4. • Celestial Sphere – an imaginary hollow sphere that encloses
the Earth, where the stars, the sun and other heavenly bodies
are embedded.
• The points where Earth’s rotational axis cuts this sphere is
called NCP (North Celestial Pole) and SCP (South Celestial Pole).
• The Celestial Equator – projection of the Earth’s equator in the
celestial sphere.
• Ecliptic - the path that the sun appears to take around the
celestial sphere. It is inclined 23.5 degrees with respect to the
celestial equator.
5. • Solstices –the two points on the ecliptic with the greatest
distance from the celestial equator.
• Summer Solstice – point where the sun is at its northernmost
position above the celestial equator. It happens every June 21.
• Winter Solstice - point where the sun is at its southernmost
position at the celestial equator. It happens every December
21.
• Equinoxes – the two points where the ecliptic intersects the
celestial equator. Earth’s rotational axis is perpendicular to the
line joining the Earth and the sun. Day and night are equal.
• Autumnal Equinox – happens every September 22.
• Vernal Equinox – happens every March 21.
• Constellations- a series of star clusters where the ecliptic
crosses.
• Zodiac – sequence of constellation
6.
7.
8. Precession – change in the orientation of the rotational axis of any rotating
body. Earth requires 26 000 years to complete one cycle of precession.
(50.2seconds/year)
• Hipparchus of Nicaea – was credited on the discovery of the precession of
the equinoxes.
• Lunisolar Precession - Earth’s precession due to the gravitational pull of the
moon and the sun.
• Diurnal Motion – the apparent daily motion of stars and other celestial
bodies across the sky caused by the Earth’s rotation about its axis.
Responsible for the daily rising and setting of the sun.
• Annual Motion – the apparent motion of the sun caused by Earth’s
revolution around it. It accounts for the visibility of the zodiac constellations
at a specific time of the year. It is responsible for the seasons.
9.
10.
11.
12. Proposal that Earth is Spherical
• It was Pythagoras and his pupils who were first to propose a spherical
Earth.
• Anaxagoras further supported Pythagoras' proposal
through his observations of the shadows that the Earth
cast on the Moon during a lunar eclipse. He observed that
during a lunar eclipse, the Earth's shadow was reflected
on the Moon's surface. The shadow reflected was circular.
13. Proposal that Earth is
Spherical
• Aristotle listed several arguments for a
spherical Earth which included the positions
of the North star, the shape of the Moon
and the Sun, and the disappearance of the
ships when they sail over the horizon.
14.
15. Figure 1: The Sky around Us. The horizon is where the sky
meets the ground; an observer’s zenith is the point
directly overhead.
16. Gazing up, you get the impression that the sky is a
great hollow dome with you at the center (Figure
1), and all the stars are an equal distance from you
on the surface of the dome. The top of that dome,
the point directly above your head, is called the
zenith, and where the dome meets Earth is called
the horizon.
18. Figure 4: Star Circles at Different Latitudes. The turning of
the sky looks different depending on your latitude on Earth.
(a) At the North Pole, the stars circle the zenith and do not rise
and set.
(b) At the equator, the celestial poles are on the horizon, and
the stars rise straight up and set straight down.
(c) At intermediate latitudes, the north celestial pole is at some
position between overhead and the horizon. Its angle above the
horizon turns out to be equal to the observer’s latitude. Stars
rise and set at an angle to the horizon.
20. 3000 years ago - Egyptians
• Some 3000 years ago, the
Egyptians established a
365-day calendar based
on the tracks of the star
SIRIUS.
• The pyramids of Giza in
Egypt were constructed in
such a way that each side
faced north, south, east or
west of a compass within a
tenth of degree. The three
pyramids represent the
belt of stars of the
Constellation Orion.
21. Early Universe
• At 600 BCE,
Thales of
Miletus
proposed that
Earth is a disk
floating on
water.
22. Early Universe
• At 520 BCE, Anaximander
of Miletus, proposed that
Earth is a cylinder and
that its surface is curved.
25. GEOCENTRIC MODELS
A. THE
PYTHAGOREAN
MODEL
• Proposed by
Pythagoras. First
to assert that Earth
is round and that
the heavenly
bodies move in
circles.
• In this model,
Earth is at rest at
the center of the
universe, and
26. GEOCENTRIC MODELS
• PLATO’S SAVING
THE APPEARANCES
• Plato assumed that
all motions in the
universe are
perfectly circular
and that all
heavenly bodies
are ethereal or
perfect.
27. GEOCENTRIC MODELS
• Retrograde Motion - the apparent motion of a planet in a direction
opposite to that of other bodies within its system, as observed
from a particular vantage point.
• Direct motion or prograde motion is motion in the same direction
as other bodies
28. GEOCENTRIC MODELS
B. EUDOXUS’ MODEL
• First use Plato’s Saving the
Appearances using a 27 series
of concentric spheres on which
the sun, the moon and the
planets moved in perfect
circular motion.
• 1 sphere – fixed stars
• 3 spheres – moon
• 4 spheres – each for every five
known planet (Jupiter, Mercury,
Venus, Mars and Saturn)
29. GEOCENTRIC MODELS
ARISTOTLE’S MODEL
• Also used 27 celestial spheres of
Eudoxus.
• He added: 27 “buffering” spheres
between celestial spheres and an
outermost sphere that was the
domain of what called the Prime
Mover. The Prime Mover causes the
other spheres to rotate.
• The prime mover was considered
God, and the sphere of the firmament
as heaven.
• There are two realms – terrestrial and
celestial with the orbit of the moon as
the boundary. Below the moon’s orbit
is the terrestrial realm. The realm was
composed of four primordial
elements in the sequence: earth,
water, air and fire. The celestial realm
consists of the fifth element called
30.
31.
32. TO DO:
HOW DID ERATOSTHENES
CALCULATED THE
CIRCUMFERENCE OF THE
EARTH?
33.
34.
35. GEOCENTRIC MODELS
PTOLEMY’S MODEL
• Epicycle – a circle on which a
planet moves. The center of this
small circle in turns moves around
the Earth along a bigger circular
path called deferent.
• Hipparchus refined this model by
considering that the Earth was off
center or eccentric in the deferent
where the sun moved.
• In 140 AD, he defined a point on
the other side of the deferent’s
center and called it the equant.
• The circumference of the Earth is
25000 miles. Eratosthenes
measured it in 253 BCE using
trigonometry and the knowledge
of elevation of the sun at noon in
36.
37. HELIOCENTRIC MODELS
COPERNICUS’S MODEL
• Nicolaus Copernicus asserted that
Earth spins on its axis every day and
revolves around the sun just like the
other planets; only the moon orbits
the Earth.
• Uniformed circular motion and
Ptolemy’s Epicycles
• FLAWS: 1. Absence of Stellar Parallax
2. Lack of perceived motion of Earth
• Stellar Parallax – the apparent
displacement of a star because of a
change in the observer’s point of view.
• It is contained in Copernicus’s Book:
Revolutionibus Orbium Coelestium (On
the Revolution of Celestial Orbs
38.
39. Tycho Brahe
• He measured and
recorded the
positions of the sun,
moon and the planets
for 20 years.
• His data did not fit
models of Ptolemy
and Copernicus.
• He proposed that the
sun orbited the Earth,
but the other planets
revolved around the
Sun.
40. GALILEO’S ASTRONOMICAL
DISCOVERIES:
•Four major moons of Jupiter
•The phases of Venus
•The changes in apparent sizes of Venus
and Mars
•The mountains of the moon.
•Sunspots
•The small apparent sizes of the stars
41. KEPLER’S THREE LAWS OF PLANETARY
MOTION
LAW OF ELLIPSES
Planets move around the Sun in ellipses, with the Sun at one
focus
LAW OF EQUAL AREAS
in eq
The line connecting the Sun to a planet sweeps equal areas
ual times.
LAW OF HARMONIES
to
The square of the orbital period of a planet is proportional
the cube of the mean distance from the Sun.
42.
43.
44.
45.
46.
47. Problem 1:
The average distance of Mercury to Sun is 0.387AU. If
the eccentricity is 0.206, what is its semi-minor axis?
48. Problem 2:
The average distance of Mercury to Sun is 0.387AU. If
the eccentricity is 0.206. What is its perihelion and
aphelion distances?
49. TO DO:
DRAW THE ELLIPTICAL
ORBITS OF THE MERCURY
AND VENUS
Use the data table shown earlier. Compute the eccentricities and aphelion
and perihelion distances of the two planets using the equations given. Plot
the position of the Sun in your sketches.
DATA: 1 AU = 10cm
MERCURY = 0.38700 AU (Semi-Major), 0.37870 AU
(Semi-Minor)
50. LAW OF EQUAL AREAS
The line connecting the Sun to a planet sweeps equal areas
in equal times.
51. LAW OF HARMONIES
• The square of the orbital period of a planet is
proportional to the cube of the mean distance from the
Sun.
52.
53. TO DO:
PROVE KEPLER’S
• LAW OF HARMONIES
GRAPH THE CUBES OF THE SEMI MAJOR AXES OF
PLANETS (AU) IN THE Y-AXIS VS THE SQUARES OF
THEIR ORBITAL PERIODS (YEARS) IN THE X-AXIS.
56. Problem 1:
The orbital period of Mars is 1.881 years. Its average
distance to
the Sun is 1.524 AU. If Saturn’s average distance to the Sun
is 9.58 AU,
(a)how long does it take for Saturn to orbit the Sun (in
years);
(b)What are the perihelion and aphelion distances of
Saturn and Mars;
(c)What is the eccentricity of Saturn and Mars if their semi-
minor axes are 9.567and 1.5174 AU respectively?
57. Problem 2:
The aphelion radius of Venus is 0.728 AU, and its
perihelion radius is 0.718 AU. Considering it is on a leap
year, it takes 225 days for Venus to complete its
revolution around the Sun. If the average distance of
Jupiter to Sun is 5.203 AU, how long does it take for Jupiter
to orbit the Sun (in years)?
58. 1. Annual motion is the apparent yearly movement of the stars as
observed from Earth as a direct effect of the Earth’s revolution
around the sun.
2. The sun revolves 360 degrees a year around a path on the celestial
sphere called the ecliptic.
3. The closer you get to the poles, the larger the circle of circumpolar
stars is.
4. The circular path that the celestial bodies take to complete the
diurnal motion is called diurnal circle.
5. The apparent motion of celestial bodies viewed from Earth is east
to west
59. 6. Diurnal motion is the apparent daily revolution of the
celestial sphere around the celestial poles as a direct effect of
the Earth’s rotation on its axis.
7. The celestial equator is tilted by 23.5° to the ecliptic.
8. The inclination of the ecliptic is the reason the Sun moves
north and south in the sky as the seasons change.
9. At the North Pole, the stars circle the zenith and do not
rise and set.
10. At the equator, the celestial poles are on the horizon, and
the stars rise straight up and set straight down.
60.
61. 1. Proposed that Earth is a disk floating on
water.
2.Proposed that Earth is a cylinder and that its
surface is curved.
3. He assumed that all motions in the universe
are perfectly circular and that all heavenly
bodies are ethereal or perfect.
4. The apparent motion of a planet in a
direction opposite to that of other bodies
within its system
62. •5. The motion in the same direction as other
bodies
6. Planets move around the Sun in ellipses, with the
Sun at one focus
7.
eq
The line connecting the Sun to a planet
sweeps equal areas in equal times.
8. The square of the orbital period of a planet is
proportional the cube of the mean distance from
the Sun.
63. 9. He measured and recorded the positions of
the sun, moon and the planets for 20 years.
10. He proposed that the sun orbited the Earth,
but the other planets revolved around the Sun.
11.
