Video FYI

Brian Cox is a British astrophysicist who has produced some great BBC documentaries over the past few years.  Here is episode 1 of his "Wonders of the Universe" series.  Some of us watched part of it on Friday.

http://www.dailymotion.com/video/xyr1ly_wonders-of-the-universe-destiny_shortfilms

He also has a "Wonders of the Solar System" series and a "Wonders of Life" series.  All good stuff.

Final talk topics

black holes

neutron stars

variable stars

SETI

Drake equation

Supernovae

Galaxy types

end of the universe 

Olber's paradox

dark matter

dark energy

origin of the Moon

life on Earth?

Exoplanets

wormholes

relativity / twin paradox

general relativity

NASA

moon landing

radio waves from space - radio astronomy (K. Jansky)

WMAP

inflation (Adam Riess)

James Webb

Hubble (legacy / telescope)

astronaut training

planet colonizing

Mars One

entropy?  (2nd law of thermodynamics)

Stellar Evolution Images

Images FYI

Stars and the Main Sequence

There are 4 fundamental forces of nature:

Strong nuclear - this keeps protons close together
Weak nuclear a responsible for radioactive decay
Electromagnetism - light, electricity, magnetism, etc
Gravity - weakest of all, but furthest reaching



A star (Latin root stella-) is essentially a ball of gas powered by nuclear reactions, held together by gravity.

Stars may appear white, but their color is a conbination of many colors (and non visible e-m waves like uv).

Spectral types are listed in order of decreasing temperature:

O B A F G K M

with a temperature range from 60,000 K down to under 3500 K.

There are further subdivisions (C and S stars under M).

You can learn a lot about a star from where it lies on the Hertzsprung-Russel diagram.

The H-R diagram plots magnitude (brightness, from dim to bright) vs. temperature (high to low, usually as spectral type).
Hottest stars are on the left if the graph - they are normally brighter than cooler stars.

Most stars fall on along a diagonal band from upper left to lower right on the H-R diagram. We call this the Main Sequence, and the stars there are main sequence stars or dwarfs (which is a misleading term).

Stars above and to the right of the MS are giants (including supergiants).

Faint hit objects (white dwarfs) are below and to the left of the MS.

>

Electromagnetic Waves

Recall that waves can be categorized into two major divisions:

Mechanical waves, which require a medium. These include sound, water and waves on a (guitar, etc.) string

Electromagnetic waves, which travel best where there is NO medium (vacuum), though they can typically travel through a medium as well. All electromagnetic waves can be represented on a chart, usually going from low frequency (radio waves) to high frequency (gamma rays). This translates to: long wavelength to short wavelength.

All of these EM waves travel at the same speed in a vacuum: the speed of light (c). Thus, the standard wave velocity equation becomes:

c = f l

where c is the speed of light (3 x 10^8 m/s), f is frequency (in Hz) and l (which should actually be the Greek letter, lambda) is wavelength (in m).

General breakdown of e/m waves from low frequency (and long wavelength) to high frequency (and short wavelength):

Radio

Microwave

IR (infrared)

Visible (ROYGBV)

UV (ultraviolet)

X-rays

Gamma rays

In detail, particularly the last image:

http://hyperphysics.phy-astr.gsu.edu/hbase/ems1.html

http://csep10.phys.utk.edu/astr162/lect/light/spectrum.html

http://www.unihedron.com/projects/spectrum/downloads/full_spectrum.jpg

Don't forget - electromagnetic waves should be distinguished from mechanical waves (sound, water, earthquakes, strings on a guitar/piano/etc.). 

ALL E/M waves (in a vacuum) travel at the SPEED OF LIGHT (c).

Blackbody Radiation

The Doppler Effect

http://www.lon-capa.org/~mmp/applist/doppler/d.htm

The key in the Doppler effect is that motion makes the "detected" or "perceived" frequencies higher or lower.

If the source is moving toward you, you detect/measure a higher frequency - this is called a BLUE SHIFT.

If the source is moving away from you, you detect/measure a lower frequency - this is called a RED SHIFT. Distant galaxies in the universe are moving away from us, as determined by their red shifts. This indicates that the universe is indeed expanding (first shown by E. Hubble). The 2011 Nobel Prize in Physics went to local physicist Adam Riess (and 2 others) for the discovery of the accelerating expansion of the universe. Awesome stuff!

http://www.nobelprize.org/nobel_prizes/physics/laureates/2011/

It's worth noting that the effect also works in reverse. If you (the detector) move toward a sound-emitter, you'll detect a higher frequency. If you move away from a detector move away from a sound-emitter, you'll detect a lower frequency.

Mind you, these Doppler effects only happen WHILE there is relative motion between source and detector (you).

And they also work for light. In fact, the terms red shift and blue shift refer mainly to light (or other electromagnetic) phenomena.

If your computer runs Java:

http://falstad.com/mathphysics.html

Run the Ripple tank applet -

http://falstad.com/ripple/

oops!

I handed back the Astronomy quiz without telling you what the maximum number of points was.  It was 35.  If you need a percentage, take 35 minus the points you missed.  Then divide by 35.

Good weekend to ya!

Planet Quest

I decided against the idea of Planet presentation in favor of a "Planet Quest" lab.  This will be due in 2 classes - April 6.

Lab 4 - Tour of the Planets

In preparation for the upcoming Solar System test, I would like you to determine many interesting tidbits of trivia about our solar neighbors.  This may be useful:

http://nineplanets.org/

Please answer the following questions, based on your reading and web discovery.  Some questions might have several answers, while the answer to others might be "none of them."

Which planet(s):

1.     Rotates backwards?

2.     Revolves backwards?

3.     Rotates nearly on its side?

4.     Have more than 10 moons?

5.     Have only one moon?

6.     Has an orbit with the greatest inclination to the ecliptic?

7.     Is the furthest planet known to the ancients?

8.     Has a largely methane atmosphere?

9.     Has a nondescript, pale greenish color?

10.   Has a blemish known as the great dark spot?

11.   Has a fine iron oxide regolith?

12.   Is most similar to Earth in its surface gravity?

13.   Has the greatest mass?

14.   Has the smallest diameter?

15.   Have been visited by humans?

16.   Has the strongest magnetic field?

17.   Has rings?

18.   Has sulfuric acid clouds?

19.   Has the tallest mountain in the Solar System (and what is it)?

20.   Has a day longer than its year?

21.   Has been landed on most recently by spacecraft?

22.   Experiences global dust storms?

23.   Has a moon that rotates retrograde (and what is it)?

24.   Was once thought to be a failed star?

25.   Is heavily cratered?

26.   Has moons which are likely candidates for life?

27.   Was hit by a large comet in the last several years?

28.   Is most oblate?

Now for the minor bodies.

1.     Which body is an asteroid with its own orbiting asteroid?

2.     Which moon has erupting volcanoes?

3.     Which body is the largest asteroid?

4.     Approximately how many known asteroids are there?

5.     Approximately how many known Kuiper objects are there?  What is the Kuiper belt?

6.     How large is the Oort Cloud?  What is the Oort Cloud?\

7.   What are the Galilean satellites?

8.     Which moon was the first discovered after the Galilean satellites?

9.     What are Sedna and Eris?

10.     What exactly is Pluto?

Etcetera – Write anything else of interest you have uncovered during this exercise.

Star Stuff 2 - the Doppler Effect

See this simple, but effective applet:

http://lectureonline.cl.msu.edu/~mmp/applist/doppler/d.htm

In this simulation, v/vs is the ratio of your speed to the speed of sound; e.g., 0.5 is you, or the blue dot, traveling at half the speed of sound. Note how the waves experienced on one side "pile up" (giving an observer a greater detected frequency, or BLUE SHIFT); on the other side, the waves are "stretched apart" (giving an observer a lower detected frequency, or RED SHIFT).

Play with this for a bit, though it's a little less obvious:

http://falstad.com/ripple/

In astronomy, the red shift is very important historically: Edwin Hubble found that light from distant galaxies (as measured in their spectra) was red shifted, meaning that distant galaxies were moving away from us (everywhere we looked). The conclusion was obvious (and startling): The universe is expanding. Last year, local astrophysicist Adam Riess discovered that the rate of expansion was accelerating.

http://www.nobelprize.org/nobel_prizes/physics/laureates/2011/


It's worth noting that the effect also works in reverse. If you (the detector) move toward a sound-emitter, you'll detect a higher frequency. If you move away from a detector move away from a sound-emitter, you'll detect a lower frequency.

Mind you, these Doppler effects only happen WHILE there is relative motion between source and detector (you).

And of course, they also work for light. That's why we care about them. In fact, the terms red shift and blue shift refer mainly to light (or other electromagnetic) phenomena.

In practice, for astronomy:

v = [ (change in wavelength) / (original wavelength) ] c

Star Stuff 1

Angular Measurement

Consider the following convention which has been with us since the
rise of Babylonian mathematics:

There are 360 degrees per circle.
Each degree can be further divided into 60 minutes (60'), each called
an arcminute.
Each arcminute can be divided into 60 seconds (60"), each called an arcsecond.
Therefore, there are 3600 arcseconds in one degree.

Some rough approximations:
A fist extended at arm's length subtends an angle of approx. 10º.
A thumb extended at arm's length subtends an angle of approx. 2º.
The Moon (and Sun) subtend an angle of approx. 0.5º.

Human eye resolution (the ability to distinguish between 2 adjacent
objects) is limited to about 1 arcminute – roughly the diameter of a
dime at 60-m.  Actually, given the size of our retina, we're limited
to a resolution of roughly 3'

So, to achieve better resolution, we need more aperture (ie., telescopes).

The Earth's atmosphere limits detail resolution to objects bigger than
0.5", the diameter of a dime at 7-km, or a human hair 2 football
fields away.  This is usually reduced to 1" due to atmospheric
turbulence.

The parsec (pc)

The distance at which 1 AU subtends an angle of one arcsec (1") is
definite as one parsec – that is, it has a parallax of one arcsec.

For example, if a star has a parallax angle (d) of 0.5 arcsec, it is
1/0.5 parsecs (or 2 parsecs) away.

The parsec (pc) is roughly 3.26 light years.

Distance (in pc) = 1 / d

where d is in seconds of arc.

Measuring star distances can be done by measuring their angle of
parallax – typically done over a 6-month period, seeing how the star's
position changes with respect to background stars in 6 months, during
which time the Earth has moved across its ellipse.

Unfortunately, this is limited to nearby stars, some 10,000.  Consider
this:  Proxima Centauri (nearest star) has a parallax angle of 0.75" –
a dime at 5-km.  So, you need to repeat measurements over several
years for accuracy.

This works for stars up to about 300 LY away, less than 1% the
diameter of our galaxy!
[If the MW galaxy were reduced to 130 km (80 mi) in diameter, the
Solar System would be a mere 2 mm (0.08 inches) in width.]

Apparent magnitude (m) scale

This dates back to the time of Hipparchus who classified things as

bright or small.
Ptolemy classified things into numbers:  1-6, with 1 being brightest.
The brightest (1st magnitude) stars were 100 times brighter than the
faintest (6th magnitude).  This convention remains standard to this
day.  Still, this was very qualitative.

In the 19th century, with the advent of photographic means of
recording stars onto plates, a more sophisticated system was adopted.
It held to the original ideas of Ptolemy

A difference of 5 magnitudes (ie., from 1 to 6) is equivalent to a
factor of exactly 100 times.  IN other words, 1st magnitude is 100x
brighter than 6th magnitude.  Or, 6th magnitude is 1/100th as bright
as 1st mag.

This works well, except several bodies are brighter than (the
traditional) 1st mag.

So….. we have 0th magnitude and negative magnitudes for really bright objects.
Examples:
Sirius (brightest star):  -1.5
Sun:  -26.8
Moon:  -12.6
Venus:  -4.4
Canopus (2nd brightest star):  -0.7
Faintest stars visible with eye:  +6
Faintest stars visible from Earth:  +24
Faintest stars visible from Hubble:  +28

The magnitude factor is the 5th root of 100, which equals roughly
2.512 (about 2.5).

Keep in mind that this is APPARENT magnitude, which depends on
distance, actual star luminosity and interstellar matter.
Here's a problem:  What is the brightness difference between two
objects of magnitudes -1 and 6?

Since they are 7 magnitudes apart, the distance is 2.5 to the 7th power, or 600.
For the math buffs:  the formula for apparent magnitude comparison:
m1 – m2 = 2.5 log (I2 / I1)

The m's are magnitudes and the I's are intensities – the ratio of the
intensities gives a comparison factor.  A reference point is m = 100,
corresponding to an intensity of 2.65 x 10^-6 lumens.

Absolute Magnitude, M

Consider how bright the star would be if it were 10 pc away.  This is

how we define absolute magnitude (M).

It depends on the star's luminosity, which is a measure of its brightness:

L = 4 pi R^2 s T^4

R is the radius of the body emitting light, s is the Stefan-Boltzmann
constant (5.67 x 10-8 W/m^2K^4) and T is the effective temperature (in
K) of the body.

So, a star's luminosity depends on its size (radius, R) and absolute temperature (T).

If the star is 10 pm away, its M = m (by definition).
m – M = 5 log (d/10)

We let d = the distance (in pc), log is base 10, m is apparent
magnitude and M is absolute magnitude.

A problem:  If d = 20 pc and m = +4, what is M?  (2.5)

And another (more challenging):

If M = 5 and m = 10, how far away is the star?  (100 pc)

Newton

Newton's take on orbits was quite different. For him, Kepler's laws were a manifestation of the bigger "truth" of universal gravitation. That is:

All bodies have gravity unto them. Not just the Earth and Sun and planets, but ALL bodies (including YOU). Of course, the gravity for all of these is not equal. Far from it. The force of gravity can be summarized in an equation:

F = G m1 m2 / d^2

or.... the force of gravitation is equal to a constant ("big G") times the product of the masses, divided by the distance between them (between their centers, to be precise) squared.

Big G = 6.67 x 10^-11, which is a tiny number - therefore, you need BIG masses to see appreciable gravitational forces.

This is an INVERSE SQUARE law, meaning that:

- if the distance between the bodies is doubled, the force becomes 1/4 of its original value
- if the distance is tripled, the force becomes 1/9 the original amount
- etc.

Weight

Weight is a result of local gravitation. Since F = G m1 m2 / d^2, and the force of gravity (weight) is equal to m g, we can come up with a simple expression for local gravity (g):

g = G m(planet) / d^2

Likewise, this is an inverse square law. The further you are from the surface of the Earth, the weaker the gravitational acceleration. With normal altitudes, the value for g goes down only slightly, but it's enough for the air to become thinner (and for you to notice it immediately!).

Note that d is the distance from the CENTER of the Earth - this is the Earth's radius, if you're standing on the surface.

If you were above the surface of the earth an amount equal to the radius of the Earth, thereby doubling your distance from the center of the Earth, the value of g would be 1/4 of 9.8 m/s/s. If you were 2 Earth radii above the surface, the value of g would be 1/9 of 9.8 m/s/s.

The value of g also depends on the mass of the planet. The Moon is 1/4 the diameter of the Earth and about 1/81 its mass. You can check this but, this gives the Moon a g value of around 1.7 m/s/s. For Jupiter, it's around 25 m/s/s.

>


Newton, Philosophiae naturalis principia mathematica (1687) Translated by Andrew Motte (1729)

Newton's 3 laws of motion:

1.  Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.


2.  The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.


3.  To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.


In simpler language:

1.  A body will continue doing what it is doing unless there is REASON for it to do otherwise.  It will continue in a straight line at a constant velocity, unless something changes that motion.  This idea is often referred to as INERTIA.

2.  The second law is trickier:

An unbalanced force (F) causes a mass (m) to accelerate (a).  Recalling that acceleration means how rapidly a body changes its speed (in meters per second per second, or m/s/s):

F = m a

There is a new unit here:  the kg m/s/s - this is called a newton (N)

Note that a larger force gives a larger acceleration.  However, with a constant force - the larger the mass is the smaller the acceleration.  Imagine pushing me on a skateboard vs. pushing a small child with the same force - who would accelerate more rapidly?

3.  To every action there is always opposed an equal reaction.

You move forward by pushing backward on the Earth - the Earth, in turn, pushes YOU forward.

A rocket engine pushes hot gases backward - the gases, in turn, push the rocket forward.

If you fire a rifle or pistol, the firearm "kicks" back on you.

Kepler's Laws

Kepler's laws of planetary motion

http://astro.unl.edu/naap/ssm/animations/ptolemaic.swf

http://astro.unl.edu/naap/pos/animations/kepler.swf


Johannes Kepler, 1571-1630

Note that these laws apply equally well to all orbiting bodies (moons, satellites, comets, etc.)

1. Planets take elliptical orbits, with the Sun at one focus. (If we were talking about satellites, the central gravitating body, such as the Earth, would be at one focus.) Nothing is at the other focus. Recall that a circle is the special case of the ellipse, wherein the two focal points are coincident. Some bodies, such as the Moon, take nearly circular orbits - that is, the eccentricity is very small.

2. The Area Law. Planets "sweep out" equal areas in equal times. See the applets for pictorial clarification. This means that in any 30 day period, a planet will sweep out a sector of space - the area of this sector is the same, regardless of the 30 day period. A major result of this is that the planet travels fastest when near the Sun.

3. The Harmonic Law. Consider the semi-major axis of a planet's orbit around the Sun - that's half the longest diameter of its orbit. This distance (a) is proportional to the amount of time to go around the Sun in a very peculiar fashion:

a^3 = T^2

That is to say, the semi-major axis CUBED (to the third power) is equal to the period (time) SQUARED. This assumes that we choose convenient units:

- the unit of a is the Astronomical Unit (AU), equal to the semi-major axis of Earth's orbit (approximately the average distance between Earth and Sun). This is around 150 million km or around 93 million miles

- the unit of time is the (Earth) year

The image below calls period P (rather than T), but the meaning is the same:

Example problem:  Consider an asteroid with a semi-major axis of orbit of 4 AU. We can quickly calculate that its period of orbit is 8 years (since 4 cubed equals 8 squared).

Likewise for Pluto: a = 40 AU. T works out to be around 250 years.


The applets I referenced::

http://www.physics.sjsu.edu/tomley/kepler.html

http://www.physics.sjsu.edu/tomley/Kepler12.html
for Kepler's laws, primarily the 2nd law

http://www.astro.utoronto.ca/~zhu/ast210/geocentric.html
for our discussion on geocentrism and how retrograde motion appears within this conceptual framework

Cool:
http://galileo.phys.virginia.edu/classes/109N/more_stuff/flashlets/kepler6.htm

Lab 2

LAB 2 - Time and Space

In this lab, you will investigate several ways of keeping time in the universe. Measuring the passing of astronomical time is by no means a trivial task - keep that in mind, as you find the current time according to various websites. This lab is structured as a series of topics, followed by questions and suggested websites. Have fun, and take your time!

Local Time

Give the current local time (whenever you are performing this lab).  Specify whether  we are on EST or EDT, and when (and how) this will change.

Interested in the time elsewhere? Try this:

http://www.timeanddate.com/worldclock/ 

Universal Time and Greenwich Mean Time

UT is counted from 0 hours at midnight, with unit of duration the mean solar day, defined to be as uniform as possible despite variations in the rotation of the Earth. Find the current UT. The clock applet below may be helpful:

http://tycho.usno.navy.mil/utclock.html

UT is very similar to Greenwich Mean Time (GMT), though this term is not used often these days. Both are 5 hours ahead of EST. Is this currently true? If not, why not?  What is the current GMT?

Longitude and Latitude

These quantities give the location on the surface of the semi-spherical Earth, by laying a grid atop it. Lines of longitude are measured with respect to the Prime Meridian. Find the longitude of your hometown: Lines of latitude are measured with respect to the equator. Find the latitude of your hometown.  Google maps may help.

Julian Date (JD)

Julian Day Number is a count of days elapsed since Greenwich mean noon on 1 January 4713 B.C., Julian proleptic calendar. The Julian Date is the Julian day number followed by the fraction of the day elapsed since the preceding noon.

Find the current JD.

Calendar

Which calendar do we currently use?

What calendar was this switched from, and when?

Why was the switch made?

Does all the world use the calendar we do? Explain.

Sidereal Time

ST is time based on duration of the Earth's rotation with respect to a point nearly fixed relative to the stars. Local Sidereal Time (LST) is computed from ST using a longitude correction. Find the current LST.

The Lunar and Solar Cycles

Have a look at sunrisesunset.com. Determine how the sunrise and sunset times change from day to day. Also determine how the moonrise and moonset times change daily.  What is the pattern, if there is one?

Eclipses
Locate a source of upcoming lunar and solar eclipses.  Answer these questions:

Where and when is the next total solar eclipse?
Where and when is the next total lunar eclipse?
When will be the next total solar eclipse visible in North America?  Will there be more than one total solar eclipse visible in North America in your lifetime?

Etcetera

Discuss any other times and/or calendars that are of interest to you.  Pick one calendar to discuss (at least in brief).