the Earth
Earth/planets orbit the Sun
Direct and Retrograde motion
of planets is explained using
epicycles and deferents
Direct and retrograde motion
explained by orbit around Sun
Planets orbit the Sun in perfect circles
Planets orbit the Sun in ellipses
Stars are fixed on a crystal sphere
Equidistant from the Earth
Stars are present at different
distances as supported by
parallax measurement
The Earth does not move
Newton’s laws of motion
Indicated that we are moving
but so is everything around us.
Everything falls toward the Earth
Gravity causes objects to be
attracted to one other (you to
Earth; Earth to Sun)
All objects, even moons orbit the Earth
Galileo’s observations of four
moons of Jupiter and the
phases of Venus indicate that
objects orbit objects other
than the Earth.
The heliocentric model is accepted today because of observational
evidence supported by mathematical predictions. The science (or our
knowledge) has increased.
Acceptance of the heliocentric model encountered technological
boundaries which limited the understanding of the universe at that time.
The telescope, mathematics, the printing press and the pursuit of
knowledge via empirical methods led to new understandings.
3.
What is parallax and why is it important to the heliocentric model?
Parallax is the variation in angle between an object that is viewed from
the Earth at different times.
Parallax is important to the heliocentric model because according to the
model, not every star is equidistant from Earth. The change in the parallax
angle would indicate variable distances (the greater the angle, the closer
the object). The parallax angle for stars cannot be viewed by the
unaided eye. The telescope made it possible to measure this previously
unseen angle or change.
4.
What is the difference between kilometers, AU, light-years and
parsecs? Which measure or measures is/are best for describing distances
to stars and why?
The difference is in the astronomical distance to be measured. Kilometers
can be used for orbiting satellites and even the distance to the Moon.
Astronomical units (or AU) are used to describe distances within the solar
system. One AU is the average distance from the Earth to the Sun. Lightyears and the larger parsecs are much larger that kilometers. A light-year
is the distance light travels in one year (in a vacuum). A parsec is 3.26
light years.
Light-years or parsecs are distances used to describe stars beyond the
reaches of the solar system.
5.
Using Kepler’s three laws, Newton’s three laws of motion, and
Newton’s Universal law of gravitation, explain how and why the planets
orbit the Sun.



Kepler’s first law: The orbit of a planet is an ellipse with the Sun at
one focus.
Kepler’s second law: A line joining a planet and the Sun sweeps out
equal areas in equal intervals of time. Perihelion (closest to Sun)
and aphelion (furthest from Sun) . A planet moves most rapidly
when it is nearest the Sun and most slowly when it is farthest from
the Sun.
Kepler’s third law: The square of a planet’s sidereal period around
the Sun is directly proportional to the cube of the length of its orbit’s
semimajor axis.
--Kepler determined that planets have elliptical orbits.
--Kepler’s laws accurately described how planets move.
--So, planets do not travel at constant speeds, do not orbit in circles and
do not orbit the Sun at the same speed.
--Most planets have a low eccentricity. 0 to 1 (0 is a circle, 1 is flat).
--Kepler’s laws apply to all orbiting objects.
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Newton’s 1st law: There must be an outside force acting on planets
to keep them from moving in a straight line (change direction and
stay in orbit)
Newton’s 3rd Law: Planets pulling on each other will pull with the
equal and opposite force.
Newton’s 2nd Law: Planets with the smaller mass will be more easily
accelerated than the larger mass(F = ma)
--The force required to cause the planets to orbit the Sun is called gravity
(the force of attraction of one object to another).
Newton universal law of gravitation: Two bodies attract each other with a
force that is directly proportional to the product of their masses and
inversely proportional to the square of the distance between them.
--The speed of the orbiting planet is just fast enough to keep from falling
into the Sun and just slow enough to keep from moving in a straight line
(no escape velocity).
--Newton’s precise description of the action gravity accounts for Kepler’s
findings. It provides an explanation of why the planets orbit the Sun.
6.
What is the difference between a superior and inferior orbit? What
are the planetary configurations and to which location does each refer?
--A superior planet is beyond the orbit of the Earth, an inferior planet is
inside the Earth’s orbit.
--Planetary configurations are the locations or geometric configurations of
the planets with respect to the Sun and Earth.
--Superior planets have conjunction and opposition
--Inferior planets have inferior and superior conjunction, and greatest
eastern and western elongation.
7.
For which planet is the sidereal year the longest? The shortest?
Explain why.
Pluto has the longest sidereal year, Mercury has the shortest. This is
because as the orbital path for planets increases away from the Sun, so
will the time it takes for the planet to complete one orbit around the Sun.
8.
What is the sidereal orbit for Venus and what is its synodic period?
Explain why is there a difference. Why is the synodic period for Neptune
very close to the length of the Earth year?
Venus: sidereal orbit = .615 year
synodic = 584 days
It makes sense that Venus takes less time to orbit the Sun with respect to
the stars that does the Earth. The synodic period represents the time it
takes Venus to move from two successive identical configurations as
viewed from the Earth, which is also orbiting the Sun. This causes the
difference in days.
The synodic period for Neptune is close to the length of an Earth year
because relative to the time it takes Earth to orbit the Sun, Neptune moves
only a small distance along its orbital path.