Transcript PHYS_3380_082416_bw

PHYS 3380 - Astronomy
Homework Set # 1
8/24/16
Due: 8/31/16
Chapter 2
Review questions: 8, 10
Discussion question 2
Problems 3,5,9
1. Rigel ( Orionis) has a declination of -8 12’ 6” and a
right ascension of 5h 14m 32.3s. It is at an elevation of 34
at the meridian, looking to the north. What is your latitude?
2. You have a sundial that tells you that your solar local
time is 5:15 PM. Your watch tells you that the Greenwich
Mean Time is 10:00 hours. What is your longitude?
PHYS 3380 - Astronomy
Star Names
Brightest stars named thousands of
years ago - most come from ancient
Arabic
Astronomers now use Bayer
designations for the brighter stars introduced by Johann Bayer in his star
atlas Uranometria in 1603 - consists of a
Greek letter followed by the genitive (in
Latin) of the name of the constellation in
which the star lies:
Aries → Arietis; Taurus → Tauri; Gemini
→ Geminorum; Virgo → Virginis; Libra →
Librae; Pisces → Piscium; Lepus →
Leporis.
- brightest star of the constellation given the designation Alpha, the next brightest
Beta, and so on.
Flamsteed designations (introduced by John Flamsteed in 1712) - used when no
Bayer designation exists - use numbers instead of Greek letters. Numbers were
originally assigned in order of increasing right ascension within each constellation due to the effects of precession they are now slightly out of order in some places.
PHYS 3380 - Astronomy
Magnitude Scale
Brightness of stars specified with the magnitude system. Devised by Greek
astronomer Hipparchus (~150 BC) devised
- brightest stars into the first magnitude class, the next brightest stars into
second magnitude class, until all of the visible stars grouped into six
magnitude classes. The dimmest stars were of sixth magnitude.
- therefore based on how bright a star appeared to the unaided eye.
By 19th century technology developed to objectively measure a star's brightness magnitude system refined and quantified
- they thought that the eye sensed differences in brightness on a
logarithmic scale so a star's magnitude is not directly proportional to the
actual amount of energy you receive.
- established a magnitude scale in which a difference of 5 magnitudes
corresponds to a factor of exactly 100 times in intensity
Some objects go beyond Hipparchus' original bounds of magnitude 1 to 6
- bright objects can have magnitudes of 0 or even negative numbers and
very faint objects have magnitudes greater than +6.
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Tycho Brahe attempted to directly measure the
“bigness” of the stars in terms of angular size - in
theory meant that a star's magnitude could be
determined by more than just subjective judgment.
• concluded that first magnitude stars measured
2’ in apparent diameter, with second through
sixth magnitude stars measuring 3/2’, 13/12’,
3/4’, 1/2’, and 1/3’, respectively.
• development of the telescope showed that
these large sizes were illusory—stars appeared
much smaller through the telescope.
However, early telescopes produced a spurious
disk-like image of a star (an Airy disk) that was
larger for brighter stars and smaller for fainter ones.
• Astronomers from Galileo to Jaques Cassini
mistook these spurious disks for the physical
bodies of stars, and thus into the eighteenth
century continued to think of magnitude in
terms of the physical size of a star
Diffraction pattern
resulting from a
uniformly-illuminated
circular aperture - has
bright region in the
center – the Airy disk,
Together with the
series of concentric
bright rings around is
called the Airy
pattern. Angular size
dependent on aperture
size – lens diameter
PHYS 3380 - Astronomy
The Modern Magnitude System
The apparent brightness of a star depends on two things:
- How much light is it emitting: luminosity (L) [watts] ~ r2T4
- How far away is it: distance (d) [meters]
App Bright = L / 4d2
Apparent magnitude:
- Apparent brightness of a celestial body based on a logarithmic scale of
luminosity.
- This scale runs backwards - the bigger the number, the fainter the star:
brightest stars are #1, next brightest are #2, etc.
- Magnitude scale: 1 is 2.5:1
2 is 6.3:1
5 is 100:1
- Each difference of 5 in magnitude corresponds to 100 in brightness
IA
 (2.512)(mB mA )
IB
and
IA 
mB  mA  2.5log 
IB 

PHYS 3380 - Astronomy
Rigel has an apparent magnitude of +0.13
Markab has an apparent brightenss of +2.48
Ratio of brightness of Rigel to Markab is:
IA
 (2.512)(m B m A )  2.512(2.480.13)  8.17
IB
Sirius has an apparent magnitude of -1.46
Ratio of brightness of Sirius to Rigel is:
IA
 (2.512)(m B m A )  2.512(2.48(1.46))  37.7
IB
Luminosity of Stars
Luminosity – the total amount of power radiated by a star into space.
Apparent brightness/apparent
magnitude refers to the amount of a star’s
light which reaches us per unit area.
- the farther away a star is, the fainter
it appears to us
- how much fainter it gets obeys an
inverse square law
- its apparent brightness decreases as
the (distance)2
PHYS 3380 - Astronomy
Apparent Magnitude
Absolute Magnitude
Equivalent to the apparent magnitude if star were placed 10 parsecs (32.6
light years) from sun.
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Rotation
The Earth rotates about its axis
once per day - one rotation equals
one day. The axis goes through the
north and south poles and through
the center of the Earth. It rotates
counterclockwise when looking
down on the north pole which
means that the sun rises in the east
and sets in the west.
PHYS 3380 - Astronomy
The Rotation of the Earth From Space
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Earth’s rotation causes the stars
- the celestial sphere - to
appear to rotate around the
Earth. Viewed from outside, the
stars (and the Sun, Moon, and
planets) therefore appear to
make simple daily circles
around us. The red circles
represent the apparent daily
paths of a few selected stars.
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The Celestial Sphere
Envisioned by the ancients, the celestial sphere had Earth at the
center with the stars emblazoned on the sphere. They thought the
stars rose and set because the celestial sphere (the sky) rotated,
carrying the stars from east to west. All stars appear to move
around two points on the celestial sphere, the north and south
celestial poles—projections of earth’s axis of rotation. Earth's
equator projected on the celestial sphere becomes the celestial
equator.
PHYS 3380 - Astronomy
Our lack of depth
perception when
we look into space
creates the illusion
that the Earth is
surrounded by a
celestial sphere.
Thus, stars that
appear very close
to one another in
our sky may
actually lie at very
different distances
from Earth.
PHYS 3380 - Astronomy
A model of the celestial
sphere shows the
patterns of the stars, the
borders of the 88 official
constellations, the
ecliptic, and the celestial
equator and poles.
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Latitude and Longitude
Dallas:
latitude = 32.78º N
longitude = 96.78º W
We can locate any place on the Earth's surface by its latitude and longitude.
Latitude measures angular distance north or south of the equator. Longitude
measures angular distance east or west of the prime meridian (which passes
through Greenwich, England).
PHYS 3380 - Astronomy
Zenith is the point directly overhead, nadir is the point directly underneath.
The meridian is the line drawn from the horizon in the south through zenith to
the horizon in the north.
PHYS 3380 - Astronomy
A circumpolar constellation never rises or sets - they are always visible.
Your latitude determines the portion of the celestial sphere visible in your
sky and what constellations/stars are circumpolar.
(a) A Northern Hemisphere sky.
(b) A Southern Hemisphere sky.
At what latitude would you see the entire sky?
PHYS 3380 - Astronomy
Star Trails
The Southern Hemisphere
The Northern Hemisphere
The Earth's rotation causes stars to trace daily circles around the sky. The north
celestial pole lies at the center of the circles. Over the course of a full day,
circumpolar stars trace complete circles, and stars that rise in the east and set
in the west trace partial circles. Here, the time exposure lasted about 6 hours we see only about one-quarter of each portion of the full daily path.
PHYS 3380 - Astronomy
Finding the Celestial Poles
You can always find north using the North Star. Polaris can be found
using the big dipper. Draw a line through the two “pointer” stars at the
end of the big dipper and follow it upwards from the dipper about four
outstretched hand’s width. The big dipper is circumpolar in the US so is
always above the horizon. The south celestial pole can be found using
the Southern Cross. There is no “South Star”
PHYS 3380 - Astronomy
The Big and Little Dippers
PHYS 3380 - Astronomy
Motion of the Night Sky Animation
PHYS 3380 - Astronomy
The height in degrees of the north star above the horizon is the same as
your latitude.
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
The angle  between the horizon and Polaris is the latitude of the observer.
If Dallas is at 33º latitude, where is Polaris in the sky? Where is it at the
Equator?
PHYS 3380 - Astronomy
Angular Size
Distances in the sky
measured by angular
distance:
Minute of arc = 1/60th of
a degree
Second of arc = 1/3600th
of a degree
Angular diameter angular distance from
one side of an object to
the other
PHYS 3380 - Astronomy
Revolution
Earth travels around the sun (orbits) once per year in the same direction it
rotates. It’s orbit is not quite a perfect circle - it is elliptical. The location in
the orbit of the minimum and maximum distances from the Sun are called
perihelion and aphelion. The plane of the orbit is called the ecliptic.
PHYS 3380 - Astronomy
Earth’s Axial Tilt
Ecliptic
Plane
The Earth’s axis is currently tilted 23.5º to the ecliptic. It varies over time
between 22º and 25º due the the gravitational forces from Jupiter and the
other planets.
PHYS 3380 - Astronomy
The axis remains at the same tilt angle - pointed at Polaris - throughout the
orbit because of conservation of angular momentum. The ecliptic plane is the
plane of the Earth’s orbit. Looking from the Earth, it is the apparent path of
the Sun (and planets) in the sky.
PHYS 3380 - Astronomy
The Relationship of the Celestial Equator and the
Ecliptic Plane
PHYS 3380 - Astronomy
The Zodiac
The Sun appears to move steadily eastward along the ecliptic, through the
constellations of the zodiac. As Earth orbits the Sun, we see the Sun
against the background of different zodiac constellations at different times
of year. For example, on August 21 the Sun appears to be in the
constellation Leo. Defines astral calendar.
PHYS 3380 - Astronomy
Sun’s Path Through the Zodiac
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Celestial
Sphere
The apparent
Sphere of the
sky
Celestial
Poles
The points
about which
the celestial
sphere
appears to
rotate
Celestial
Equator
Projection of
the Earth’s
equator on the
celestial
sphere
Ecliptic
Apparent
annual path of
the sun on the
celestial
sphere
PHYS 3380 - Astronomy
Coordinate Systems
Geographic
Latitude - lines of latitude parallel to
Earth’s equator - labeled north or south
relative to equator - from 90º N to 90º S
Celestial
Declination - lines of declination parallel to
celestial equator - labeled positive or
negative relative to celestial equator - from 90º to +90º
Longitude - lines of longitude extend from
North Pole to South Pole - by international Right ascension - lines of right ascension
run from north celestial pole to south
treaty, longitude 0 (the prime meridian)
celestial pole - by convention 0 runs through
runs through Greenwich, England
spring equinox - measured in hours, minutes
and seconds east of spring equinox - one
hour is 15º
PHYS 3380 - Astronomy
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Sun’s Altitude vs Latitude and Season Animation
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Local Skies
Lines of constant declination cross the sky at different altitudes,
depending on your location on Earth.
declination line = your latitude - goes through your zenith
the altitude of the N or S celestial pole = your latitude
PHYS 3380 - Astronomy
Local Skies
PHYS 3380 - Astronomy
Determining latitude
Find celestial pole - latitude equal to angular altitude - in northern
hemisphere Polaris is within 1º of celestial pole
For more precision - use star
with known declination determine angular altitude as it
crosses your meridian imaginary half circle drawn from
your horizon due south, through
zenith (point directly overhead)
to horizon due north - or when
star is at its highest altitude in
the sky. Ancients used crossstaff or Jacob’s ladder to
determine angular altitude.
Modern device called a sextant.
Sextant
PHYS 3380 - Astronomy
Vega crosses your meridian in the southern sky at 78º 44’. You know it
crosses your meridian at 38º 44’ north of the celestial equator. So the celestial
equator must cross your meridian at an altitude of 40º so your latitude is 50º.
The formula for latitude is
  Elevation  declination
north 
90 
south 

north/south of zenith. Sun can also be used if you know the date and the
Sun’s declination on that date.
PHYS 3380 - Astronomy
Annual Motion of the Sun
The R.A. of the Sun…
increases about 2 hours
per month
The Declination of the Sun…
varies between –23º and
+23º
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Celestial Navigation
Determining longitude
Need to compare current positions of objects in your sky with positions at
known longitude - Greenwich (0º Longitude). For instance - use sundial to
determine local solar time is 3:00 PM. If time at Greenwich is 1:00 PM, you
are two hours east of Greenwich and your longitude is 15º X 2 = 30º East
Longitude.
Accurate determination of longitude required invention of clock that could
remain accurate on a rocking ship. By early 1700s, considered so
important, British government offered large monetary prize for the solution claimed by John Harrison in 1761. Clock lost only 5 seconds during a 9week voyage.