Mercury
and Venus move side to side about the Sun: Mercury maximum 28 degrees, Venus
maximum 47 degreesPage last modified 16 February 2005 09:54 AM
In this section we focus on the problem of trying to understand the motions of the planets in the sky. This question has enormous historical importance; getting the right answer was a key step in the rise of science and rationality. One of the things we will learn is a common feature of science: you try to solve a particular problem, and the end result turns out to explain all sorts of things that are not directly connected to the original problem.
The word planet is from the Greek word for wanderers
Ancients knew of five planets plus the Sun and Moon: Mercury, Venus, Mars, Jupiter, Saturn. They did not think of the Earth as a planet at this time. Since the invention of telescopes we have also had Uranus, Neptune, Pluto.
The planets rise and set with the daily rotation of the Earth, of course, but their positions as compared to the background stars change slowly from week to week
Starry night demonstration.
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They move roughly (but not exactly) along the ecliptic.
Mercury
and Venus move side to side about the Sun: Mercury maximum 28 degrees, Venus
maximum 47 degrees
Jupiter
Mars and Saturn move all around the ecliptic. They make retrograde motions
sometimes
Crucial point is to explain these motions so you can predict the future positions of the planets.
The
Greeks knew Earth was round because of the shapes of the shadows on lunar eclipses.
Note that it is a fallacy that the Greeks, or early Europeans (Christopher Columbus?)
thought that the Earth was flat.
.
The Greeks knew that distance to the Moon was about 120 times its diameter, by using the small angle theory.
They
looked more at shadows of eclipses and deduced that the Earth was about 4 times
the diameter of the Moon. They also realized that the Sun was much farther
away than the Moon, but didn't know how far.
Eratosthenes
measured the diameter of the Earth by looking at the shadows cast by the Sun at
two different places on Earth. We don't know exactly how accurate it was.
The Greeks could also work out the distance to the Moon, but not to the Sun.
But the thing that the Greeks got wrong was that they put Earth at center of the solar system instead of the Sun. This is called the geocentric universe. Some Greeks did get it right, but Aristotle was wrong, and Aristotle's views were given as much weight as the bible for thousands of years.
The most sophisticated version of the geocentric theory was due to Ptolemy (~ AD140). The basic thing he was trying to explain was why the planets moved so unevenly along the ecliptic.
The basis of his theory was what we call a scientific model. He had circular orbits with epicycles. There was nothing at the center of the epicyles, so one has to think of the planets making circles around an empty point in space. Circles were intellectually satisfying to Greeks, so they assumed that nature was based on circles.
Quicktime of Ptolemy's Universe (275
kBytes)
Ptolemy's theory gave very nearly right answers His equations and tables were
used for over 1000 y to predict positions of planets. Ptolemy was held in so
much respect that sky blamed when theory wrong.
The dispute between the geocentric and heliocentric (sun-centered) theories is one of the most important events in the history of Western civilization. The acceptance of the heliocentric theory led directly to the rise of physics and the scientific way of looking at the world. No modern technology would exist if the heliocentric theory had not won the day.
Dispute is not just about whether the Earth goes round the Sun or the Sun goes round the Earth. The key difference is whether the other planets go round the Earth or round the Sun.
98.4 00.5
(Polish 1473 - 1543)
Copernicus is recognized as the driving force behind the acceptance of the Heliocentric theory, although at least one ancient Greek philosopher had proposed the idea first. The theory was disliked by authorities because it relegated the Earth's position to no more than a planet. The Earth was no longer the center of everything. The change from the geocentric to the heliocentric view of the Universe is so important, we refer to the Copernican Revolution.
Copernicus'
heliocentric model
Quicktime of Copernicus' Universe
Copernicus's picture is much simpler conceptually; planets no longer go round "nothing". The Earth behaves in much the same way as the other planets do. It is a much simpler model, and it simplicity is the main reason for its acceptance. This is an example of one of the great guiding principles of science, called "Occam's Razor": Roughly what is says is that if you have two theories that fit the observations, the simpler one is almost certainly the better one.
Copernicus model has a natural explanation for the fact that Mercury and Venus are always close to the Sun and for the retrograde motion of Mars
But the theory is still based on perfect circles and did not make predictions
any better than Ptolemy's theory.
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(Italian 1564 - 1642)
Galileo
was the first person to use telescope methodically for astronomy. His notebooks
survive and still provide important details for people who need to know how the
sky looked in the 17th Century. He made studies of the craters
of the Moon, of sunspots and of the stars in the Milky Way galaxy, but there
were two particularly interesting observations that he made that pertain to the
heliocentric controversy.
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Moons of Jupiter.
He
discovered four large moons, Io, Europa, Ganymede & Callisto. . Just too
faint to be seen with the naked eye.
Starry night demo
Galileo's
observations of Jupiter's moons
The philosophical importance of these observations is that they show that not everything orbits Earth. Moons obey Kepler's laws themselves.
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Phases of Venus
He could see the changes in the apparent shape of Venus due to changes in the way it is illuminated. This is a crucial confirmation of the Copernican theory since it proves that Venus goes behind the Sun
Phases
of Venus as seen through telescope
Ptolemy's universe
Copernicus' universe
Galileo also made important experiments on mechanics; he showed that heavy and light things fall at same rate, he introduced the idea of acceleration and realized that friction is what slows things down.
Acceleration is the rate of change of velocity.
Galileo did not try to connect his astronomy with his mechanics experiments.
Galileo got into serious trouble with the Catholic Church because of his views, and only by political skills avoided being burnt at the stake.
(Danish 1546 - 1601)
Danish nobleman with false nose.
Collected superb data, without telescopes.
All angle measuring; planets with respect to stars, and timing of when stars cross meridian.
Did not support Copernicus, but that does not diminish him as a collector of data.
(German 1571 - 1630)
Kepler
was a pupil of Tycho Brahe. Inherited and analyzed Tycho's observations in order
to look for the pattern there. Had several false starts. Concentrated on trying
to find "model" to fit the observations of Mars. Finally, after 20
years discovered that the crucial point was that the planets move in ellipses,
not circles.
Keplers laws:
Law 1. The Orbit of a planet around the
Sun is an ellipse with Sun at one focus
Note that the circle is a special case of an ellipse, so orbits can be circular
The
Focus is a special point in the ellipse
In this Figure, a is the semi-major axis. You can think of it as equivalent to the "largest radius" of the ellipse
Law
about speeds in an orbit.
P2/a3 is the same for all planets orbiting the Sun
P is the period, which is the time the planet takes to make one orbit of the Sun. If the orbit is circular then a is the same as the radius.
Demo of the sky "Solar system view"
If we compare the periods and sizes of two different planets we get the equation:
P12/a13 = P22/a23
If we know any three of P1 a1 P2 a2 we can calculate the fourth one
For the Solar System we usually measure P in years and a in "Astronomical Units", shortened to "AU"
1 AU is the average distance between the Earth and the Sun,
1 AU = 1.5 x 108 kilometers, (150 million km) or 9.3 x 107 miles (93 million miles)
Approximate values for a and P for the Solar System (Table A-1 in your book)
| a (AU) | P ( yrs) | |
| Mercury | 0.39 | 0.24 |
| Venus | 0.72 | 0.62 |
| Earth | 1.00 | 1.00 |
| Mars | 1.52 | 1.88 |
| Jupiter | 5.20 | 11.86 |
If we use P in units of years and a in astronomical units we can write:
P2/a3=1 for every planet. (you can check this with a calculator)
For planets orbiting a different star, or moons orbiting a planet (like Jupiter's moons) then the value of P2/a3 will be different from 1.
Kepler offered no explanation of why these laws hold. The strength of his theory is that it allows a much more precise prediction of the positions of planets that does Ptolemy's. Also his three laws are much simpler than the complicated ones of Ptolemy. In science simplicity is one of the most important aspects of any theory. Another example of Occam's Razor
(English 1643 - 1727)
Newton
is generally regarded as the greatest physicist ever. He wrote the book on
optics and mechanics (the science of how things move), and invented calculus. He
knew all about Galileo's and Kepler's discoveries, and looked for the underlying
physical laws that could make sense of the patterns his predecessors had
discovered. Why, for example, should planets move in ellipses rather than some
other shape, such as a figure of eight?
Newton is also responsible for unifying the laws that explain both the behavior of planets and of things on Earth. Nowadays scientists take it for granted that the laws of nature are basically the same everywhere, but before Newton's time there was no reason to assume that the "heavens" behaved the same way as the Earth.
The most fundamental of Newton's laws are the three laws of motion. In getting these laws Newton built on the work of Galileo.
The three laws apply to any matter, not specifically planets, and they deal with the way that motions are related to forces.
Before Newton it had been widely held that objects have a natural tendency to stop moving. Newton recognized the role of friction in stopping things, and realized that friction is itself a force. Take away friction (as in Space, for example) and things keep moving indefinitely. Another consequence of Newton's first law is that you need a force to change the direction of a motion, such as in going round a bend or round an orbit.
The most mathematical of the laws. It is sometimes written:
Force = mass x acceleration
or
F = ma
The force could be a push, gravity, magnetism, air pressure, friction or whatever.
Acceleration is the rate of change of velocity. For physicists braking is a form of negative acceleration.
The mass of a body is the amount of matter it contains. Loosely speaking it is the same as the body's weight. The mass is not the same as the volume, which is essentially the size of an object. If a handful of shaving cream expands its mass stays the same, but its volume increases.
The link between mass and volume is the density
Density = Mass/Volume
Iron has a high density, while air has a low density.
The equation also implies that the acceleration is in the direction of the force.
This equation looks simple, but as physics students soon find out, mechanics gets very complicated when a single object is acted on by lots of forces, or when we have to consider a complicated object made up of many small ones. Newton's laws show us how even really complicated motions are actually the result of a simple interplay between force and mass. This is the analytical aspect of science.
This law is often written "For every action there is an equal and opposite reaction"
The recoil of a gun is one example. Jumping off a skateboard is another
The other great law of Newton is not called the fourth law, because it deals with one particular kind of force, unlike the first three laws which are completely general.
Or
Before Newton, gravity was a force produced by the Earth and nothing else. But when Newton thought about the implication of his three first laws he noticed that since the earth's gravity made objects accelerate, gravity must be a force like any other. Thus an apple accelerates towards the Earth because the Earth exerts a force (gravity) on the apple. But by Newton's third law, if the Earth pulls the apple, then the apple must also pull the Earth. Newton's genius was to realize that if the apple could pull the earth it could probably pull anything else as well. So he hypothesized that all matter attracts all other matter.
He also realized that it was gravity that pulled the planets into orbits, and when he calculated how strong gravity had to be to keep the Moon in orbit around the Earth he discovered the "inverse square law" of gravity.
The inverse square law shows that gravity gets weaker as things move apart. (This is opposite to the force from a piece of elastic, which gets stronger the longer it is stretched)
The force between two objects can be measured in the lab, but it is difficult because the force between small bodies is so weak.
The letter G in the equation is the Universal constant of gravitation. You can look it up in a book if you want it. As far as we know it has the same value everywhere in the Universe.
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One of the greatest successes of Newton's law of gravity (coupled with his other three laws) is that it explains how orbits work, both qualitatively and quantitatively
In
Newtonian physics the reason that the Moon is in orbit around the earth is that
the force towards the center of the earth continually pulls the object towards
the center of the earth, but its forward motion tends to carry it away from the
Earth. A good way to think about this is Newton's
cannonball
Satellites do not fall out of sky because they are moving so fast. (about 18,000 mph in the case of the Space Shuttle). Once you get them up to the right speed they will stay there indefinitely, or at least until the small amount of friction generated by the residual atmosphere of the Earth slows them down.
Newton showed that there was a relationship between the speed that a satellite moves round a planet and the distance from the planet's center.
This gives us a method of determining the mass of a distant planet; we measure the radius and the orbital speed of one of its moons. For example we can get the mass of Jupiter from measuring the orbits of the Galilean satellites. We will find adaptations of this idea throughout astronomy; it is the main way that astronomers measure the mass of distant objects.
Newton showed that if you start with his four laws and consider a small object in orbit around a large one one can derive all three of Kepler's laws exactly mathematically.
This is not easy, and it was to solve this problem that Newton invented differential calculus.
Note that Newton's laws are much more fundamental than Kepler's, because they don't only apply to planets, and also because they allow you to understand things that Kepler never considered
Newton's laws allow for even greater accuracy than Kepler's laws
If
you look hard enough at the orbits of the planets you find that they are not
exactly ellipses after all. There are gravitational forces between the planets
as well as between each planet and the Sun. These extra forces perturb
the motion of the planets away from being a perfect ellipse. Newton's theory
tells us exactly how to deal with this problem, while Kepler's laws do not help
the situation at all. It was the idea of perturbations that led to the discovery
of the planet Neptune.
Any
civilization that lives near the ocean can make the link between the tides and
the moon; the times of high tide vary in a similar way to the times that the
moon transits the meridian. But until Newton's time it was not realized that the
connection between the moon and the tides was actually gravity. Newton's theory
can explain the timing of the tides, why there are two tides a day, and account
for the effects of the Sun's pull as well as the Moon's. This is a good example
of a scientific theory that was developed for one purpose being successfully
applied to another phenomenon
To understand why there are two tides a day one has to consider the balance between the gravitational force of the moon and the centrifugal force on the water. These together produce bulges on both sides of the Earth. As the Earth rotates "under" the bulges a person standing on a shore experiences two tides a day. The Sun also raises tides of about 1/3 the size of the lunar tides. They sometimes add to the Moon's and sometimes tend to neutralize it, depending on the time of the month. The sizes and timing of the times depends on where you are. Tides are small in Hawaii, but can easily reach 20-30 vertical feet in some places in the world.
See section 4.8 in your book
Newton's theory of gravitation is not the last word on the theory of gravitation. If you deal with very strong gravitational fields the theory starts to be inaccurate, and eventually illogical. Einstein's general theory of relativity (1912) supersedes Newton's theory; the differences between Newton's and Einstein's theory are immeasurably small for all normal situations, including almost everything we will meet in this astronomy course, which is why we continue to learn Newton's theory, which is much simpler. But when we get very strong gravitational fields (such as near a black hole) Einstein's and Newton's theories diverge and Einstein's work better. Now people (such as Steve Hawking) are finding situations where Einstein's theory is not working, and are looking for something even better.
Rockets
are an example of Newton's third law in action. You heat gas very hot so that it
shoots out of the back of the rocket. Reaction causes the rocket to accelerate
forwards. The only difference between a rocket and a jet plane is that a jet
sucks in air (oxygen) to burn the fuel, but a rocket carries everything it needs
to burn inside, including oxygen if that is the fuel it needs to burn.
Satellites are launched by a rocket upwards to clear the atmosphere, but they turn on their side to boost the satellite horizontally at a speed of at least 18,000 mph.
Straight
up, then turn round and "shoot" satellite horizontally into orbit
Got to get speed and direction just right, or else the orbit is the wrong shape.
Acceleration phase lasts only a few minutes
On the launch pad it consists of the shuttle itself, the main fuel tank and the
boosters
It
is launched like a rocket
In
orbit the shuttle can move in any direction since it does not need engine power,
and there is no air resistance
.
It orbits at a few hundred miles altitude where it is used to perform
experiments and do observations. An astronaut doing a space walk would travel in
the same orbit as the shuttle. The astronaut moves with the shuttle, so
experiences weightlessness, or "microgravity". In orbit it can travel
in any direction since it the is no air to "fly" through.
To
come back to earth, it flies backwards and fires engines, then turns forward to
re-enter the Earth's atmosphere. The shuttle lands like a plane with no engines.
Movie of weightlessness.(VHS 29 part 1, 23 minutes)
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Many satellites (including the space shuttle) travel within a few hundred miles of the Earth's surface. They take about 90 minutes to make one orbit. As described by Kepler's third law, higher orbits take longer (think of the moon 250,000 miles up taking a month for an orbit), and an orbit 22,000 miles above the Earth's surface has a period of 24 hours. If you put a satellite above the Equator at this altitude flying East at the right speed it will appear to hover above the same point continuously. These satellites are called geostationary satellites and they are the ones that are used for communications and for television transmission, since your satellite dish does not have to move around the sky.
To escape the gravity of the Earth (if you want to go to the Moon or planets, for example) you need to travel above 25000 mph. If you launch with a velocity less than this you fall back to Earth or stay in orbit. By comparison, the minimum speed needed to go into orbit around the Earth is 18,000 mph.
All bodies have a specific escape velocity. We will meet this idea later in several other parts of the course.
There are two reasons to go into space.
a) You can study the planets close up by sending spacecraft up close.
b) You can put telescopes into orbit around the Earth in order to avoid Earth's atmosphere. This is particularly important for ultraviolet, X-rays, which do not penetrate the Earth's atmosphere.
Astrology is the idea that the location of the Sun and planets along the ecliptic influences human activity. The positions of the planets at one's birth is thought to be particularly important.
Now we see how planets actually move under the forces of gravity, what's left for astrology? As far as professional astronomers are concerned: nothing. Let us look at why
It is not enough to ask people if they believe their horoscopes. People believe what they want to believe. One needs to do scientific tests to see if it works.
We can try a simple experiment of the newspaper column as a test
The fact that a single newspaper column does not work does not itself disprove astrology. This could be a bad day, or this could be a bad astrologer, but this is the idea of how you could devise a larger scale test.
Many tests these have been done. Overpowering evidence is that you can't predict human events or character by astrology.
Be particularly careful about people who claim to have predicted events. Easy to make vague predictions such as "There will be a Earthquake in California in 2004" or "Madonna will be in the news this year"
Could there be planetary influences based on forces we know about in physics?
We can calculate the influence of stuff like light, heat, X-rays, magnetism, gravity from a planet. Always, there are much larger effects either from the Sun or from nearby
For example we can calculate the gravitational force from Jupiter (the largest planet). It is less than the gravitational force from the obstetrician standing next to your mother.
There could in principle be other forces that are unknown to physics, but one of the principles of science is that you don't invent things you don't need. Scientists are not going to spend time looking for some mystical force unless they are convinced it is doing something.
Another reason astronomers are skeptical is that because of precession over the last 2000 years the Sun is not actually in the sign of the Zodiac that the newspaper column predicts. Also what about Uranus, Neptune, Pluto?
Many centuries ago there might have been some truth in the idea that aspects of a person's character depended on the time of the year they were born. Fetal development depends on the nutritional health of the mother, which might have been poorer during a winter pregnancy than a summer one. Even nowadays, children who are born in August start school 11 months younger that those born in September, which could in principle make some kind of difference to their development.
But the main reason why some people believe in astrology is that they want order in their lives. The stately motions of planets offered an attractive combination of order and mystery, that suggested something significant was going on.
But we have solved the mystery of the motions. It's just gravity.
Why do people still go to astrologers? Because some people like to be told what to do. And because it is easier to second-guess someone's character by asking their birth sign rather than taking the trouble to get to know them properly. And because astrologers tend to be optimistic and stroke egos. Read the columns carefully and you will see this.
Does it matter? Newspaper columns promote ignorance and superstition, which is generally a bad thing. But much of the advice is harmless and even mildly beneficial.
The harm comes when US presidents make diplomatic decisions based on astrology, and when ignorant people are ripped off by TV shows charging $240 per hour.
05.15
Ptolemy's
Universe
Ptolemy's
Epicycles
Picture
of Copernicus
Picture
of Tycho Brahe
Observatory
at Uraniborg
