Aristarchus (~ 300 BC)

1
A short History Of observing and measuring
the Solar system and beyond

• Aristarchus ( 300 BC)
• Greek astronomer - 1st to hypothesize that
  Earth ________________ and revolves around the
  ____.
• Most rejected it for the next 1800 years because
  an earth-centered model better fit their
  observations it sure looks like the sun revolves
  around the earth!!

spins on its axis
sun
2

• and the argument went IF the earth were
  revolving around the sun, the positions of stars
  in the sky should vary when viewed from opposite
  sides of earths alleged orbit. (This is called
  ________ __________ and is similar to the
  difference between the speed read by a driver and
  a passenger both viewing the speedometer needle
  in a car.)
• But, NO such observation had ever been observed!
• Aristarchus counter-argued that the stars are
  simply too far away to observe this variation.
  (To see how distance affects parallax, hold your
  finger up at different distances from your eye
  close/open each eye the bigger the distance, the
  _____ the parallax.)

stellar parallax
less
Click to see Animation
Stellar Parallax was finally observed in the mid
nineteenth, with the increase of technology!
3

• Eratosthenes (200 BC)
• Greek astronomer, mathematician
  measured the circumference of the
  earth.

• On June 21st (summer solstice), at noon, the sun
  is directly overhead at Syene (S) on the Tropic
  of Cancer, so there is no shadow at that time.
  Eratosthenes set up a stick on the same day to
  the north in Alexandria (A) and measured the
  angle of its shadow at noon (shortest shadow of
  the day!)

Tropic of Cancer
Drawing NOT drawn to scale!
4
The shadows angle was about 7. How, then, can
the circumference be calculated?
x
By __________ _________ angles, the angle marked
x in the picture is _____. This angle is about
______ of a complete circle. So, the earths
circumference ____ times the distance between
Syene and Alexandria. The accepted value today
is 40,090 km. His exact result is debated, but
some believe he measured the circumference to
within 1 error!!
alternate interior
7
1/50th
50
5

• Ptolemy (100 AD)
• Astronomer and Mathematician
• Proposed a model of the universe
  with the ______ at the
  center that accounted mathematically for the
  observed movement of the sun, moon, and known
  planets against the backdrop of unmoving stars.
  He accounted for the observed irregularities in
  the way some planets (Greek word meaning
  wanderer) moved as viewed from earth
  specifically, his model attempted to explain the
  planets observed ____________ or
  __________motion.

earth
retrograde
backward
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He proposed a device termed an epicycle to
explain retrograde motion
The resulting motion matched observation
His Theory
Click for Animation
At times, the epicycles velocity added to the
planets orbital velocity. At other times, the
epicycles velocity opposed the planets orbital
velocity, making the planet change
directions. This theory was widely accepted until
the 15th/16th century BECAUSE it matched the
observational data so well!!!
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• Copernicus (1473-1543)
• Polish astronomer
• Became convinced that a simpler
  model of the universe was more likely to be
  correct.
• He proposed that a ____-centered universe would
  more simply logically explain the motion of the
  heavens. Beyond that, he
  used very little
  mathematical reasoning.

sun
8
Pattern produced against the backdrop of distant
stars

• Copernicus explanation of Retrograde motion
• Some planets (such as Mars) have a larger orbit
  than Earth and also move slower in their orbit.
• As earth overtakes Mars, the relative motion
  makes it look like Mars went backwards, when, in
  fact, it continued forwards!

Click to See Animation
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2005 Mars Retrograde Motion dates
(image credit NASA/JPL)
2008 Mars Retrograde time-lapse photograph
Note that this pattern does NOT occur each
evening!! The pattern would appear if you
charted Mars' position in our night sky over
several months' time (during retrograde).
Simulation in Cartes du Ciel program
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Why is the retrograde path a loop and not a
straight line?
The orbits of the planets don't quite lie in the
same plane - slightly tilted!
11

• What about the inner planets Venus and
  Mercury?... Do we observe retrograde motion
  for them?
• _____.... instead of earth overtaking the
  outer planets, __________________
  ____________________ to produce the motion.
• Copernicus theory was also consistent with the
  mystery of why Venus and Mercury were (and
  are!) always observed near the _____! (We never
  see them in the middle of the night like we do
  the other planets!)

Yes
Mercury and Venus
overtake the earth
sun
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So, can we prove that Copernicus was right and
Ptolemy was wrong? Can we prove that the earth
moves and is NOT at the center of the solar
system? You would think!!... But read on. An
excerpt from the book Measuring the Universe by
Ferguson
A few years ago, Harvard astrophysicist and
science historian Owen Gingerich received a flyer
in his mail offering a 1000 prize for
scientific proof-positive that the earth moves.
A Mr. Elmendorf, who posed this question, wrote,
As an engineer, I am astounded that the question
of the Earths motion is apparently not all
settled after all these years. I mean, if we
dont know that, what do we know?
13
Indeed, whether the Earth moves can hardly be
classed as one of the great unsolved mysteries of
science. Schoolchildren learn that we live on a
planet that revolves on its axis and orbits the
Sun, that Nicolaus Copernicus introduced this
controversial idea in the sixteenth century, and
that some men were persecuted for believing it.
But in the end all settledcase closed. That
was four hundred to five hundred years ago.
What, you might ask Mr. Elmendorf, is the fuss
about? And why has no one won the 1000? History
and science turn out to be far more subtle and
ambiguous than were taught in the early grades.
14
Certainly no scientific knowledge has a better
claim to being Truth than the knowledge that
the Sun is the center of our planetary system and
that the Earth, like the other planets, orbits
it. Yet our own contemporary science backs away
and tells us that when it comes to proving what
moves and what doesnt, and whether or not there
is an unmoving center, no one can make an
airtight case that any answer is right or wrong.
Pick what you will, the Moon, Mars, the Sun, the
Earth, your great aunts dining table the
options are infinite and its possible to come
up with a successful mathematical description of
our planetary system with that as the unmoving
center.
15
In fact you are being parochial if you limit the
exercise to our planetary system. It is possible
to describe the entire universe using any chosen
point as the unmoving center the Earth will do
very well and no one can prove that choice is
wrong. The issue here is one of relative motion
only. You can measure the motion of an object
only in relation to other objects in the
universe. Scientists today prefer to picture
everything in motion and nothing as being the
center.
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If you havent given much thought to the
implications of twentieth-century science, you
may be as chagrined as Mr. Elmendorf to realize
that because of the concept of relative motion,
no one can prove that the Earth moves. Nor is
relative motion Mr. Elmendorfs only problem.
One tenet of science is that while an explanation
can be extremely convincing and useful, none
should ever be considered final or proved, or
Truth with a capital T.
17
Were Copernicus ideas accepted at first? ___!
They were not accepted until years after his
death. It was _______ and ________ that were
ultimately responsible for the triumph of
Copernicus ideas. For a look at these two men,
one more excerpt from Measuring the Universe by
Ferguson
NO
Kepler
Galileo
It would be difficult to imagine two educated
men of the same historical period more different
from each other in background and personality
than Johannes Kepler and Galileo Galilei.
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Kepler was a quiet introspective man from an
obscure village on the outskirts of the Black
Forest near Stuttgart. Galileo was a colorful,
feisty, larger-than-life character who grew up in
Pisa and Florence when Florence was a world
center of wealth, political power, and artistic
and intellectual ferment. Kepler didnt win
friends easily. He was an unassuming, private
man Galileo won both friends and enemies
readily, relished the spotlight, and lived a
public, even celebrity life. He thought highly
of himself
19
Kepler was an exuberantly devout Protestant
Galileo, a staunch Catholic. (contrary to
popular belief!) An aside It is a common
misconception that the conflict between Galileo
and the Catholic church was one of science
against religion. But, Galileo, himself would
have never characterized it as such. While he
stood against the leaders of the Catholic church
at that time, he remained a religious believer, a
believer in the God of the Bible. He once wrote
I do not feel obliged to believe that the
same God who has endowed us with sense, reason,
and intellect has intended us to forgo their
use. and in a letter another time, he wrote
The Holy Scripture never lies Though the
scripture never errs, its interpreters and
expounders are liable to err.
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But far more significant than any of these
differences was the contrast between the ways
these two men approached their science. Keplers
mind moved by leaps of fancy and intuition
inspired by his Neoplatonic Christian faith that
the universe must have a beautiful hidden harmony
to it that things as far apart as music and
geometry and cosmology must have connections and
explain one another.
21
But though much of his work appears crazy to
modern eyes, his greatest contributions were at
first equally much flights of imagination and
were equally motivated by his longing to uncover
symmetry and relationships. It took a mind that
could think as far out as Kepler, follow as
many false leads as he, and then proceed to pin
ideas down with conscientious mathematical rigor,
to discover connections that really do exist.
22
Galileo, on the other hand, started from what he
observed, in the firm conviction that the only
way to learn the truth about nature was to
examine it directly and put it systematically to
the test. Though eager and able to speculate
sometimes too optimistically about the
implications of his findings, he was reluctant to
espouse publicly or even among friends ideas for
which he didnt personally see clear support from
his own experiments or observations.
23
For all their genius, both of these men were also
remarkably favored by happenstance. Each had
fall into his hands something without which his
most important discoveries would never have been
made. For Kepler, that was the naked-eye
astronomical observations of the great Danish
astronomer Tycho Brahe. For Galileo, it was the
telescope. Together, Kepler and Galileo were
responsible for the triumph of Copernican
astronomy, yet they never met in person.
24

• Johannes Kepler (1571-1630)
• German Astronomer
• 1596 published the 1st book since Copernicus
  50 years earlier that defended Copernican
  theory
• 1601 Kepler moved to Prague, Denmark to work
  with Tycho Brahe, considered the greatest
  astronomer of his generation. 2 years later
  Brahe died, leaving all his astronomical data
  (taken with the naked eye) to Kepler.

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By examining Brahes data, Kepler concluded that
circular orbits couldnt explain the paths of the
planets. Kepler then proposed three empirical
laws Although he formulated the laws for planets
orbiting the sun and are so stated here, they
hold for any body (moons, man-made satellites,
etc.) that orbits another body. Keplers 1st Law
The Law of Orbits
All planets move in elliptical orbits, with the
_____ at one focus.
sun
26
A couple ways to describe/define an ellipse

• An ellipse is the shape produced when a cone is
  sliced without going through the base. A
  horizontal slice produces a circle, which is
  simply a special ellipse.

• Pull string taut with pencil. Moving the
  pencil, keeping the string taut, will
  produce an ellipse. Each fixed end is
  called a focus.

elongated
As foci move apart, ellipse becomes more
____________. If foci are at same
point, ellipse becomes a ________.
circle
27
Ellipse/Orbital Terminology

• Aphelion (Ra) maximum radius from sun
• Perihelion (Rp) minimum radius from sun
• Eccentricity (e)

distance between foci length of
major axis
circle
lt1
e is always _____ (e 0 is a _______)
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Keplers 2nd Law The Law of Areas
As a planet orbits, it sweeps out equal areas
in equal times.
The shaded areas are equal since they were
swept out in the same time, Dt
Click for Animation
This law accounts for the way a planet varies in
speed The nearer the planet is to the sun, the
______ it moves. This was one of Keplers far
out ideas, a connection he found between
astronomy and geometry, arising from his belief
in the intrinsic harmony of a universe created by
God (Ferguson, Measuring the Universe)
faster
Click for Animation of planets' motion
29
Keplers 3rd Law The Law of Periods
Where. R Radius of Orbit T Period of Orbit
For an ellipse, R average radius or distance
from the sun to the planet R
Length of ____________
Rmax Rmin 2
Semi-major axis
For example
Amazingly, the actual distance measurements were
NOT known yet at the time of Kepler!!
30
Table from Fundamentals of Physics by Halliday,
Resnick and Walker
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• Galileo Galilei (1564-1642)
• Italian astronomer/physicist
• Made two primary observations in
  1610 with a telescope that supplied persuasive
  evidence for the Copernican,
  sun-centered system. Still acceptance of the
  Copernican system was slowon all fronts.

• Observed that the planet Jupiter had _______,
  demonstrating conclusively that not everything
  directly orbits the earth.

moons
(Jupiters moons as drawn by Galileo)
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2. Observed a complete range of phases for
Venus, from 0 to 100 illumination
(Galileos actual drawings of Venus)
Photos taken at Calvin College Observatory of
Venus
2/12/01
3/1/01
3/21/01
4/04/01
So, how does this support the Copernican
system? This entire range of phases would be
expected if Venus moves around the sun. However,
in the earth-centered Ptolemaic system, Venus
moves around an epicycle between the earth and
the sun, so it could never be more than 50
illuminated!
34
A Comparison
Ptolemaic system
Copernican system
Illumination greater than 50 is impossible
(Since Venus is always observed near sun, they
are always on the same side of Earth in the
Ptolemaic system)
Phases from 0 to 100 possible matched
observation!
Demonstration Starry Night Astronomy computer
program
35
The rotation of our moon around earth also gives
a complete range of phases
So why isnt there a solar eclipse at every new
moon? Moons orbit is ________________
______________. If it were in the same ________
we would see ___ solar and ___ lunar eclipses
every year!
inclined to earths by about 5 deg.
plane
12
12
Simulation of phases and difference between
synodic and sidereal month at
Click to see Animation
36
Giovanni Cassini (1625 1712)

• Born in Italy, but moved to France
• 1st to measure the ____________of Mars, resulting
  in a measurement of the _________ to Mars!

parallax shift
distance

• Two observers observed Mars in the night sky at
  the same time one in Paris and one in South
  America (Cayenne)
• By measuring the angle from each location to Mars
  and knowing the baseline distance between them (
  4500 miles), geometry/trigonometry can be used to
  find the distance, d!

NOT To Scale!
d
Paris
Cayenne
Baseline distance 4500 miles
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• The distance from Earth to Mars, d, was then used
  to calculate the distance from the earth to the
  sun using Keplers 3rd Law

• Since the periods had been measured and d was now
  known from parallax, the distance from the earth
  to the sun can be easily (?) calculated with
  algebra (messy)!

38

• Cassinis calculation for d resulted in a sun to
  earth distance of 87 million miles. The modern
  measurement is 93 million miles!
• Keplers 3rd Law can then be used to calculate
  the ____________________________________ (for
  whom the periods had been measured!)
• As technology increased, stellar parallax (of
  stars) was finally observed in the 18th century.
  The method is the same except that the angles are
  measured 6 months apart, so the baseline
  distance is the _______________________ (large
  enough to see a difference in the angle).

distance from the sun to all the known planets
diameter of the earths orbit
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• The distances to only the nearest stars can be
  measured this way. Just over 2.5 million stars
  have been measured using parallax, which are all
  the stars less than 500 light years away from us.
  For any stars farther than that, the parallax
  angle is too small to be measured with todays
  technology.

The parallax angle is measured in arcseconds.
The distance unit known as a Parsec is the
distance that results from a parallax angle of 1
arcsecond. (1 Parsec 3.26 light years)
40

• So, how do we estimate the distances to stars
  that are over 500 light years away?
• A little background first Inverse-square law
  Apparent magnitude (apparent brightness) is
  ________ proportional to the the ______ of the
  _______ between the source and the observer.
• The absolute magnitude (brightness of the star
  if it was very close to the earth) can then be
  calculated if we know the _______to a star and
  its apparent magnitude.
• So, for a star that is too far away to measure
  the distance via parallax, the ________can be
  calculated if the absolute magnitude and the
  apparent magnitude are known. The apparent
  magnitude is measured directly and the absolute
  magnitude is estimated based on the stars
  spectrum (comparison to spectrum of close stars
  whose absolute magnitude has been calculated).

inversely
distance
square
distance
distance
41

• Isaac Newton (1642-1727)
• Born same year as Galileo died!!
• English physicist, mathematician, philosopher,
  etc.
• Newton used Keplers 2nd Law and Galileos ideas
  of uniform motion (inertia) to infer that there
  MUST be a force _______ the planets _______ the
  sun (as opposed to a force that pushes them
  around as previously believed)

pulling
towards
42

• Newton recognized that the same force that pulls
  objects down at the earths surface could result
  in a body continually falling toward it forever.
  (what we now call an orbit!!)

Click for Animation of "Newton's Cannon"
From A Treatise of the System of the World,
written by Newton in the 1680s
43

• He realized that the presence of this pulling
  force could be the key to explaining the planets
  motion... So, how did he figure out the nature
  of this force??
• Newton knew how centripetal force varied with
  radius and period

• Keplers 3rd Law, then, provided Newton with the
  key that unlocked the nature of this force for
  orbits

Then
If
44

• He then inserted this expression for T2 into the
  Fc equation

• Newton termed this center-seeking force a
  ___________ force (from the Latin gravis, meaning
  heavy.) It was _________ proportional to the
  ________ of the distance between the planet and
  the sun and _______ proportional to the _____ of
  the planet. He reasoned further that this force
  must also depend on the _____ of the sun (the
  body that is being orbited). This mass was part
  of the constant!

gravitational
inversely
square
directly
mass
mass
45
Newton further reasoned that this
same force that causes the earth to remain in its
orbit around the sun is the same force that
holds the moon in its orbit around the earth,
and its also the same force that causes an
apple to fall from a tree! Not only that, but he
claimed that EVERY BODY in the universe attracts
EVERY other BODY!
His generalized result has come to be known as
Newtons Law of Universal Gravitation
46

• So, what is G? (known as Big G)
• Newton never knew!!
• All he knew was that the constant in his
  equation was equivalent to
• the product of ___ and the ______of the _____
  _____________

G
mass
body
being orbited
From The Cartoon Guide to Physics
by Gonick and Huffman
47
Henry Cavendish, in 1798, was the first to
perform such an experiment that allowed a
measurement of Big GHe used what is now termed
a Cavendish Balance. When the two very large
masses (m2) were brought near the smaller masses
(m1), the gravitational
attraction between the masses twists the system
through a small angle, moving the reflected light
beam along the scale, providing a measure of the
strength of the gravitational force.
48

• With F, m1, m2, and r now measured, Cavendish was
  able to use Newtons equation to calculate
  Big G! And now that Big G was known, the
  ______of bodies in the solar system (such as the
  sun and the earth) could be calculated. In fact,
  Cavendish cleverly titled his famous scientific
  paper that reported his experimental results
  Weighing the Earth!!

mass
Click for Animation of Cavendish Balance
Demo!

• The result?
• Gravitational Constant
  (expressed in the standard SI units)
• NOTE Use kg, m and sec in ALL PROBLEMS!!

G6.67x10-11 Nm2/kg2
49
So, how can Big G be used to weigh the
earth? First, we need to calculate the
required velocity, v, for a
circular orbit
around the earth
velocity
satellite
Fg
R
earth
R Radius of ORBIT
(If mE is replaced with msun, the result gives
the required velocity to circularly orbit the
sun!)
50
The required circular orbit velocity
for any satellite (natural or
man-made) is,
then, inversely proportional to the ___________
of the ____________. Examples (1) If a planet
is in a circular orbit around our sun with an
orbital radius 9 times greater than the earths
orbital radius, the speed of the planet in its
orbit would be ______ the earths orbital
speed. (2) If a planets orbital radius were
1/4th that of earths, the speed of
the planet in its orbit would be _______
earths speed.
square root
orbital radius
1/3rd
double
51
If we now set this orbital velocity formula equal
to our the speed of any object in circular
motion, we get a result that will allow us to
measure the mass of the earth
Square both sides
Hey! Were back to Keplers 3rd Law, but now we
know what the constant is!
Rearrange terms
So, using the moons orbital radius, the period
of the moon, and Big G, the mass of the earth
was calculated as 5.98 x 1024 kg!
52
From The News-Gazette, 2007
53
Popular Science reported the following in Sep. of
2000.
54

• More Example Problems and Applications of
  Newtons Universal Law of Gravitation
• Explains observed perturbations in the planets
  orbits (deviations from a perfect elliptical
  orbit). Each planet exerts a small
  gravitational force on the other planets (small
  in comparison to the large force from the sun).
  These small forces cause the perturbations,
  especially noticeable when a 2nd planet is fairly
  close.
• -Newtons observations of Saturns
  perturbations helped him formulate the
  Universal Gravitation Law. -Later,
  observations of Uranus orbit led to prediction
  of location of a new planet. Telescopes were
  aimed there and Neptune was found!
  -Similar observations of
  Neptunes orbit led to Plutos discovery in 1930!
  

55

• Calculate the gravitational force between a 100
  kg person and the earth. Mass of earth
  5.98 x 1024 kg and radius of
  earth 6.38 x 106 m.
• (We can solve this problem because of what is
  known as the Shell Theorem A Uniform
  spherical shell of matter attracts a particle
  outside the shell as if all of the shells mass
  were at its center).

Hey, thats just the weight of the person!! Duh!
56
While the forces on the person and the earth are
both the same, the ____________ are NOT the
same!! Because the ________ are different
accelerations
masses
Force of person on earth
Force of earth on person
57

• Use Newtons Law of Gravitation to find an
  expression for the acceleration of gravity, g, at
  a distance, r, away from the center of the earth
  (same as the centripetal acceleration of a
  satellite orbiting at that distance).

If r RE, the value for g in this equation
___________
9.8 m/s2!
58

• Technically, g (theoretical gravitational
  acceleration) gapparent (measured free fall
  acceleration). Why??
• Calculation assumes earth is spherical, but its
  slightly flattened at the poles and bulging at
  the equator.
• Calculation assumes that earth is uniform, but a
  quick calculation of the average density of the
  earth shows this is not so

Most rock near the earths surface has a density
of 3 g/cm3, so parts of the interior of the
earth MUST be more dense!
59

• Earth is rotating apparent free fall
  acceleration is _____ because of the centripetal
  acceleration

less
Recall that a bathroom scale reads our Normal
Force (apparent weight). But, only at the poles
is there no circular motion, resulting in N
W. Anywhere else, a person is rotating in a
circle...
by m
At equator, R RE, and T24 hours
gapparent9.8 - 0.039.77m/s2 Elsewhere, R
REcosq where q latitude angle
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4. Find the net gravitational force (magnitude
and direction) on the mass, m.
Direction is along the ________ because the
______________ cancel!
x-axis
y-components
Or if the vectors are added head-to-tail, an
___________ triangle results!
equilateral
61
5. The tides (Again, cartoons from The Cartoon
Guide to Physics by Gonick and Huffman)
62
6. More complex orbits
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Phew So after all that, you would think that we
understand gravity, right?? WRONG!! Read on
(from Discover mag)
65
Pioneer 10, launched in 1972 on what was
expected to be a 21-month voyage to Jupiter, is
now some 8 billion miles from home. On January
23, tracking stations picked up the last feeble
transmission from the probes plutonium-powered
radio transmitter, which can no longer muster a
signal strong enough to reach Earth. As project
scientists listened to that final fading whisper,
they were left to ponder a mystery The
spacecraft seems to be defying the laws of
gravity. Pioneer 10 has been slowing down, as if
the gravitational pull on it from the sun is
growing progressively stronger the farther away
it gets. Pioneer 10 is not the only spacecraft
acting strangely. Pioneer 11, launched in 1973,
also slowed down as it pulled away from the sun,
right until NASA lost contact with it in 1995.
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Is it possible that a single, identical
malfunction struck all these vehicles? Or is
some unknown force in the universe slowing them
down? For Michael Nieto, a theoretical physicist
at Los Alamos National Laboratory in New Mexico,
the mystery involves much more than a few hunks
of spacefaring hardware it reveals that there
might be something wrong with our understanding
of gravity, the most pervasive force in the
universe. We dont know anything, he says.
Everything about gravity is mysterious.
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An Israeli physicist named Moti Milgrom argues
that a fudge factor like dark matter isnt
necessary if physicists just make one small tweak
to Newtons laws of gravityIts very
embarrassing, says Milgrom of the situation
astronomers find themselves in today. I hear
even people who adhere to dark matter call this
the preposterous universe. Milgrom asked a
reasonable question What if the laws of gravity
as we understand them dont apply on a galactic
scale? After all, the only direct experience we
have with Newtons Laws has been within the
confines of our solar system. Maybe the rules
are different for galaxiesWe infer that dark
matter exists only because we think we understand
gravity on these scales.
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Following a few false starts, Milgrom hit on an
approach that seemed to reproduce the peculiar
movements of galaxies without the need to invoke
dark matter. The key was acceleration. Gravity
accelerates things. When you jump off a cliff,
Earths gravity pulls you down at a rate of 9.8
m/s each second. Likewise our sun and every
other star in the visible sky accelerates toward
the center of the Milky Way galaxy at a rate that
works out to about the width of an atom per
second each second. Thats weak!! Milgrom
proposed that Newtons laws might change at these
paltry accelerations. Below a transition
acceleration equal to one 10-billionth of m/s
each second, the force of gravity might no longer
be directly proportional to acceleration, as
decreed by Newton. Instead gravity might be
slightly stronger, proportional to the square of
acceleration.
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With this minor (?) change, Milgrom found that he
could perfectly predict the motions of galaxies
without introducing the fudge factor of dark
matter. Milgrom calls his brainchild MOND, for
Modified Newtonian Dynamics. Most astronomers
refuse to embrace MOND. Milgrom understands I
think the science community should give any such
idea a hard time. If you really want to shake
the principles, it shouldnt be an easy matter.
Milgrom also acknowledges that MOND has a serious
flaw It has no connection to any deeper theory.
MOND works, but no one has explained why!