Chapter 2: The Rise of Astronomy
Kepler's third law:
Relates a planet's orbital period to the size of its orbit around the Sun.
Galileo used his observations of the changing phases of Venus to demonstrate that:
Venus follows an orbit around the Sun rather than around the Earth.
"Ockham's razor" refers to:
A metaphor for the process of discriminating between models based on their simplicity.
A total solar eclipse demonstrates that the Moon and Sun are very nearly the same angular size. If the Sun is 400 times farther from us than the Moon, then the radius of the Moon must be _________ the radius of the Sun.
1/400th of.
If an asteroid has an average distance from the Sun of 4 AU, what is its orbital period?
2 years.
Kepler's Three Laws
I. Planets move in elliptical orbits with the sun at one focus of the ellipse. II. The orbital speed of a planet varies so that a line joining the Sun and the planet will sweep over equal areas in equal time intervals. III. The amount of time a planet takes to orbit the Sun is related to its orbits size, such that the period, P, squared is proportional to the semi major axis, a, cubed. (P^2=a^3) •These three laws describe the essential features of planetary motion around the Sun. •The second law implies that when a planet is near the Sun, it moves more rapidly than when it is further away. •The third law states that a planet far from the Sun has a longer orbital period than one near the Sun. •Kepler's laws are the first mathematical formulas to describe the heavens correctly.
Islamic Astronomy
Islamic civilization relied on celestial phenomena to set its religious calendar, and Islamic astronomers made many detailed studies of the sky and the motions of the Sun, Moon, and planets.
A planet in retrograde motion:
Shifts westward with respect to the stars.
A major objection to the heliocentric model not resolved until the development of high quality telescopes was that:
The stars did not exhibit parallax.
In 1054 Asian and Persian astronomers described a "guest star" in the constellation of Taurus, it is now believed that this was a supernova that produced the Crab Nebula.
True.
Distances and Sizes of the Sun and Moon
•*Aristarchus* used geometric methods to estimate the relative sizes of the Earth, Moon, and Sun, and the relative distances to the Moon and Sun. These estimates were not very accurate but were the best estimates for almost 2,000 years. He showed that the Sun is much more distant than had been previously suspected. •*Angular size*: a measure of how large an object looks to you. It is defined as the angle between lines drawn from the observer to opposite sides of an object. (the Sun and the Moon both have an angular size of about 1/2°).
Tycho Brahe
•*Brahe* utilized his position and wealth to indulge his passion for study of the heavens. •He designed and had built instruments of far greater accuracy than any yet devised in Europe. •Tycho then used these devices to make precise measurements of planetary positions. •His meticulous observations turned out to be crucial not only for showing the superiority of the heliocentric over the geocentric system, but also for revealing the true shape of planetary orbits.
The Size of the Earth
•*Eratosthenes* succeeded in making the first measurement of the Earths size (25,000 miles=circumference).
Galileo Galilei
•*Galileo* was interested not just in celestial motion but in all aspects of motion. •He studied falling bodies and swinging weights hung on strings, and tried to find universal laws of motion. •Galileo was the first person who used the telescope to study the heavens. -in looking at the Moon, Galileo saw that its surface had mountains and was in that sense similar to the surface of the Earth. Therefore he concluded that the Moon was a ball of rock. -he looked at the Sun and saw dark spots (sunspots) on its surface. He noticed that the position of the spots changed from day to day, showing not only that the Sun blemishes and was not a perfect celestial orb but that it also changed; by observing the changing position of the spots from day to day, Galileo deduced that the Sun rotated. -Galileo looked at Jupiter and saw 4 smaller objects orbiting it which he concluded were moons of the planet (Kepler gave them the name *satellites*) -He observed that Venus went through a cycle of phases. -He was tried for heresy for going against the church. He escaped lightly and was made to recant his "heresy" and was put under house arrest for the remainder of his life.
Isaac Newton
•*Newton's* contributions span mathematics, physics, and astronomy. •He pioneered the modern studies of motion, optics, and gravity. •In his attempts to understand the motion of the Moon, Newton not only deduced the law of gravity but also discovered that he needed mathematical methods for calculating the gravitational force of a spherical body and that no such methods were then available. This realization led him to invent what we know as calculus.
Ptolemy
•*Ptolemy* developed a more elaborate model that could predict the planets motions with much better accuracy. •He wrote a book called the Almagest; in this book he fashioned a model of planetary motions in which each planet moved on one small circle, which in turn moved on a larger on. -the small circle, called an *epicycle*, was supposedly carried along on the large circle like a Frisbee spinning on the rim of a bicycle wheel. -according to Ptolemy's model, the motion of a planet from east to west across the night sky is caused by the rotation of the large circle. -retrograde motion occurs when the epicycle carries the planet in a reverse direction. By choosing epicycles of the right size and spin rate, Ptolemy's model was able to account for retrograde motion, and predict planetary positions with reasonable accuracy. •Discrepancies remained between the predicted and true positions of the planets. This led to further modifications of the model, each of which let to slightly better agreement but at the cost of adding greater complexity.
The Shape of the Earth
•*Pythagoras* taught that the Earth was spherical for mystical reasons. •*Aristotle* taught the Earth was spherical based off rational reasons and simple naked eye observations.
Johannes Kepler
•After Brahe's death, his young assistant *Kepler* was able to show that the path of Mars was not circular but elliptical. •*Ellipse*: a geometric figure related to a circle but flattened into an oval shape. •*Focus*: one of two points within an ellipse used to generate the elliptical shape; planets orbit along ellipses with the Sun at one focus. •To describe the ellipses shape, astronomers usually report is eccentricity, which indicates how far from the center of the ellipse each focus is located. •Based on Tycho's measurements, Kepler could measure not only the shape of a planets path but also its speed as it changes distance from the Sun.
Explaining the Motion of the Planets
•Following the basic discoveries about the size and distance of the Sun and Moon, the main thread of astronomical research for almost the next 2,000 years centered on the motion of the planets. •*Geocentric models*: models of the solar system centered on the Earth. Many of the earliest attempts to describe the solar system were geocentric in that they supposed that the planets moved around the Earth rather than the Sun.
Nicolaus Copernicus
•He began the demolition of the geocentric model. •After many attempts to reconcile Ptolemy's geocentric model with no success, Copernicus was led to reconsider Aristarchus's ancient idea that the Earth moves around the Sun. -a *heliocentric model* is a model of the solar system centered on the Sun. Such models offer an enormously simpler explanation of retrograde motion; if the planets orbit the Sun, retrograde motion becomes a simple consequence of one planet overtaking and passing another. •Copernicus described his model of a Sun centered Universe in one of the most influential scientific books of all time, De Revolutionibus Orbium Coelestium. •Because his ideas were counter to the teachings of the catholic church, they were met with hostility and skepticism. •Although Copernicus's model was basically correct, it did not account for the observed positions of the planets any more accurately than did Ptolemy's more complicated but incorrect model.
Arguments for an Earth Centered Universe
•In ancient Greek times they did not believe that the Earth moves around the Sun. They argued that if it did, the positions of the stars should change during the course of the year. •*Parallax*: the shift in an objects position caused by the observers motion. A method for finding distances based on that shift.
The Galilean satellites are:
•Lo. •Europa. •Ganymede. •Callisto.
The Planets
•Many ancient cultures noted that there are five bright stars visible in the night sky that do not stay fixed relative to the rest of the stars in the sky. •Because these wandering stars seemed to have a will of their own, many cultures named the planets after divine beings. •Today we know that the planets move across the background stars because of a combination of the Earths and their own orbital motion around the Sun. •The planets always remain close to the ecliptic, within the constellations of the zodiac. •Planets always rise in the east and set in the west because they are carried across the sky by the Earths rotation (motions of the planets is slower than the stars). •*Retrograde Motion*: "backward", the drift of a planet westward against the background stars. Normally planets shift eastward because of their orbital motion. The planet does not actually reverse its motion, the change in its direction is caused by the change in the position from which we view the planet as the Earth overtakes and passes it.
Asian Astronomy
•The early people of Asia studied the heavens, devised constellations based on their own mythologies, and made maps of the sky. •Their careful observations of celestial events prove useful to astronomers today; they kept detailed records of unusual celestial events such as eclipses, comets, and exploding stars. •Based on their records, Chinese astronomers devised ways to predict eclipses.