Time
Tropical year 365.242 days
Solar year-365 (average) solar days, 1day=24 hours
Sidereal - relative to the stars 365.256
Julian Calendar 46 B.C.- leap year: added an extra day every 4 years, much improved over earlier lunar calendars
Gregorian Calendar 1582 A.D. (adopted by Britain and American in 1752) - omit extra day in years that are multiples of 100, except if a multiple of 400
Motions of Earth
Precession
Parallax
Small Angle Equation
distance=baseline X (360 deg/2p) / parallax
distance=baseline X (57.3 deg)/ parallax
diameter=distance X angular diameter / 57.3 deg
Eratosthenes- curvature of the Earth
7.2 deg/360 deg = 5000 stadia/Earth's circumference
Copernican Revolution
Geocentric model
Process of science- leading to the Sun-centered solar system
Contributions of Galileo and Kepler
Kepler's laws
Newton's laws
Mass of bodies from Newton's laws
Cosmology
Cosmology- theories about the origin and nature of the Universe
Science- the process of learning about nature by systematic observations and experiments from which repeatable results can be obtained
Cosmology of the Solar System
Must explain the following observations:
Orbits of inferior planets
Retrograde motion of superior planets
Phases of the moon and Venus
Eclipses
Precession
Parallax
Retrograde Motion
Copernicus
Found numerous errors in positions of planets with geocentric model
Heliocentric (Sun-centered) model
Circular orbits
Stars are immeasuraby distant
Simpler view of solar system
Tycho Brahe (late 1500s-1629)
Very precise naked-eye observations
Catalog of precise positions of planets and stars
Observed supernova of 1572
No observed parallax to the supernova
Supernova must be far from the Earth-moon system
Galileo Galilei (1564-1642)
Perfected an astronomical telescope
Observations:
Phases of Venus
Moons of Jupiter
Mountains on the moon
Sunspots
Heliocentric
Johannes Kepler (1571-1630)
Student of Brahe- used Brahe's catalog
Kepler's Laws (empirically observed)
Orbital paths of the planets are elliptical, with the Sun at one focus
A line from the Sun to a planet will sweep out equal areas in equal intervals of time
The square of the planet's perios is proportional to the cube of its semi-major axis
Ellipses
Kepler's Second Law
P2=a3
If P (the orbital period) is in years
If a (semi-major axis) is in A.U.
1 A.U.=1.5 X 108 km
Speed of planet is fastest at perihelion (closest approach)
Speed of planet is slowest at aphelion (farthest approach)
Dimensions of the Solar System
Isaac Newton (1642-1727)
Deductive- his theory of gravity predicts planetqry and stellar motions
Newton's Law
A body at rest stays at rest unless acted upon by a force. A body in motion stays in motion unless acted upon by a force ==> inertia and mass
F=ma
To every action there is an equal and opposite reaction
Newton's First Law
Consequences of Newton's Laws
Inverse square law - Every particle of matter attracts every other particle with a force that is directly proportional the product of their masses and inversely proportional to the square of the distances between them
Circular speed
Escape speed
"Weigh" planets and stars
The Moon is Falling
Gravity
Every particle of matter attracts every other particle of matter in the universe
G=6.67 X 10-11 N m2/kg2
N=kg m/s2
Orbital Mechanics
Acceleration