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Astronomy 1100
Introduction to Astrophysics
Goals: to develop a knowledge of some of the basic tools
used in the study of astronomy and astrophysics, and to
gain practical experience with them. The field depends
highly on accurate observations to make deductions about
the universe around us, and it is important to understand
which observations are fundamental and which are subject
to large observational uncertainties.
Emphasis is placed on the development of critical
judgment to separate observational information from
proposed physical models.
Astronomical Factoids
Ancient Numerology
20 = 1 × 20 = 2 × 10 = 4 × 5
Numbers 1, 2, 4, 5, 10 are factors of 20.
But 1 + 2 + 4 + 5 + 10 = 22 > 20
So 20 is an abundant number.
22 = 1 × 22 = 2 × 11
Numbers 1, 2, 11 are factors of 22.
But 1 + 2 + 11 = 14 < 22
So 22 is a deficient number.
6=1×6=2×3
Numbers 1, 2, 3 are factors of 6.
But 1 + 2 + 3 = 6 = 6 !
So 6 is a perfect number.
The first five known perfect numbers are:
6,
28,
496,
8128,
and 33,550,336.
They form a rather select group.
A perfect number is the sum of its proper positive
divisors, e.g.
6=1+2+3=123
28 = 1 + 2 + 4 + 7 + 14
= 1  2  14
=147
Very few perfect numbers exist.
6, 28, 496, 8128, 33,550,336, 8,589,869,056
The astronomical connection…
6 = the number of nights it takes the Moon to
go from a thin crescent after New Moon to
First Quarter phase.
28 = the number of nights it takes for the
Moon to go from a thin crescent after New
Moon until it disappears from view at the next
New Moon (“moonth” ≈ 29½ days).
Coincidence?
6 = number of sides on a cube
360 = 6 × 6 × 10 = number of degrees in a
circle  365, the number of days in a year
24 = 6 × 4 = number of hours in a day
The Phases of the Moon
The Phases of the
Moon
Phases of the Moon
Pictures in the Full Moon
The “Man in the Moon”
The “Lady in the Moon”
The “Beetle”
The “Rabbit”
Development of the 24-hour Day
April 19, 1990.
May 26, 1990.
May 3, 1990.
Moonrise over Seattle
Sunset and Moonset?
Development of the 24-hour Day
The “day” can be separated into four (4)
distinct segments:
Sunrise to Noon (high point)
Noon to Sunset
Sunset to Midnight (opposite of noon)
Midnight to Sunrise
If each of these segments is marked by the
Sun’s movement through 6 smaller segments
(6 is a perfect number) called “hours,” then the
day consists of 24 hours.
Circular units in Astronomy
A complete circle therefore consists of
360 = 6  6  10 units called degrees (°), or
24 = 4  6 units called hours (h).
Subdivisions are: 1° = 60 arcminutes (')
1' = 60 arcseconds (")
1h = 60 minutes (m)
1m = 60 seconds (s)
Plane Trigonometry:
Recall triangles in plane trigonometry.
A, B, and C denote
angles
a, b, and c denote
opposite sides
Interrelated through:
Scientific Notation in Astronomy
As in physics, mks units are normally used in
conjunction with powers of ten notation and
proper round-off rules. Astronomers can be
lazy at times, however, and often “stray” from
the standard usage.
For example, in the study of stellar
atmospheres, cgs units are used (an older
variant of mks units). In stellar astronomy, the
units of length, mass, and time are also
expressed typically as: parsecs (pc),
kiloparsecs (kpc), or Megaparsecs (Mpc), solar
masses (M), and years (yr) or Megayears (Myr).
Some examples.
1. The Sun’s disk has an average angular
diameter of 1920" while the Moon’s disk has an
average angular diameter of 1865". The Sun’s
average distance is 1.496  108 km, while that of
the Moon is 3.844  105 km. What are the
physical diameters of the Sun and the Moon?
Solution:
First step: outline the problem in a diagram.
r = 1.496108 km (Sun), r = 3.844105 km (Moon)
Since the angles in both cases are small, roughly
0°.5, it is possible to solve for the angular
diameter using the small angle equation, namely
where the angle θ is expressed in dimensionless
units, radians.
1 radian = 206265 arcseconds
For the Sun, r = 1.496108 km and θ = 1920".
For the Moon, r = 3.844105 km and θ = 1865".
Actual mean diameter of Moon = 3475 km.
2. The Hubble image below shows the satellites
Titan (upper right), Enceladus, Dione, and
Mimas (lower left) in transit across the planet
Saturn. The equatorial diameter of Saturn is
120,536 km. What is the diameter of Titan?
Solution: Measured diameters
of the two images are 2¼ mm
and 53 mm, respectively.
The agreement is exact to within the 2 significant
figure accuracy of the measurements.
The Summer
Triangle
Groups that
look like their
namesakes.
Hercules
Normally
pictured
holding the
world.
Sagittarius
An archer?
Better pictured
as a teapot.
The Perseus
Group
A story in the
stars.
Ursa Major
Does this group
truly look like a
bear??!
Finding Polaris
A better way? − from Rambling Through the
Skies, George Lovi, Sky & Telescope, December
1990.
The stars of Orion as pointers.
The field of Orion
The Heavenly “G.” Captain, all d’uh riggin’
seems perfectly polished.
Stars are presently designated in a variety of
ways: Greek letters, from east to west for stars of
comparable brightness (UMa)…
Greek letters, from from brightest to faintest for
stars of comparable brightness (Ori, Cas), as
well as Bayer-Flamsteed numbers…
Archaeoastronomy.
Many constellations bear names originating from
eras when the stellar configuration bore some
resemblance to the object after which they are
named, e.g. Ursa Major, the Great Bear.
Some were named for other reasons, e.g. Hydra.
Stars on the celestial equator (CE) rise due east
and set due west. In 2600 BC Hydra lay along the
CE, making then useful for navigation at night.
Only 50 of the 88
modern constellations
were known in antiquity.
They also outlined only
regions in the northern
sky, most being named
by ancient Minoans.
Ancient star maps.
Zodiacal Constellations, Astrological Eras, and
the link to precession.
The Taurus and Aries Eras.
The Beginnings? The Gemini Era.
The present.
The old constellation of Argo, the Ship, was very
large. It was but one of many symbols associated
with the story of Noah’s Ark.