#### Transcript Astronomy 360 - indstate.edu

```Astronomy without a
Telescope
Angular Measurements
• There are 360 degrees in a full circle and 90 degrees in
a right angle
• Each degree is divided into 60 minutes of arc
• A quarter viewed face-on from across the length of a
football field is about 1 arc minute across.
• Each minute of arc is divided into 60 seconds of arc
• The ball in the tip of a ballpoint pen viewed from across
the length of a football field is about 1 arc second across.
• The Sun and Moon are both about 0.5 degrees.
• Bowl of the Big Dipper is about 30 degrees from the
NCP
• Any object ``half-way up'' in the sky is about 45 degrees
above the horizon
This is the preferred coordinate system (Equatorial Coordinates) to pinpoint objects on the
celestial sphere. Unlike the horizontal coordinate system, equatorial coordinates are
independent of the observer's location and the time of the observation. This means that only
one set of coordinates is required for each object, and that these same coordinates can be
used by observers in different locations and at different times.
The equatorial coordinate system is basically the projection of the latitude and longitude
coordinate system we use here on Earth, onto the celestial sphere. By direct analogy, lines of
latitude become lines of declination (Dec; measured in degrees, arcminutes and
arcseconds) and indicate how far north or south of the celestial equator (defined by
projecting the Earth's equator onto the celestial sphere) the object lies. Lines of longitude
have their equivalent in lines of right ascension (RA), but whereas longitude is measured in
degrees, minutes and seconds east the Greenwich meridian, RA is measured in hours,
minutes and seconds east from where the celestial equator intersects the ecliptic (the vernal
equinox).
At first glance, this system of uniquely positioning an object
through two coordinates appears easy to implement and
maintain. However, the equatorial coordinate system is
tied to the orientation of the Earth in space, and this
changes over a period of 26,000 years due to the
precession of the Earth's axis. We therefore need to
append an additional piece of information to our
coordinates - the epoch. For example, the Einstein Cross
(2237+0305) was located at RA = 22h 37m, Dec = +03o05'
using epoch B1950.0. However, in epoch J2000.0
coordinates, this object is at RA = 22h 37m, Dec = +03o
21'. The object itself has not moved - just the coordinate
system.
The equatorial coordinate system is alternatively known
as the 'RA/Dec coordinate system' after the common
abbreviations of the two components involved.
Where the celestial
equator intercepts
the ecliptic
What is the Celestial Sphere?
What is the Celestial Equator?
Latitude and Longitude
Time: UTC (Zulu Time, GMT)
Sidereal Time or “Star Time”
The solar day is slightly longer than the sidereal day. The solar day is
24 hours and the sidereal day is 23 hrs and 56 minutes. See page
177 ESSAY TWO for a full explanation. We will return to this later.
You can scale sky distances with your hand. For most people a fully
the Big Dipper from the tip of the handle to the bowl. Finger widths alone
give just a few degrees.
Measuring the Diameter of Astronomical Objects
To find an astronmical’s body true diameter from its
angular diameter if we know its distance. The
angular size of a distant object changes inversely
with the objects distance.
The scaling of distances with your hand makes it easy to point out
stars to other people.
Azimuth
Two ways of measuring the position of stars. Topo-centric Coordinates (right) and
Celestial Coordinates (left). What are advantages and disadvantages of both. As a star
rises and moves across the sky, which of the following change? (a) its right ascension (b)
Its declination (c) its azimuth (d) both (a) and (b) (e) none of the above.
Note that A is
expressed in
degrees and that
L and D are in
the same units.
Problem Example
The great galaxy in Andromeda has an angular diameter along its long
axis of about 5°. Its distance is about 2.2 million light-years. What is its
linear diameter?
2 2.2 5
L
o
360
o
L = 0.192 x 106 Light Years
or
L = 1.92 x 105 Light Years
A shell of gas blown out of a star has an angular diameter of 0.1° and a
linear diameter of 1 light-years. How far away is it?
2 D A
L
o
360
o
L 360
D
2 A
1 360
D
2  0.1
D = 572.96 ~ 573 ly
• Eratosthenes measured the
shadow length of a stick set
vertically in the ground in the
town of Alexandria on the
summer solstice at noon,
length to an angle of solar
light incidence, and using the
distance to Syene, a town
where no shadow is cast at
noon on the summer solstice
Review of Eratosthenes Problem as a teaching aid to the Myrmidon problem
How you can do much of backyard astronomy by deductive reasoning. This sketch shows
how Eratosthenes (Pronunciation: \-ˌer-ə-ˈtäs-thə-ˌnēz\) of Cyrene (276 BC - 194 BC)
used the length of a shadow at two different locations to determine the Earth’s size. You
need to collaborate with someone at least several hundred miles north or south of you.
Set up a vertical stick and a piece of paper beside the stick. Record the shadow at two
different locations. You must know the straight line distance between the two locations.
Measure the angles A and B at the top of the triangles. Suppose the earth’s
circumference is 40,007.86 km (meridional) and the radius is 6367 km. What would be
the angle A – B for B at the equator and A 250 km due North?
The Myrmidon Size Problem
Suppose you were an alien living on the fictitious warlike planet
Myrmidon and you wanted to measure its size. The Sun is shining
directly down a missile silo 1000 miles to your south, while at your
location, the Sun is 36° from straight overhead. What is the
circumference of Myrmidon? What is its radius?
You are here
a
36o
360o
Angle a is 36o
1000

therefore
C
C = 10,000 miles
a
2R= 10000
R = 10000/ 2
R = 1592 miles
Myrmidon
Missile silo is here a
1000 miles south of
you
Figure 1.26
The Geocentric Theory of Ptolemy, Aristotle et al
Astronomy in the Renaissance
• However, problems remained with
the geocentric theory:
– Could not predict planet positions
any more accurately than the
model of Ptolemy
– Could not explain lack of parallax
motion of stars
– Conflicted with Aristotelian
“common sense”
– Problems were solved by
Nicolaus Copernicus with his
heliocentric theory. He placed
the sun at the center (of our solar
system)
Nicolaus Copernicus (19 February 1473 – 24 May 1543)
motion was one of the
reasons that the geocentric
theory was not accepted by
Nicholaus Copernicus but
was easily explained by
heliocentric theory
Copernican Theory was also accepted by Galileo
Galilei (born 15 February 1564– died 8 January
1642)
Both Galileo and Copernicus had difficulty
with the Copernican theory because of
religious views
Diagram of the Copernican
system, from De Revolutions
The moon returns to the same position with
respect to the background stars every 27.323
days. This is its sidereal period.
Astronomy in the Renaissance
• Tycho Brahe (15461601)
– Designed and built
instruments of far
greater accuracy than
any yet devised
measurements of the
planets
Astronomy in the Renaissance
• Tycho Brahe (15461601)
(supernova and comet)
that suggested that the
heavens were both
changeable and more
complex than previously
believed
– Proposed compromise
geocentric model, as he
observed no parallax
motion!
Astronomy in the Renaissance
• Johannes Kepler
(1571-1630)
– Upon Tycho’s death,
his data passed to
Kepler, his young
assistant
– Using the very
precise Mars data,
Kepler showed the
orbit to be an ellipse
Kepler’s 1st Law
• Planets move in
elliptical orbits with
the Sun at one
focus of the ellipse
Kepler’s 2nd Law
• The orbital speed of
a planet varies so
that a line joining
the Sun and the
planet will sweep
out equal areas in
equal time intervals
• The closer a planet
is to the Sun, the
faster it moves
Kepler’s 3rd Law
• The amount of time
a planet takes to
orbit the Sun is
related to its orbit’s
size
• The square of the
period, P, is
proportional to the
cube of the
semimajor axis, a
Kepler’s 3rd Law
• This law implies that
a planet with a
larger average
distance from the
Sun, which is the
semimajor axis
distance, will take
longer to circle the
Sun
• Third law hints at
the nature of the
force holding the
planets in orbit
Kepler’s 3rd Law
• Third law can be
used to
determine the
semimajor axis,
a, if the period, P,
is known, a
measurement
that is not difficult
to make
Some Tips in General Observing
• The longer you stay out at night the more sensitive your eyes will
• The pupils open wider. The pubils have a normal diameter of 2 mm
but in total darkness they may expand to 7 or 8 millimeters
• Chemical changes in the retina make it about 1 million times more
sensitive to light than in full daylight
• In addition to becoming more sensitive to light your eye also
changes sensitivity to color (Purkinje effect). It becomes more
sensitive to the blue. (this is why blue lights are used in insect
attractors)
• It is easier to see faint objects if you look to the side of them
(averted vision). The center of your field of view is densely packed
with receptors that allow you to see fine detail.
Tip of the Day: (1) How sunrise to sunset is defined. Sunrise is time from just when the top of the
sun clears the horizon to sunset when the last bit of sun disappears.
(2) Astronomy Magazine Sept. 2002 issue defines the faintest naked eye star at 6.5 apparent
magnitude.
“Apparent Magnitude” was defined by Hipparachus in 150 BC. He devised a
magnitude scale based on:
However, he underestimated
the magnitudes. Therefore,
many very bright stars today
have negative magnitudes.
Magnitude
Constellation
1
(Orion)
2
Big Dipper
6
Star
Betelgeuse
various
stars just barely seen
Magnitude Difference is based on the idea that the difference between the
magnitude of a first magnitude star to a 6th magnitude star is a factor of 100.
Thus a 1st mag star is 100 times brighter than a 6th mag star. This represents a
range of 5 so that 2.512 = the fifth root of 100. Thus the table hierarchy is the
following.
Absolute Magnitude is defined
Magnitude Difference of 1 is 2.512:1, 2 is
2.5122:1 or 6.31:1, 3 is 2.5123 =
15.85:1 etc.
as how bright a star would appear
if it were of certain apparent
magnitude but only 10 parsecs
distance.
From: www.astronomynotes.com by Nick Strobel
Table 2.1
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