Title: Chapter 2: The Copernican Revolution The Birth of Modern Science
1Chapter 2 The Copernican RevolutionThe Birth of
Modern Science
- Ancient Astronomy
- Models of the Solar System
- Laws of Planetary Motion
- Newtons Laws
- Laws of Motion
- Law of Gravitation
2- The universe is full of magical things,
patiently waiting for our wits to grow
sharper. Eden Philpotts
3Cosmology study of the structure and
evolution of the universe
- Ancient civilizations
universe solar system fixed stars - Today
universe totality of all space,
time, matter and energy
4There are three principle means of acquiring
knowledge. observation of nature, reflection,
and experimentation.Observation collects
factsreflection combines themexperimentation
verifies the result of that combination.
- Denis Diderot (1713 - 1784)
5Scientific Method
Form theory
Test theory
6Astronomy in Ancient Times
- Ancient people had a better, clearer chance to
study the sky and see the patterns of stars
(constellations) than we do today. - Drew pictures of constellations
created stories to account for the figures being
in the sky. - Used stars and constellations for navigation.
- Noticed changes in Moons shape and position
against the stars. - Created accurate calendars of seasons.
7Ancient Astronomy
- Stonehenge on the summer solstice.
- As seen from the center of the stone circle,
- the Sun rises directly over the "heel stone" on
the longest day of the year.
The Big Horn Medicine Wheel in Wyoming, built by
the Plains Indians. Its spokes and rock piles
are aligned with the rising and setting of the
Sun and other stars.
8Astronomy in Early Americas
- Maya Indians developed written language and
number system. - Recorded motions of Sun, Moon, and planets --
especially Venus. - Fragments of astronomical observations recorded
in picture books made of tree bark show that
Mayans had learned to predict solar and lunar
eclipses and the path of Venus. - One Mayan calendar more accurate than those of
Spanish.
9Ancient Contributions to Astronomy
- Egyptians
- recorded interval of floods on Nile
- every 365 days
- noted Sirius rose with Sun when floods due
- invented sundials to measure time of day from
movement of the Sun. - Babylonians
- first people to make detailed records of
movements of Mercury, Venus, Mars, Jupiter,
Saturn - only planets visible until telescope
10Greek Astronomy
- Probably based on knowledge from Babylonians.
- Thales predicted eclipse of Sun that occurred in
585 B.C. - Around 550 B.C., Pythagoras noted that the
Evening Star and Morning Star were really the
same body (actually planet Venus). - Some Greek astronomers thought the Earth might be
in the shape of a ball and that moonlight was
really reflected sunlight.
11Time Line
- Ancient Greeks
- Pythagoras 6th century B.C.
- Aristotle 348-322 B.C.
- Aristarchus 310-230 B.C.
- Hipparchus 130 B.C.
- Ptolemy A.D. 140
12Pythagorean Paradigm
- The Pythagorean Paradigm had three key points
about the movements of celestial objects - the planets, Sun, Moon and stars move in
perfectly circular orbits - the speed of the planets, Sun, Moon and stars in
the circular orbits is perfectly uniform - the Earth is at the exact center of the motion of
the celestial bodies.
13Aristotles UniverseA Geocentric Model
- Aristotle proposed that
- the heavens were literally composed of
concentric, crystalline spheres - to which the celestial objects were attached
- and which rotated at different velocities,
- with the Earth at the center (geocentric).
The figure illustrates the ordering of the
spheres to which the Sun, Moon, and visible
planets were attached.
14Planetary Motion
- From Earth, planets appear to move wrt fixed
stars and vary greatly in brightness. - Most of the time, planets undergo direct motion -
moving W to E relative to background stars.
- Occasionally, they change direction and
temporarily undergo retrograde motion - motion
from E to W -before looping back.
(retrograde-move)
15Planetary Motion Epicycles and
Deferents
- Retrograde motion was first explained as follows
- the planets were attached, not to the concentric
spheres themselves, but to circles attached to
the concentric spheres, as illustrated in the
adjacent diagram. - These circles were called "Epicycles",and the
concentric spheres to which they were attached
were termed the "Deferents". - (epicycle-move)
16Motions of Mercury and Venus
- Mercury and Venus exhibit a special motion, not
observed in the other planets. - They always remain close to the Sun,
first moving away from it, then pausing,
and then moving toward it. - Venus and Mercury can be seen in the morning and
evening skies, but never at midnight (except in
polar latitudes). - Venus never gets gt48o from the Sun Mercury more
distant than 28o.
17Epicycles, Deferents, and the Orbits of Mercury
and Venus
- Special features of the orbits of Mercury and
Venus modeled by requiring that the center of the
epicycle of the planet be firmly attached to the
line joining the Earth and Sun.
18Epicycle/Deferent Modifications
- In actual models, the center of the epicycle
moved with uniform circular motion, not around
the center of the deferent, but around a point
that was displaced by some distance from the
center of the deferent.
This modification predicted planetary motions
that more closely matched the observed motions.
19Further Modifiations
- In practice, even this was not enough to account
for the detailed motion of the planets on the
celestial sphere! - In more sophisticated epicycle models further
"refinements" were introduced
In some cases, epicycles were themselves placed
on epicycles, as illustrated in the adjacent
figure. The full Ptolemaic model required 80
different circles!!
20Ptolemy
- 127-151 A.D. in Alexandria
- Accomplishments
- completion of a geocentric model of solar
system that accurately predicts motions of
planets by using combinations of regular circular
motions - invented latitude and longitude (gave
coordinates for 8000 places) - first to orient maps with NORTH at top
and EAST at right - developed magnitude system to describe brightness
of stars that is still used today
21Aristarchus
- 310-230 B.C.
- Applied geometry to find
- distance to Moon
- Directly measure angular diameter
- Calculate linear diameter using lunar eclipse
- relative distances and sizes of the Sun and Moon
- ratio of distances to Sun and Moon by observing
angle between the Sun and Moon at first or third
quarter Moon. - Proposed that the Sun is stationary and that the
Earth orbits the Sun and spins on its own axis
once a day.
22Hipparchus
- 190-125 B.C.
- Often called greatest astronomer of
antiquity. - Contributions to astronomy
- improved on Aristarchus method for calculating
the distances to the Sun and Moon, - improved determination of the length of the year,
- extensive observations and theories of motions of
the Sun and Moon, - earliest systematic catalog of brighter stars ,
- first estimate of precession shift in the vernal
equinox.
23Time Line
- Ancient Greeks
- Pythagoras 6th century B.C.
- Aristotle 348-322 B.C.
- Aristarchus 310-230 B.C.
- Hipparchus 130 B.C.
- Ptolemy A.D. 140
- Dark Ages A.D. 5th - 10th century
- Arabs translated books, planets positions
- China 1054 A.D. supernova Crab Nebula
24Heliocentric Model - Copernicus
- In 1543, Copernicus proposed that the Sun,
not the Earth, is the center of the solar system.
- Such a model is called a heliocentric system.
- Ordering of planets known to Copernicus in this
new system is illustrated in the figure. - Represents modern ordering of planets.
- (copernican-move)
25Stellar Parallax
- Stars should appear to change their position with
the respect to the other background stars as the
Earth moved about its orbit. - In Copernicus day, no stellar parallax was
observed, so the Copernican model was considered
to be only a convenient calculation tool for
planetary motion. - In 1838, Friedrich Wilhelm Bessel succeeded in
measuring the parallax of the nearby, faint star
61 Cygni. ( penny at 4 miles)
26Time Line
- Ancient Greeks
Pythagoras 6th century B.C.
Aristotle 348-322
B.C. Aristarchus 310-230
B.C. Ptolemy
A.D. 140 - Dark Ages A.D. 5th - 10th century
- Renaissance Copernicus
(1473-1543) Tycho
Brahe Kepler Galileo
(1546-1601) (1571-1630)
(1564-1642) Newton
(1642-1727)
27Galileo Galilei
- Galileo used his telescope to show that Venus
went through a complete set of phases, just like
the Moon. - This observation was among the most important in
human history, for it provided the first
conclusive observational proof that was
consistent with the Copernican system but not the
Ptolemaic system.
28Galileo and Jupiter
- Galileo observed 4 points of light that changed
their positions with time around the planet
Jupiter. - He concluded that these were objects in orbit
around Jupiter. - Galileo called them the Medicea Siderea-the
Medician Stars in honor of Cosimo II de'Medici,
who had become Grand Duke of Tuscany in 1609.
29Proof of the Heliocentric Hypothesis
- In 1729, James Bradley (British Astronomer
Royal) discovered a phenomenon called aberration
of starlight while trying to observe stellar
parallax. - In one year, noted 20 shift in a stars
observed position from its true position. - Information yields value for the speed of Earth
through space (18.6 miles/sec).
30Aberration of Starlight
31Time Line
- Ancient Greeks
Pythagoras 6th century B.C.
Aristotle 348-322
B.C. Aristarchus 310-230
B.C. Ptolemy
A.D. 140 - Dark Ages A.D. 5th - 10th century
- Renaissance Copernicus
(1473-1543) Tycho
Brahe Kepler Galileo
(1546-1601) (1571-1630)
(1564-1642) Newton
(1642-1727)
32Tycho Brahe
33Tycho Brahe
- Danish astronomer
- Studied a bright new star in sky that faded
over time. - In 1577, studied a comet
- in trying to determine its distance from Earth by
observing from different locations, noted that
there was no change in apparent position - proposed comet must be farther from Earth than
the Moon. - Built instrument to measure positions of planets
and stars to within one arc minute (1).
34Johannes KeplerLaws of Planetary Motion
35Keplers Firsts
- First to investigate the formation of pictures
with a pin hole camera - First to explain the process of vision by
refraction within the eye - First to formulate eyeglass designing for
nearsightedness and farsightedness - First to explain the use of both eyes for depth
perception. - First to describe real, virtual, upright and
inverted images and magnification - First to explain the principles of how a
telescope works - First to discover and describe the properties of
total internal reflection. - His book Stereometrica Doliorum formed the basis
of integral calculus. - First to explain that the tides are caused by the
Moon. - Tried to use stellar parallax caused by the
Earth's orbit to measure the distance to the
stars the same principle as depth perception.
Today this branch of research is called
astrometry. - First to suggest that the Sun rotates about its
axis in Astronomia Nova. - First to derive the birth year of Christ, that is
now universally accepted. - First to derive logarithms purely based on
mathematics, independent of Napier's tables
published in 1614. - He coined the word "satellite" in his pamphlet
Narratio de Observatis a se quatuor Iovis
sattelitibus erronibus
36Kepler Elliptical orbits
- The amount of "flattening" of the ellipse is the
eccentricity. In the following figure the
ellipses become more eccentric from left to right.
A circle may be viewed as a special case of an
ellipse with zero eccentricity, while as the
ellipse becomes more flattened the eccentricity
approaches one.
(eccentricity-anim)
37Elliptical Orbits and Keplers Laws
- Some orbits in the Solar System cannot be
approximated at all well by circles
- for example, Plutos separation from the Sun
varies by about 50 during its orbit!
According to Keplers First Law, closed orbits
arounda central object under gravity are
ellipses.
38As a planet moves in an elliptical orbit, the Sun
is at one focus (F or F) of the ellipse.
r
C
39The line that connects the planets point of
closest approachto the Sun, the perihelion ...
As a planet moves in an elliptical orbit, the Sun
is at one focus (F or F) of the ellipse
perihelion
v
r
C
40 and its point of greatest separation from the
Sun, the aphelion
As a planet moves in an elliptical orbit, the Sun
is at one focus (F or F) of the ellipse
perihelion
is called the major axis of the ellipse.
v
r
C
aphelion
41The only other thing we need to know about
ellipses is howto identify the length of the
semi-major axis, because that determines the
period of the orbit.
Semi means half, and so the semi-major axis a
is half thelength of the major axis
v
r
C
42Keplers 1st Law
- The orbits of the planets are ellipses, with
the Sun at one focus of the ellipse.
43Keplers 2nd Law
- The line joining the planet to the Sun sweeps out
equal areas in equal times as the planet travels
around the ellipse.
Orbit-anim
44An object in a highly elliptical orbit travels
very slowlywhen it is far out in the Solar
System,
but speeds up as it passes the Sun.
45According to Keplers Second Law,
the line joining the object and the Sun ...
46 sweeps out equal areas in equal intervals of
time.
equal areas
47That is, Keplers Second Law states that
The line joining a planet and the Sun sweeps
outequal areas in equal intervals of time.
48For circular orbits around one particular mass -
e.g. the Sun - we know that the period of the
orbit (the time for one completerevolution)
depended only on the radius r
- this is Keplers 3rd Law
M
For objects orbiting a common central body (e.g.
the Sun)in approximately circular orbits,
r
r
m
v
the orbital period squared is proportional to the
orbital radius cubed.
49Lets see what determines the period for an
elliptical orbit
For elliptical orbits,the period dependsnot on
r, but on thesemi-major axis a instead.
v
r
C
50It turns out that Keplers 3rd Law applies to
all ellipticalorbits, not just circles, if we
replace orbital radiusby semi major axis
For objects orbiting a common central body (e.g.
the Sun)
the orbital period squared is proportional to
the orbital radius cubed.
the orbital period squared is proportional to
the semi major axis cubed.
51So as all of these elliptical orbits have the
same semi-majoraxis a, so they have the same
period.
52So if each of these orbits is around the same
massiveobject (e.g. the Sun),
53So if each of these orbits is around the same
massiveobject (e.g. the Sun),
then as they all have the same semi-major axis
length a,
54So if each of these orbits is around the same
massiveobject (e.g. the Sun),
then as they all have the same semi-major axis
length a,
then, by KeplersThird Law, they have the
sameorbital period.
55Ellipses and Orbits
56Keplers 3rd Law
- The ratio of the squares of the revolution
periods (P) for two planets is equal to the ratio
of the cubes of their semi-major axes (a).
P2 a3 or P2/a3 1 where P is the
planets sidereal orbital period
(in Earth years) and a is the length of
the semi-major axis (in astronomical
units)
57Astronomical Unit
- One astronomical unit is the semi-major
axis of the Earths orbit around the Sun,
essentially the average distance between Earth
and the Sun. - abbreviation A.U.
- one A.U. 150 x 106 km
58Keplers 3rd Law for the Planets
P2 a3 or P2/a3 1
59Planetary Motions
- The planets orbits (except Mercury and Pluto)
are nearly circular. - The further a planet is from the Sun, the greater
its orbital period. - Although derived for the six innermost planets
known at the time, Keplers Laws apply to all
currently known planets. - Do Keplers laws apply to comets orbiting
the Sun? - Do they apply to the moons of Jupiter?
60Chapter 2 Homework
- Text, page 58.
- Problem 1 - accuracy of Tycho Brahes
observations - Use equation on page 26 relating unknown
diameter (uncertainty in position) to angular
diameter (1 1 arc minute), and distance to
object (distance to Moon, Sun, Saturn
from Earth). - distance to Moon - p. 198
- distance to Sun - 1 A.U.
- distance from Sun to Saturn at perihelion
p. A-5, Table 3A - Problem 6 - elliptical orbit of Halleys comet
61Keplers Laws
- 1st Law Each planet moves around the Sun in an
orbit that is an ellipse, with the Sun at one
focus of the ellipse. - 2nd Law The straight line joining a planet and
the Sun sweeps out equal areas in equal intervals
of time. - 3rd Law The squares of the periods of
revolution of the planets are in direct
proportion to the cubes of the semi-major axes of
their orbits.
62Whats important so far?
- Through history, people have used the scientific
method - observe and gather data,
- form theory to explain observations and predict
behavior - test theorys predictions.
- Greeks produced first surviving, recorded models
of universe - geocentric (Earth at center of universe),
- other celestial objects in circular orbits about
Earth, and - move with constant speed in those orbits.
- Geocentric models require complicated
combinations of deferents and epicycles to
explain observed motion of planets. Ptolemaic
model required 80 such combinations. - Copernicus revived heliocentric model of solar
system, but kept circular, constant speed orbits.
63Whats important so far? continued
- Without use of a telescope, Tycho Brahe made very
accurate measurements of the positions of
celestial objects. - Johannes Kepler inherited Brahes data and
determined three empirical laws governing the
motion of orbiting celestial objects. - 1st Law Each planet moves around the Sun in an
orbit that is an ellipse, with the Sun at
one focus of the ellipse. - 2nd Law The straight line joining a planet and
the Sun sweeps out equal areas in equal
intervals of time. - 3rd Law The squares of the periods of revolution
of the planets are in direct proportion to
the cubes of the semi-major axes of their
orbits. - Galileo used a telescope to observe the Moon and
planets. The observed phases of Venus validated
the heliocentric model proposed by Copernicus.
Also discovered 4 moons orbiting Jupiter,
Saturns rings, named lunar surface features,
studied sunspots, noted visible disk of planets
(stars - point sources).
64Why do the planets move according to Keplers
laws? Or, more generally, why do objects move as
they do?
65How do you describe motion?
- A piece of paper and a rubber ball are dropped
from the same height, at the same time. - Predict which will hit the ground first.
- The piece of paper is crushed into a ball,
approximately the same size as the rubber ball.
The paper ball and the rubber ball are dropped
from the same height, at the same time. - Predict which will hit the ground first.
- A wooden block and piece of paper have the same
area. They are dropped at the same time from the
same height. - Describe the motion of the block and of the
paper.
66Historical Views of Motion
- Aristotle two types of motion
- natural motion
- violent motion
- Galileo
- discredited Aristotelian view of motion
Animations Air resistance Free-fall
67Galileo Why do objects move as they do?
speed increases.
speed decreases.
does speed change?
Without friction, NO, the speed is constant!
68What is a natural state of motion for an
object?
Moving with constant velocity?
At rest?
69Inertia and Mass
Inertia a bodys resistance to
a change in its motion.
Mass a measure of an
objects inertia or, loosely, a measure of
the total amount of matter contained within an
object.
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71Newtons First Law
- Called the law of inertia.
- Since time of Aristotle, it was assumed that a
body required some continual action on it to
remain in motion, unless that motion were a part
of natural motion of object. - Newtons first law simplifies concept of motion.
72Animation collision-1st-law
73FORCES and MOTION
- An object will remain
- (a) at rest or
- (b) moving in a straight line at constant speed
until - (c) some net external force acts on it.
74What if there is an outside influence?
- To answer this question, Newton invoked
the concept of a FORCE acting on a body to cause
a change in the motion of the body.
75Forces can act
through contact
instantaneously (baseball bat
making contact with the baseball),
or at a distance.
or continuously (gravity
keeping the baseball from flying into space).
76Velocity and Acceleration
Velocity describes the change in
position of a body divided by the time interval
over which that change occurs.
Velocity is a vector quantity, requiring
both the speed of the body and its direction.
Acceleration The rate of change of
the velocity of a body, any change in
the bodys velocity speeding up, slowing down,
changing direction.
Animation circularmotion
77Newtons Second Law F ma
- Relates
- net external force F applied to object of
mass m - to resulting change in motion of object,
acceleration a.
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79If there is a NET FORCE on an object,how much
will the object accelerate?
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81Questions - Newtons Laws of Motion
- Consider a game of kick-the-can played with two
cans --- one empty and one filled with concrete. - Which can has greater mass?
- If someone came along and kicked the two cans
with exactly the same force, which can would have
a greater acceleration? Explain in terms of
Newtons laws of motion. - What does Newtons 3rd law predict about the
effect on the foot that kicks the two cans?
82Hows That?
- Newtons Laws of Motion
- Inertia
- penny/cup/paper
- F ma
- chair/empty/person
- Action/reaction
- hand-to-hand
83Newton and Gravitation
- Newtons three laws of motion enable calculation
of the acceleration of a body and its motion,
BUT must first calculate the forces. - Celestial bodies do not touch ------ do not
exert forces on each other directly. - Newton proposed that celestial bodies exert an
attractive force on each other at a distance,
across empty space. - He called this force gravitation.
84- Isaac Newton discovered that two bodies share a
gravitational attraction, where the force of
attraction depends on both their masses
85- Both bodies feel the same force, but in opposite
directions.
86This is worth thinking about - for example, drop
a pen to the floor. Newtons laws say that the
force with which the pen is attracting the Earth
is equal and opposite to the force with which
the Earth is attracting the pen, even though the
pen is much lighter than the Earth!
87- Newton also worked out that if you keep the
masses of the two bodies constant, the force of
gravitational attraction depends on the distance
between their centers
mutual force of attraction
88- For any two particular masses, the gravitational
force between them depends on their separation
as
as the separation between the masses is
increased, the gravitational force of
attractionbetween them decreases quickly.
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91Gravity and Weight
- The weight of an object is a measure of the
gravitational force the object feels in the
presence of another object. - For example on Earth, two objects with different
masses will have different weights. - Fg m(GmEarth/rEarth2) mg
- What is the weight of the Earth on us?
92Mass and Weight
- Mass A measure of the total
amount of matter contained within an object
a measure of an objects
inertia. - Weight The force due to gravity
on an object. - Weight and mass are proportional.
- Fg mg where m
mass of the object and g acceleration
of gravity acting on the object
93Free Fall
- If the only force acting on an object is force of
gravity (weight), object is said to be in a state
of free fall. - A heavier body is attracted to the Earth with
more force than a light body. - Does the heavier object free fall faster?
- NO, the acceleration of the body depends on both
- the force applied to it and
- the mass of the object, resisting the motion.
- g F/m F/m
94Newtons Law of Gravitation
- We call the force which keeps the Moon in its
orbit around the Earth gravity.
Sir Isaac Newtons conceptual leap in
understandingof the effects of gravity largely
involved his realizationthat the same force
governs the motion of a falling objecton Earth -
for example, an apple - and the motion of the
Moon in its orbit around the Earth.
95- Your pen dropping to the floor and a satellite in
orbit around the Earth have something in common -
they are both in freefall.
96Planets, Apples, and the Moon
- Some type of force must act on planet otherwise
it would move in a straight line. - Newton analyzed Keplers 2nd Law and saw that the
Sun was the source of this force. - From Keplers 3rd Law, Newton deduced that the
force varied as 1/r2. - The force must act through a distance, and
Newton knew of such a force - the one that
makes an apple accelerate downward from the tree
to the Earth as the apple falls. - Could this force extend all the way to the Moon?
97To see this, lets review Newtons thought
experiment Is it possible to throw an object
into orbit around the Earth?
98On all these trajectories,the projectile is in
free fall under gravity.(If it were not, it
would travel in a straight line - thats
NewtonsFirst Law of Motion.)
99If the ball is not given enough sideways
velocity, its trajectory intercepts the Earth
...
that is, it falls to Earth eventually.
100On the trajectories which make complete orbits,
the projectile is travelling sideways fast
enough ...
On all these trajectories, the projectile is in
free fall.
On all these trajectories, the projectile is in
free fall.
101 that as it falls, the Earth curves away
underneathit, and the projectile completes
entire orbits without ever hitting the Earth.
On all these trajectories, the projectile is in
free fall.
102Gravity and Orbits
- The Suns inward pull of gravity on the planet
competes with the planets tendency to continue
moving in a straight line.
103One had to be Newton to see that the Moon is
falling, when every one sees that
it doesnt.Paul Valery French poet and
philosopher, 1871-1945
104Navigating in Space
- Newton's law of universal gravitation combined
with Kepler's three laws explain planetary
orbits. - They also suggested the possibility of placing
artificial satellites in orbit around the Earth
or sending space probes to the planets. - According to Newton's laws of motion and
gravitation, if an object moves fast enough, its
path will match the curvature of the Earth, and
it will never hit the ground. It goes into orbit.
- Circular orbital velocity for a low Earth orbit
is 5 miles/sec. - If the object's velocity is gt 5 miles/sec, but lt
7 miles/sec, its orbit will be an
ellipse. - Velocities gt7 miles/sec reach escape velocity,
and the object moves in a curved path that does
not return to Earth.
105The effect of launch speed on the trajectory of a
satellite.
- Required launch speed for Earth satellites is
- 8 km/s (17,500 mph) for circular orbit
just above atmosphere, - 11 km/s (25,000 mph) to escape from
Earth.
106Navigating in Space Transfer Orbits
- To send a spacecraft to another planet, it is
launched into a transfer orbit around the Sun
that touches both the Earth's orbit and the orbit
of the planet. - Once the spacecraft is in the transfer orbit, it
coasts to the planet. The gravitational force of
the Sun takes over and this part of the ride is
free. - But transfer orbits put constraints on space
travel. - The launch must occur when the planet and the
Earth are in the correct relative positions in
their orbits. - This span of time is called a launch opportunity.
- During each launch opportunity, which can be a
few weeks in duration, the spacecraft must be
launched during a specific time of the day -
launch window. - If the spacecraft is headed for an inner planet
(Mercury or Venus), the launch window occurs in
the morning. - For outer planets (Mars and beyond), the launch
window occurs in the early evening.
107Navigating in Space Gravity Assist
- Another technique used by space navigators is
called gravity assist. - When a spacecraft passes very close to a planet,
it can use the strong gravitational field of the
planet to gain speed and change its direction of
motion. - According to Newton's laws of motion, the planet
looses and equal amount of energy in the process,
but because the mass of the planet is so much
greater than the mass of the spacecraft, only the
spacecraft is noticeably affected.
108Apparent Weightlessness in Orbit
This astronaut on a space walk is alsoin free
fall.
The astronauts sideways velocityis
sufficient to keephim or her in orbitaround the
Earth.
109Lets take a little time to answer the following
question
- Why do astronauts in the Space Shuttle in Earth
orbit feel weightless?
110- Some common misconceptions which become apparent
in answers to this question are
(a) there is no gravity in space, (b) there is no
gravity outside the Earths atmosphere, or (c) at
the Shuttles altitude, the force of gravity is
very small.
111In spacecraft (like the Shuttle) in Earth orbit,
astronauts are in free fall, at the same rate as
their spaceships.
On all these trajectories, the projectile is in
free fall.
That is why they experience weightlessness just
as a platform diver feels while diving down
towards a pool, or a sky diver feels while in
free fall.
112Newtons Form of Keplers 3rd Law
- Newton generalized Keplers 3rd Law to include
sum of masses of the two objects in orbit about
each other (in terms of the mass of the Sun). - (M1 M2) P2 a3
- Observe orbital period and separation of a
planets satellite, can compute the mass of the
planet. - Observe size of a double stars orbit and its
orbital period, deduce the masses of stars in
binary system. - Planet and Sun orbit the common center of mass of
the two bodies. - The Sun is not in precise center of orbit.
113Mass of Planets, Stars, and Galaxies
- By combining Newtons Laws of Motion and
Gravitation Law, the masses of
astronomical objects can be calculated. - a v2/r , for circular orbit of radius r
- F ma mv2/r
- mv2/r Fg GMm/ r2
- v (GM/r)1/2
- P 2?r/v 2? (r3/GM)1/2
- M rv2/G
- If the distance to an object and the orbital
period of the object are known, the mass can be
calculated.
114Whats important in the last half?
- Definitions and examples
- inertia
- mass
- acceleration
- force
- gravity
- weight
- free fall
- orbits
- Newtons Laws of Motion and how they relate to
one another and to objects. - Newtons Law of Gravitation
115Review
1. Briefly describe the geocentric model of the
universe. Who developed the model? What are the
models basic flaws? 2. What is the Copernican
model of the solar system? Flaws in the
Copernican model? 3. What discoveries of Galileo
helped confirm views of Copernicus? 4. Briefly
describe Keplers three laws of orbital motion.
List two modifications made by Newton to
Keplers laws. 5. What are Newtons three laws
of motion? 6. What is Newtons law of gravity?
What is gravity? How does the gravitational
force vary with the mass of the two objects?
with distance between centers? 7. Discuss
orbiting objects and free-fall. 8. What is
escape speed?
116Exploring the Solar System
Solar System Object Flyby Orbit Probe Lander Sample Return Human
Mercury
Venus
Moon
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Asteroid ? ?
Comet