AST101
Lecture 2 Jan. 27, 2002
Eclipses
When the Moon enters the
Earth’s shadow it causes a
LUNAR eclipse – at time of full
moon only. Can see lunar eclipse
from anywhere on earth.
Moon’s shadow falling on Earth causes
SOLAR eclipse. There is a solar eclipse
only in limited region of moon’s shadow.
Solar eclipse occurs at full moon.
Lunar eclipse
Solar eclipse
Moon’s orbit is not exactly in the ecliptic plane. Can only get a solar eclipse
when Earth, Sun and Moon line up exactly, so there is not an eclipse every
month.
Ecliptic
(earth’s orbit
plane)
No eclipses if moon is above
or below the Earth-Sun line.
 Why is a solar eclipse more rare than a lunar eclipse?
Distances to astronomical objects
For all objects in the universe except the sun and the planets in our solar
system, we cannot visit and observe their nature at first hand. We have to
infer the nature of stars, galaxies etc. just on the basis of the light and other
radiation that they send us. The amazing thing is that despite this, we know
so much!
One of the most basic things we need to
know about an object in the universe is
“How far away is it?”
So measurement of distances is a big deal
in Astronomy, and there are a large range
of methods used, with those used to get
more distant objects based on those for
nearer objects. Over the semester, we
will discuss a set of methods used at ever
larger distances (see next to last page of
textbook). Typically the methods used for
further objects are less precise.
The ‘cosmic distance ladder’ – sequence
of methods to measure distances. We
will build this ladder rung-by-rung.
The solar system as we know it today
The planets orbiting the sun, going outward from Sun:
o Mercury
o Venus
o Earth
o Mars
o (asteroid belt)
o Jupiter
o Saturn
o Uranus
o Neptune
o Pluto
(Uranus, Neptune,
Pluto not known
before telescopes)
The orbital planes of the planets are nearly the same (near the ecliptic),
except for Pluto whose orbit is inclined at 17O
Planets rotate on axes in
same sense as revolution
around the sun. Our moon
revolves around Earth in
the same sense too.
Planetary sizes vary widely;
Jupiter, Saturn, Uranus
and Neptune are large and
have many moons.
Radar distancing:
What is distance from Earth to Moon? (or to nearby planets)
Can measure by bouncing a radar pulse off the moon and measuring
the time for the pulse to return. Call the time for pulse to return Dt
(generally use D to denote a difference or interval).
d
Moon
Earth
radar pulse
Radar (Electromagnetic wave) travels at the speed of light.
Speed of light ( c ) = 186,000 mi/s = 300,000 km/s = 3 x 10 8 m/s = 3 x 1010 cm/s
Thus using distance = rate (speed) x time:
2 d = c Dt (2d since pulse goes to Moon and back again) or d = c Dt/2
Can measure Dt to nanosecond (10-9s) accuracy: Get d ≈ 385,000 km with error
of a few meters (actually moon’s orbit around Earth is not circular, and d varies
between 363,000 and 406,000 km over month)
 What time interval is required for radar to go to moon and back?
 How long does light travel going from sun to earth (1AU)?
Distance measurement by Parallax:
From plane geometry, we know that a triangle is completely fixed (3 sides
and 3 angles known) if we know 2 angles and a side.
d
f
90o
Knowing angles 90O and measuring f
and s, one can obtain d without
stepping on the crocodile.
s
Trigonometry: tan f = s/d
- or just make a scale drawing and
determine d from it.
For astronomical objects, distance d is much larger than s (the
‘baseline’), and the angle f in the diagram is a small angle.
d
s
f
( Relation then simplifies: s = d f (or d = s/f) if f is in radians )
f is called the PARALLAX angle (s is the ‘baseline’). For fixed s,
small f means large d
To get distance to object in space, could measure
the parallax angle using the diameter of the earth
as baseline (observe the object relative to the
very distant ‘fixed stars’ from a fixed location on
earth 12 hours apart).
 Exercise:
f
blackboard
View your finger with outstretched arm, first
with left eye and then with right eye.
Apparent location of finger relative to the
distant wall differs due to the parallax. The
distance between your eyes is the baseline
here.
To get to larger distance, can use a larger baseline – for example, use
the baseline as the diameter of the earth’s orbit (2 AU). Measure the
parallax angle for the Earth at opposite points on its orbit in January
and July.
A nearby (red) star appears at
different positions relative to the
distant ‘fixed’ stars in Jan. and July.
Ancient’s view of the Universe
The ancient Greek astronomers made some basic assumptions about the
Universe to guide their models:
 The earth is at the center of the universe (geocentric universe) – we see
the sun circling us daily; the moon changes its location in the sky over a month.
The stars move in roughly a daily pattern.
The argument was made: Man is the most important creature in the universe,
so the center of the universe is Man’s home. And if the earth were moving, we
would feel it! (or fall off).
 Sun, moon, planets and stars move on SPHERES in circular motion with
constant angular speed – because the sphere is the ‘perfect’ figure, and the
heavens are the work of a perfect creator.
 The heavens are unchanging.
The Greek’s basic idea: All bodies are attached to spheres centered on Earth.
The sphere rotates around the earth in uniform motion carrying the heavenly
body with it. The rates of the sphere’s motion differ: Sun and stars circle in
about 1 day; Moon circles in ~1 month; Venus circles in over 1 year.
Moon
Earth
Venus
Sun
Fixed stars
Simplified geocentric model
with moving spheres
carrying the Moon, Sun,
fixed stars and known
planets (Mercury, Venus,
Mars, Jupiter and Saturn.
(Mercury, Mars, Jupiter,
Saturn not shown)
Motion of Sun and Moon, seen against the pattern of the stars, is west to
east.
For example if the Moon is in front of Orion one day, the next day, it will
appear to east of Orion.
Same with the Sun – over the course of the year, it moves through the
constellations of the zodiac in an easterly direction.
There are observational problems with a simple geocentric universe:
Even the Sun and moon appear to move non-uniformly with some deviation
from circles. The planets deviate from uniform circular motion even more.
east
west
Planets – for example Mars – usually move against the stars in an easterly
direction, but about once per year, reverse and move retrograde in westerly
direction for a while before reverting to standard easterly motion.
Also Mercury and Venus are never found far from the Sun – with circular
orbits around Earth, they should be found at any angle from Sun.
Ancient Greek’s made an ingenious hypothesis to ‘explain’ non-circular motion and
retrograde motion while keeping the geocentric picture and circular motion:
‘epicycles’: A planet moves on a circle (called an epicycle), whose center moves
in a circle around the earth (called the deferent). This system was brought to
its final form by Ptolemy.
deferent
planet
earth
epicycle
The center of the epicycle moves on the deferent. Varying the speed and
size of the epicycle and deferent can give many different kinds of motion.
(later slides)
To limit the maximum angle of Venus to the Sun, the velocity of Venus’
deferent should be exactly the same as Sun’s deferent.
Center of Venus
epicycle, and Sun move
at same angular speeds
on their deferents.
Maximum angle q of
Venus from Sun fixed
by size of Venus
epicycle (and radius of
deferent).
Venus
earth
q
Note: will never see the full disk of
Venus in light – always backlit by Sun
To get all the motions of the sun, moon, major
planets approximately right, Ptolemy required
80 separate circles, each with its own speed
of rotation.
Sun
Examples of epicycle motion:
If epicycle is fixed with no rotation to
deferent, the dashed line motion of the
planet is simply a larger circle. (The
revolution on the deferent rotates the
epicycle with it.)
earth
 Plot the shape of a planet’s orbit if it
moves on the epicycle in the opposite
sense as the motion on the deferent but
with the same angular speed.
B
earth
A
If epicycle rotates twice as rapidly as
the deferent, the dashed line motion of
the planet is an oval. (In this figure,
when ¼ turn is made on deferent, the
planet moves ½ turn on the epicycle, so
planet at A is all the way outside the
deferent and at B is all the way inside.)
earth
If epicycle rotates three times as rapidly
as the deferent, the dashed line motion
of the planet shows retrograde motion.
(The backward motion while the planet is
inside the deferent is greater than the
forward motion due to revolution of
epicycle on the deferent.)
By varying the size of epicycle and deferent, and speed of revolution on
epicycle and deferent, Ptolemy was able to give an approximate
representation of the planetary motion.
But the accuracy was not good! (failed to predict dates of eclipses etc.)
The system was very cumbersome with all those 80 arbitrary numbers
needed to describe it.
The price to pay for retaining circular motion centered on Earth was
large.
 Does this look ugly or what?