Astronomy 1100Astronomy 1100Introduction to Introduction to AstrophysicsAstrophysics

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 A perfect number is the sum of its proper positive divisors, e.g.divisors, e.g.

6 = 1 + 2 + 3 = 1 6 = 1 + 2 + 3 = 1 2 2 3 328 = 1 + 2 + 4 + 7 + 1428 = 1 + 2 + 4 + 7 + 14

= 1 = 1 2 2 14 14= 1 = 1 4 4 7 7

Very few perfect numbers exist.Very few perfect numbers exist.6, 28, 496, 8128, 33,550,336, 8,589,869,0566, 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 3, 1990.

May 26, 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 denoteanglesa, 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 = 1.496108 km (Sun), r = 3.844105 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 = 1.496108 km and θ = 1920".

For the Moon, r = 3.844105 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 A better way? − from Rambling Through the Skies, George Lovi, Skies, George Lovi, Sky & TelescopeSky & Telescope, ,

December 1990.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 88modern constellationswere known in antiquity.

They also outlined onlyregions in the northernsky, most being namedby 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.