Download Jan. 14 – Jan. 21

Jan. 14 – Jan. 21
Celestial Sphere, What is out there (stars, planets, sun, moon)
Horizon
Constellations – fixed patterns
Relative Motion – We feel stationary and so “see” things orbiting us
But in reality
Rotation of Earth at Billings 323m/s (723mph)
Revolution 4756m/s (10,609mph)
Stars rise in East and set in West (as little as ten minutes)
Rotation of the Celestial Sphere
2nd
DESCRIBE CELESTIAL SPHERE
Axis of rotation = Celestial Poles
Declination and Right Ascension
(Prime Meridian vs. Sun at Vernal Equinox)
Compare to Latitude and Longitude
Different Stars appear over the year
Sun blocks different constellations
The ecliptic – tilted with respect to Celestial Equator 23.5 degrees
“Equator tilted with respect to ecliptic”
DESCRIBE ECLIPTIC
Seasons
Solstices
Equinoxes
Planets (wanderers) and Zodiac
Planets move to the East with respect to the Stars (orbital motion)
Retrograde Motion
Moon
Motion looks like planets and sun
Orbit is 5 degrees off ecliptic
Phases
STONE AGE ACCOMPLISHMENTS
Stone avenues and circles adjusted to periodic movements of sun, moon, and stars
Stonehenge
Irish Tombs
ASIAN
Detailed records of eclipses, comets, exploding stars, sunspots
Enabled them to predict eclipses
1200 BC omens mention stars by name
Also measured the diameter of Earth
Focus on observing and recording predicted return of Halley’s Comet
AUSTRALIAN/AFRICA/AMERICA
Evidence of the use of stars to guide planting
BABYLONIANS
800 BC
compiled star catalogs
recognized movements were periodic
EARLY CLASSICAL ASTRONOMY
GREEKS
500 BC Pythagoras
300 BC Aristotle
Earth is spherical (perfect shape)
Lunar eclipses show curved shadow
Traveler moving south sees different stars (previously hidden
beneath the horizon)
276-195 BC Eratosthenes Angle of Shadow versus distance MATHEMATICS
25,000 miles
(1 degree = 111km; 360 degrees = 40,000km)
Hipparchus - magnitude 1-6 (Catalog)
circa 275 BC Aristarchus Size of Earths shadow on moon to size of moon
Earth is 3 times the diameter of moon
Sun is 20 times farther than moon and larger than Earth
MATHEMATICS
Parallax
couldn’t observe parallax so Earth doesn’t move around sun
DECSRIBE PARALLAX
Geocentric Theories Eudoxus
400-347 BC
Ptolemy
150 AD
ALMAGEST
STARRY NIGHT ORBITS
Epicycles
ISLAMIC
Names of bright stars
Betelgeuse, Aldebaran
903-986
al-Sufi
refined coordinates and added names USED
Astronomical Terms
Zenith
Observatories designed to refine measurement and add precision
Jan. 21st
RENAISSANCE ASTRONOMY
1473-1543 Copernicus
Heliocentric System
Retrograde motion
Calculated Distance to Planets (Example of geometry) Relative to 1
A.U.
1564-1642
MATHEMATICS
Galileo Galilei
Precursor to Newton in studying motion
Perhaps not inventor of telescope but first to point it at the sky
Moon – mountains and plains
PHOTO OF MOON
Sun – sunspots (sun rotates)
Jupiter – moons (Galilean Satellites)
Venus has phases (must orbit the sun)
Ran afoul of the Church – house arrest (1992 church admits error)
1546-1601 Tycho Brahe
Designed and built instruments and made observations
Still couldn’t measure parallax
Abundant precise data
1571-1630
Johannes Kepler
Received (stole) Brahe’s data
Mystic (music of spheres/nested geometric shapes)
Kepler’s Laws
1. elliptical orbits with sun at one focus
2. Sweep out equal areas in equal time
3. period (years) squared is equal to semimajor axis (A.U.)
cubed
Coined the word Satellite
Jan. 26th
SIR ISAAC NEWTON
1642-1727
Gravity and Motion
Newton’s Laws
1. Inertia
An object in motion remains in motion in a
straight line at a constant speed and an
object at rest remains at rest unless acted
upon by and outside force.
Some force is making planets stay in near circular orbits or they would move in a
straight line.
2. acceleration
The acceleration (change in velocity) of an
object is directly proportional to the
unbalanced force exerted upon it and
inversely proportional to its mass.
F = ma
F is force (N)
m is mass (Kg)
a is acceleration (m/sec2)
Because planets change speed during their orbits, their must be changes in force
to accelerate and decelerate the planets.
3. reaction
When an object exerts a force upon a second
object, the second object exerts a force on
the first that is equal in magnitude and
opposite in direction.
Universal Gravitation
Every mass exerts a force of attraction on every
other mass. The strength of the force is directly
proportional to the product of the masses divided
by the square of their separation
F = Gm1m2/r2
F is force of gravity (N)
m’s are masses (Kg)
r is the distance between the masses (m)
and G is the universal gravitational constant
G = 6.67E-11 m3/kgs2
Measuring an objects mass using orbital motion.
Centripetal Force is the force required to keep an
object moving in a circular path (to overcome
inertia).
F = (mV2)/r
F is centripetal force (N)
m is mass moving in a circle (Kg)
V is the velocity of the moving object (m/sec2)
R is the radius of the circular path (m)
The planets are maintained in a roughly circular orbit by the force of the sun’s
gravity pulling them inward. This provides an explanation for Kepler’s second law and
leads to the following calculation.
F (gravity) = F (centripetal)
Gmsme/r2 = (meV2)/r (notice that the mass of the moving object
cancels out of the equation)
2
2
Gms/r = (V )/r
ms = V2r/G
Lets Try
(notice that although this calculation is for
the sun based on the orbit of the Earth, it
would work for the mass of any object
around which another object revolved)
V of the Earth is the circumference of its orbit divided by
365.25 days.
2r/(365.25 x 24 x 60 x 60 sec)
2(1.5 x 1011 m)/3.156 x 107 sec
= approx 30,000 m/sec
ms = (29,865 m/s)2 x (1.5 x 1011m) / (6.67 x
10-11 m3/kgs2)
ms = 2 x 1030 Kg
Compare to accepted value of 1.989 x 1030 Kg
Surface gravity (acceleration of dropped objects for example)
F = m1a = Gm1m2/r2
a = Gm/r2 knowing mass of Earth, we can calculate the
acceleration of gravity on Earth. (9.8 m/sec2)
The relationships between gravity, mass, acceleration and distance provide us
with a powerful tool to determine attributes of the planets and their moons.
ALL OF A SUDDEN WE CAN CALCULATE MASSES OF OBJECTS (AND WE
DON’T HAVE TO FIT THEM ON A BALANCE)!!!!!
The accepted mass of the Earth is 5.97 x 1024 Kg.
Can you demonstrate this by using the distance from the Earth to the moon 3.84 x 108 m
and its orbital period of 27.3 days.