=
2.5 AUAncient Non-European Astronomy
Stonehenge
- Built 2800BC - 1100BC, used in Stone Age and Bronze Age
- The sun rises at the "heel stone" on the day of the Summer Solstice
- Also features other solar and planetary alignments
- The stones are aligned to within 1 deg (for comparison, full moon is 0.5 deg in diameter)
- An amazing feet of engineering even moreso than astronomy. Some blocks weigh as much as 50 tons (the weight of a few cars) and were carried from quarries several miles away.
Chinese astronomers have best known records of the supernova of 1054AD. It was so bright that one could see it during the day for a few days. The remnant from this supernova is now known as the Crab Nebula.
Arab astronomy florished while Europe was in the Dark Ages. We still use Arab names for various stars, such as Betelgeuse, Rigel, and Mira. The Arabs coined the term "zenith." The numerals we use today are Arabic in origin.
Ancient European Astronomy
In ancient times, the only planets we knew of were Mercury, Venus, Mars, Jupiter and Saturn. The rest (Uranus, Neptune and Pluto) are too faint to be observed with the naked eye.
How did the ancients know that planets were different from stars?
- Planets exhibited motion different from and relative to the background stars. Planetary motion was not as uniform as the motion of the Moon and Sun.
- Venus was observed as the "morning star" or "evening star" and could be seen at varying times of the year.
- Mars, Jupiter and Saturn could be seen at varying times of the year. These planets exhibited "retrograde" motion.
- Mercury was observed in a manner similar to Venus (ie as a morning or evening star). Mercury is much harder to observe than Venus because Mercury is much closer to the Sun.
Mercury and Venus are inferior planets, meaning that their orbits are closer to the Sun than Earth's orbit. They are closer to the Sun than the Earth is.
Mars, Jupiter and Saturn are superior planets, meaning that their orbits are farther from the Sun than Earth's orbit. They are farther from the Sun than the Earth is.
Where do Venus and Mercury appear?
Sunset: Sun and planet moving down
* -> Planet would be seen setting in the West since the Sun will set
before the planet
O
* -> Planet would not be seen since it sets before the Sun leaves the sky
_______________________ (horizon)
Sunrise: Sun and planet moving up
* -> Planet would be seen rising in the East since the Sun rises after the
planet
O
* -> Planet would not be seen since it rises after the Sun enters the sky
_______________________ (horizon)
Mercury and Venus can only be seen setting in the West after sunset or rising in the East before sunrise, otherwise the Sun's light easily outshines the planet.
The word "planet" comes from the Greek word for wanderer.
- The ancients knew that the Sun and Moon fall into this category. How did they know?
- The Moon and Sun don't vary much in brightness, the planets do.
- The Moon and Sun follow predictable paths, so predictable in fact that you can base
months and years on their motions. The motion of planets is not so regular.
The solar system is more or less flat, meaning that while the paths of the different planets are not parallel, their paths also don't stray far from the ecliptic. The ecliptic, by definition is the path that the Sun appears to follow throughout the year.
The Sun (always) and the planets (most of the time) move from West to East around the Celestial Sphere.
- Over the course of one day, the Sun, Moon, stars and planets all rise in the East and set in the West.
- Over the course of several days, weeks, etc. the Sun and planets all move from West to East as observed at the same time of day over the course of days, weeks, etc.
- Why is this? Examining the Sun: each point on the Celestial Sphere rises 4 min
earlier per day (because of difference between solar and sidereal day length), which
means that each point moves further East each day -> the Sun's rising position along
the Sphere shifts by 4 min of Right Ascension (similar to longitude on Earth's globe)
each day -> if points on the Celestial Sphere are moving East, then the Sun must be
moving West.
The typical West to East motion of planets is called prograde motion. As the planets move across the sky over the course of a year, they are sometimes not visible at all and they mostly move in the prograde direction when they are visible. But sometimes, a planet will appear to slow to a stop, reverse direction for a few days, stop again, then continue in the original direction. Motion in the opposite direction, meaning from East to West, is called retrograde motion. See Figure 2.4 page 37.
Planets shine by reflecting sunlight, they do not produce light of their own. The ancients correctly deduced that an increase in a planet's brightness meant that the planet was moving closer to Earth. They also observed that a planet was at it's brightest when it was exhibiting retrograde motion.
Proposed models of the Solar System had to explain and be able to predict all of the above observations of the heavens.
The Geocentric Model
Geocentric = the Earth is the center of the Solar System and the rest of the universe. This model was devised and popularized by Ptolemy and Aristotle, two very prominent Greek philosophers. Aritotle first proposed that Earth was the center of the Universe, Ptolemy, in 140AD or so, actually created a detailed model that showed how a geocentric universe worked. See Figures 2.5 and 2.6 on page 38 to see how these models worked. Each planet followed a large circular orbit called a deferent as well as a smaller circular orbit called an epicycle. The center of each planet's epicycle travels along the deferent in a circular orbit around the Earth.
The circle was to believed to be the perfect and harmonious shape that all planets must follow. Epicycles were required in addition to deferents in order to explain retrograde motion and varying brightnesses of planets. This model was good at predicting future locations of planets, as far as available accuracy allowed (no telescopes yet).
At about 200BC, another Greek by the name of Aristarchus put forth a heliocentric model, but he couldn't compete with the popularity of Aristotle, Ptolemy, and the deepset idea that the Earth was the center of the universe. The geocentric model also seemed to make more sense based on available observing capabilities. If the Earth was in fact moving, then why didn't we feel a strong breeze? If the stars are stationary and the Earth is orbiting the Sun, then why don't we observe stellar parallax? We now know that the stars closest to us do indeed exhibit parallax, but the parallax values are too small to be measured with the technology available to ancient Greece.
The Heliocentric Model by Copernicus
13 centuries later, a Polish cleric named Copernicus came along. He rediscovered the heliocentric (Sun at the center) model written by Aristarchus. Copernicus saw that this model could account for seasons, retrograde motion, and variations in brightness.
Copernican Revolution - truly revolutionary ideas at the time
- The "spheres" (ie heavenly bodies) do not have one common center. The Moon revolves around the Earth, but the Earth and planets revolve around the Sun.
- The background stars are a lot farther from Earth than the Sun. This explains why stellar parallax was not observed.
- The daily motions of the heavens (rising and setting of the Sun and stars) is due to the Earth rotating on it's axis.
- The yearly motions of the Sun are due to the Earth moving around the Sun, not the other way around.
- Retrograde motion is a direct consequence of a heliocentric model. See figure 2.8 page 40.
Why Copernicus wasn't quite successful
- He clung to the idea of circles as orbital shapes. His model still required epicycles, but now the deferents were centered on the Sun.
- There was some observational data available to him, but he didn't utilize it to prove his theory. He just "felt" that he was right.
- He published his work in Latin. Only the academic community read Latin, and Copernicus didn't produce a convincing enough argument to refute 1300 years of teachings.
- The church rejected Copernicus' model, but they didn't ban his work or otherwise harass him. Since he didn't publish his work for the general population, the general population still followed the church without question.
The Heliocentric Model by Galileo
Galileo
- Publishes his work in the century following Copernicus' death (1600s).
- Devises and is the first to use the Scientific Method
1. Theory - an explanation of the way something works
2. Hypothesis - a prediction of what data you will observe if your theory is correct
3. Observation - take and analyze real world data
4. Theory - see what parts of the theory held up and change the theory as needed to fit
data. Repeat cycle until theory can predict any known observations.
- 1609 - Galileo builds and uses a telescope, which at the time was a brand new invention. Who invented the telescope? Most likely a Dutch spectacle maker. Galileo was the first to use a telescope for groundbreaking science.
- Galileo pointed his telescope at the Sun and saw sunspots. Nobody had ever seen them before, and people then believed the Sun to be a perfect unblemished sphere. DO NOT EVER LOOK AT THE SUN THROUGH A TELESCOPE (however, there are filters that can be added to a telescope to make it safe). Galileo observed that some sunspots would travel across all or part of the Sun's surface. This occurs because the Sun rotates about its axis.
- When Galileo looked at Jupiter, he saw four points of light lying in an imaginary line that passed through Jupiter's center. These points changed their positions over time, moving back and forth across or behind Jupiter. These points are actually the four largest moons of Jupiter, also called the Galilean moons. They are named (in order of increasing distance from Jupiter) Io, Europa, Ganymede, and Callisto.
- The observation that Jupiter had it's own moons, which didn't revolve around the Earth at all, was Galileo's strongest argument for the Copernican (heliocentric) model.
- He observed Venus to have phases, something that the geocentric model could not explain. See figure 2.10 page 42.
Galileo published his work in the language of the main population; Italian. Now that people were reading about a heliocentric universe and questioning the church's geocentric views, the church got angry. The church banned the work of both Galileo and Copernicus, but not before the cat had been let out of the bag.
Galileo was also able to furnish observational proof of his work, which convinced the academic community of the heliocentric model. Galileo published Starry Messenger in 1610 and Dialogue Concerning the Two Chief World Systems in 1632.
Note that Galileo's work did NOT address the shape of planetary orbits. He, in fact, also liked the idea of circles.
Actual hard proof of the heliocentric model came when aberration of starlight (a consequence of our motion towards background stars) and stellar parallax could finally be measured. That said, the heliocentric model has been the accepted model since the time of Galileo.
Kepler's Laws
Johannes Kepler's three very important laws came from two men working together at about the time Galileo was first becoming well known; Kepler (a theorist) and Tycho Brahe (an experimentalist).
Tycho Brahe - took extensive observations and records of star and planets over the course of several years. He even found a comet and a supernova. He did all of his observations with the naked eye, meaning that while he had the use of things such as sextans for determining altitudes, he did NOT use a telescope. Brahe believed in the heliocentric model.
Kepler - Spent the last 29 years of his life devising a theory that would fit Brahe's extensive data and be able to predict future data. He also believed in the heliocentric model. Kepler wanted his theory to explain planetary motion WITHOUT the use of epicycles.
Kepler's 3 Laws
1. Planets follow elliptical orbits with the Sun at one focus. See Ellipse Diagram on my website.
- We measure the shape of an orbit by its eccentricity. The lower the eccentricity, the more circular the orbit. Most planets have low eccentricity orbits. Mercury and Pluto have higher eccentricities.
- Comets have highly eccentric orbits.
2. A planet sweeps out equal areas in equal time intervals along its orbit. See Figure 2.14 page 47.
- This law is true because angular momentum must be conserved.
- This law means that planets, comets, and asteroids move faster when they are closer to the Sun, and slower when they are farther away.
These first two laws explain variations in brightness and observed planetary locations over time without the use of epicycles. Kepler finally killed the epicycle.
3. P2 = a3, where the period P is measured in years, and the semimajor axis a is measured in AU.
- Period = how long it takes a planet to complete one revolution around the Sun.
- semimajor axis a = one half of the length of the major axis of a planet's elliptical orbit
- see figure 2.13, page 46.
- All comets, planets, and asteroids follow these orbits.
- An increase in P will cause a to increase, and vice versa.
Example problems involving Kepler's 3rd Law:
1. If P = 4 years, then find a
a3 = P2 = (4)2 = 16
a =
=
2.5 AU
2. If a = 7 AU, then find P
P2 = a3 = (7)3 = 343
P =
=
18.5 years
Newton and Gravity
Copernicus, Galileo, Tycho and Kepler made amazing strides in explaining how the solar system works. Copernicus and Galileo put the Sun at the center of the Solar System, then Tycho's observations allowed Kepler to devise the 3 basic laws of planetary motion. What had not yet been researched and explained was the underlying physics telling why the planets moved as they did. Enter Isaac Newton, born 1642 (the year of Galileo's death).
Newton's 3 Laws of General Motion
1. A body will either stay at rest or continue to move at a constant velocity in a straight line unless a force acts on the body, changing its motion.
- force = a push or a pull which changes the direction and speed of motion.
- mass = a measure of how much matter an object contains.
- Mass is not the same thing as weight.
- mass is measured in grams or kilograms (1 kg = 1000 g), force is measured in
Newtons (1 N = 1 kg*m/s2).
- An object would have the same mass on if it travelled to a different planet, but its
weight would change.
- acceleration = a change (increase or decrease, or change in direction) in velocity.
- measured in meters/sec2 = m/s2
2. F = ma (force = mass * acceleration)
- on Earth, the acceleration due to gravity g = 9.8m/s2
- Examples of force: weight (a consequence of gravity), friction.
- Example problem: F = 6 N, a = 9.8m/s2, calculate mass in grams and kilograms.
F = 6 N = 6 kg*m/s2 = 9.8m/s2 * (mass in kg)
mass = 6 kg*m/s2 / (9.8 m/s2) = 0.61 kg (the "m/s2" cancels out)
convert this mass to g: 0.61 kg * 1000g / 1 kg = 610 g
3. For every action, there is an equal and opposite reaction.
Newton postulated that every object containing mass exerts a gravitational force which attracts other objects containing mass. The strength of this gravitational force is directly proportional to the masses of two interacting objects and inversely proportional to the square of the distance between the objects.
FG = Gm1m2/r2 G = a constant = 6.67x10-11 Nm2/kg2
m1, m2 are the mass of the two interacting bodies
r = the distance between the two bodies
As r increases, FG decreases.
As m1 or m2 increase, FG increases.
Example problems with the gravitational force eq
1. An object of m = 1000kg exerts how much stronger a gravitational force than an object of m = 100 kg?
F1 = G*1000kg*m2/r2 F2 = G*100kg*m2/r2
F1/F2 = G/G * (1000kg/100kg) * m2/m2 / (r2/r2) = 1000/100 = 10
An 1000kg object exerts 10 times as much gravitational force as a 100kg object.
2. A planet of distance r = 5 AU from the sun feels how much more or less of the Sun's gravitational force as the Earth feels? Assume that this new planet has the same mass as the Earth. mass of Sun = mS, mass of Earth = mE = mass of new planet.
FE = G*mE*mS/(1 AU)2 FP = G*mE*mS/(5 AU)2
FP/FE = G/G * mE/mE * mS/mS / [ (25 AU2)/(1 AU2) ]
The new planet feels 1/25 as much of the Sun's gravitational force.
The Sun's gravitational force pulls planets inward, towards the Sun. The Sun's gravitational force is what causes the planets to move as they do.
Newton's correction to Kepler's 3rd Law:
P2 = a3/Mtotal Mtotal = sum of Sun's mass and planet's mass as
measured in Solar masses
- Why didn't Kepler catch this? Because, for the case of our Solar System, this is not a large correction at all. Even the most massive planet, Jupiter, has a mass of only 0.001 Solar Masses (ie one thousanth the mass of the Sun); 1 Solar Mass + 0.001 Solar Mass = 1.001 ~ 1 Solar Mass. The correction needed for Earth is much smaller still.
Escape Velocity
This is, by definition, the speed an object must travel at if it is to escape the pull of a planet's gravity. For an object to remain in orbit around the planet, it must travel at a speed less than the escape velocity.
vesc =
G
= constant defined earlier
M = mass of planet
r = distance between moving object and planet's
center of gravity
- At or near the surface of the planet, r is equal or approximately equal to the radius of the planet.
- As M increases, the escape velocity increases.
- As r increases, the escape velocity decreases.
Example problem with escape velocity
1. Jupiter has a mass of about 318 times that of Earth. Jupiter's radius is about 11 times greater than Earth's. How many times greater or smaller is Jupiter's escape velocity?
M = mass of Earth, r = radius of Earth.
vE =
vJ =
vJ/vE =
=
= 5.4
Jupiter's escape velocity is 5.4 times greater than that of Earth.