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