Chapter 2 Copernican Astronomy
Early Observations
Stella sphere or celestial sphere: the Earth is surrounded by a giant spherical canopy or dome
Diurnal rotation/motion: the daily rotation of the celestial sphere. East to West. Period = 24hours.
Background stars: fixed in position on the rotating celestial sphere
Certain objects appear to move over the course of a year in a ecliptic path.
The Sun’s daily motion: east to west
Annual motion: west to east, titled at an angle of 23.5 degrees from the celestial equator.
The moon: similar to the Sun’s motion
Planet: wanderer
Annual motion: normally west to east, occasionally varies its direction
Retrograde motion: changing direction (east to west) and wandering slightly off the ecliptic path
Alternate motion: at times a planet is ahead of the Sun and at other times behind the Sun
Morning stars: just west of the Sun. Seen in the morning
Evening stars: just east of the Sun. Seen just after sunset
Observation you can see by the naked eye. These observations would have been made by early civilization
Competing Models of the Universe
Ancient Greek: the universe is a long rectangular box
Geocentric model: Earth-centered
Heliocentric model: Sun-centered
Geocentric Theory— Aristotle
Homocentric model:
The Earth is the center of the universe
The earth is stationary
The planets’ circular paths all have the same center
Auxiliary spheres
trying to explain new data
planets are still orbiting around the Earth but they are on different spheres
In order to generate the observed non-uniform motions
Weaknesses
The moon varies in size
The planets vary in brightness
Doesn’t agree with the observed data
Geocentric Theory — Ptolemy
Ptolemy (~ 150 A.C.)
Eccentric: the planets’ spheres are off center
Epicycle, deferent: the epicycle’s center moves around the deferent
Equant: the Earth is on one side of the eccentric and the equant an equal distance on the other side of the eccentric
Necessary to correctly calculate the speed
Significance and Weakness
Pure mathematical scheme. No speculative philosophy
Agree very well with observed data
Too complicated
Geocentric Theory
Problems with Geocentric Model
The rotational speed of faraway stars will be impossibly high
Any place could be chosen as the center of the universe since the universe is infinite.
In order to explain retrograde motion, very complicated scheme is necessary. Ockham’s razor: simple explanations are preferable to complicated explanations.
Heliocentric Theory
Heliocentric Theory: sun-centered. The sun is the center of planetary motion and the Earth is also a planet.
Nicolaus Copernicus: ~1530
Can easily explain retrograde motion
The Earth is spinning on its own axis tilted 23.5 degrees
Period = 23 hours and 56 minutes
Explains the diurnal motion
Can explain the phases of the moon
Can explain the apparent various sizes of the planets
Can explain the differences between inner- and outer orbit planets
Inner- orbit is smaller than ours (mercury and Venus). Have phases like the moon.
Outer orbit is larger than ours ( all planets after us). Doesn’t have phases like the moon
Problems with Copernican Model:
The calculated positions of stellar objects gave poorer results than the Ptolemaic theory. Mainly because he made use of large amounts of very ancient, possibly inaccurate data.
Stellar parallax: had never been observed. Because no sufficiently powerful telescope was available at the time.
Look at apparent motion of object against distant background from two vantages points.
Big shift: the object is close by
Small shift: the object is far away
Telescope: invented in 1608
Galileo Galilei (1564-1642)
Discoveries
The Moon’s surface is very much like that of the Earth, with mountains and craters
The Sun’s spots
The Sun spins on its own axis
Jupiter has moons, too. So there are other centers of rotation in the universe
Venus has phases like the Moon, (full or crescent)
Many more stars than previously realized
Tycho Brahe: accumulated great amount of accurate data
Johannes Kepler: inherited Brahe’s data and did mathematical analysis with it
Kepler’s Laws
Kepler’s Laws
The orbit of each planet about the Sun is an ellipse with the Sun at one focus of the ellipse
The line joining the Sun and the planet (called the radius vector) sweeps over equal areas times as the planet travels around the orbit
Square of period of planet’s orbital motion is proportional to cube of semimajor axis
T² is proportional to D³
Copernican Revolution
Conflict between science and religion
Adaptable to new data and discoveries
Scientific method
Newtonian Mechanics
Newton’s First Law- Law of Inertia
In the absence of a net external force, an object will continue in a state of uniform motion (including rest) in a straight line
Why do objects keep moving?
Why do objects stop moving?
Force is the reason to change the motion of an object, not to keep the motion
Newton’s Second Law - Law of Acceleration
The time rate of change of motion(momentum) of an object is directly proportional to the magnitude of the impressed force and in the direction of the impressed force
F=ma
force= mass x acceleration
Newton’s Third Law- Law of Action and Reaction
The mutual actions of two bodies on each other are always equal and directed toward contrary parts
Fa→b= -Fb→a
Newton’s Universal Law of Gravitation
Every material particle in the universe attracts every other material particle with a force that is proportional to the product of the masses of the two particles, and inversely proportional to the square of the distance between their centers. The force is directed along a line joining their centers.
Fgravity= Gm1m2/r2
gearth=9.8m/s²
Projectile Motion
If ignore air resistance, no force is exerted on the object in the horizontal direction. So it moves at constant speed horizontally. Gravity is exerted on the object in the vertical direction. So it accelerates down with acceleration of g vertically.