Substitute Lab 1

Activity 2 – Observing:  Using a Star Chart

A star chart is a very useful tool for orienting yourself to the night sky.  Use the chart provided, accurate for this month (and our latitude), between 9 and midnight to answer the questions below.  If it is not clear, answer the questions based on the chart and then go outside on the next clear night.  Enjoy!

Note:  Relative brightnesses are indicated by the size of the dots.  Also, you may find it useful to use the reverse side of the chart to answer some of the other questions.

1.     If you look directly overhead (to the zenith), what do you see?

2.     What constellation(s) lie directly overhead?

3.     What asterism(s) lie directly overhead?

4.     What other asterisms can you locate?

5.     What are the brightest stars visible tonight?  Locate and identify them.

6.     What are the three stars of the Summer Triangle?  Locate each.

7.     Find the Big Dipper.  Can you see the double star in the handle?  This was used in the past as a test of visual acuity.

8.     Follow the arc of the handle toward the next bright star.  What star is this?  What is the next bright star past this one, following along the same basic arc?

9.     Follow the pointer stars of the Dipper to the next bright star.  What star is this?  Where is it located (constellation or asterism)?

10.   Is this star especially bright?  That is, is it one of the 5 brightest stars visible tonight?

11.   Continuing on, following the pointer stars past this star, find Cassiopeia.

12.   Describe or draw its shape.

13.   What constellation comes next?

14.   List two interesting features or objects close to or parts of this constellation.

15.   What is the lowest object you can see on your horizon?

16.   Can you find the teapot.  What constellation is this in?

17.   What interesting objects are located close to it?  Can you find them?

18.   What planet(s) is/are visible at this time?

19.   List 2 other interesting events worth viewing this month.

20.   Comment on the general viewing conditions in your region.

Questions

1.  What are the easiest ways to tell the difference between a star and a planet?

2.  Are there any comets viewable right now (with telescope)?

3.  When is the next full Moon?

4.  What is the brightest star visible in the evening sky?

5.  In your conclusion, tell me anything interesting that you learned in this lab.

Quiz 3

Sites used tonight:

 

http://scaleofuniverse.com/

http://xkcd.com/482/

http://astro.unl.edu/classaction/animations/renaissance/kepler.html

 

http://www.physics.sjsu.edu/tomley/Kepler12.html

 

http://www.youtube.com/watch?v=8yCzzTkDSMo

 

http://www.stumbleupon.com/su/2jRGYC/dd.dynamicdiagrams.com/wp-content/uploads/2011/01/orrery_2006.swf/

 

Quiz 3

 

Kepler's laws:

 

1.  Elliptical orbits

2.  Equal areas in equal times - and how the speed varies with the planet's position in its orbit

3.  a cubed = P squared.  The semi-major axis of orbit (cubed) is equal to the time around the Sun (squared), as long as you choose appropriate units (a is in AU - astronomical units; P is in Earth years)

 

Rough chronology:

 

Ptolemy

Copernicus

Tycho

Kepler / Galileo

Newton

 

Review the websites above if time allows.

The Acceleration due to Gravity

Friends....

We discussed the acceleration due to gravity in class. It is a value (g), and it is approximately equal to 9.8 m/s/s, near the surface of the Earth. At higher altitudes, it becomes lower - a related phenomenon is that the air pressure becomes less (since the air molecules are less tightly constrained), and it becomes harder to breathe at higher altitudes (unless you're used to it). Also, the boiling point of water becomes lower - if you've ever read the "high altitude" directions for cooking Mac n Cheese, you might remember that you have to cook the noodles longer (since the temperature of the boiling water is lower).

On the Moon, which is a smaller body (1/4 Earth radius, 1/81 Earth mass), the acceleration at the Moon's surface is roughly 1/6 of a g (or around 1.7 m/s/s). On Jupiter, which is substantially bigger than Earth, the acceleration due to gravity is around 2.2 times that of Earth. All of these things can be calculated without ever having to visit those bodies - isn't that neat?

Consider the meaning of g = 9.8 m/s/s. After 1 second of freefall, a ball would achieve a speed of .....

9.8 m/s

After 2 seconds....

19.6 m/s

After 3 seconds....

29.4 m/s

We can calculate the speed by using the simple equation:

vf = g t

In this case, vf is the speed at some time, g is 9.8 m/s/s, and t is the time in question.


Got it?

The distance is a bit trickier to figure. This formula is useful:


d = 0.5 gt^2

Or.....

d = 4.9 t^2

(if you're near the surface of the Earth, where g = 9.8 m/s/s)

This is close enough to 5 to approximate.

So, after 1 second, a freely falling body has fallen:

d = 5 m

After 2 seconds....

d = 20 m

After 3 seconds....

d = 45 m

After 4 seconds...

d = 80 m

This relationship is worth exploring. Look at the numbers for successive seconds of freefall:

0 m
5 m
20 m
45 m
80 m
125 m
180 m

If an object is accelerating down an inclined plane, the distances will follow a similar pattern - they will still be proportional to the time squared. Galileo noticed this. Being a musician, he placed bells at specific distances on an inclined plane - a ball would hit the bells. If the bells were equally spaced, he (and you) would hear successively quickly "dings" by the bells. However, if the bells were located at distances that were progressively greater (as predicted by the above equation, wherein the distance is proportional to the time squared), one would hear equally spaced 'dings."

Check this out:

Equally spaced bells:

http://www.youtube.com/watch?v=06hdPR1lfKg&feature=related

Bells spaced according to the distance formula:

http://www.youtube.com/watch?v=totpfvtbzi0


Furthermore, look at the numbers again:

0 m
5 m
20 m
45 m
80 m
125 m
180 m

Each number is divisible by 5:

0
1
4
9
16
25
36

All perfect squares, which Galileo noticed - this holds true on an inclined plane as well, and its easier to see with the naked eye (and time with a "water clock.")

Look at the differences between successive numbers:

1
3
5
7
9

All odd numbers. Neat, eh?

FYI:

http://www.mcm.edu/academic/galileo/ars/arshtml/mathofmotion1.html

Newton's laws

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 and Newton

First, the applets:

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

http://physics.unl.edu/~klee/applets/moonphase/moonphase.html

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Now, the notes.

Johannes Kepler, 1571-1630

Kepler's laws of planetary motion - of course, these apply equally well to all orbiting bodies

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

e.g. 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.

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

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Newton's take on this 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 2.5 m/s/s.

Some history of astronomy

First, some history:  epicycles

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

Worldviews:

http://www.stumbleupon.com/su/2jRGYC/dd.dynamicdiagrams.com/wp-content/uploads/2011/01/orrery_2006.swf/

http://www.solarsystemscope.com/

Some background details will be discussed in class. Here are some dates of note:

Nicolaus Copernicus
1473 - 1543
De Revolutionibus Orbium Celestium


Tycho Brahe
1546 - 1601


Johannes Kepler
1571 - 1630
Astronomia Nova

Galileo Galilei
1564 - 1642
Siderius Nuncius
Dialogue on Two Chief World Systems
Discourse on Two New Sciences


Isaac Newton
1642 - 1727
Philosophiae Naturalis Principia Mathematica (1687)

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For Galileo:

http://galileo.rice.edu/

http://galileo.rice.edu/bio/index.html

I also recommend "Galileo's Daughter" by Dava Sobel. Actually, anything she writes is pretty great historical reading. See also her "Longitude."

It is also worth reading about Copernicus and the Scientific Revolution.

For those of you interested in ancient science, David Lindberg's "Beginnings of Western Science" is amazing.

In general, John Gribbin's "The Scientists" is a good intro book about the history of science, in general. I recommend this for all interested in the history of intellectual pursuits.

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More historical information regarding Newton:

http://en.wikipedia.org/wiki/Isaac_Newton

This is really exhaustive - only for the truly interested.

This one is a bit easier to digest:

http://galileoandeinstein.physics.virginia.edu/lectures/newton.html

We'll return to Newton's gravitation (along with Kepler) later in the course.

Size and structure in the universe

The size of things:

http://htwins.net/scale2/

http://www.rense.com/general72/size.htm

http://scaleofuniverse.com/

http://xkcd.com/482/



Epicycles:

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

http://physics.syr.edu/courses/java/demos/kennett/Epicycle/Epicycle.html

http://www.jgiesen.de/geocentric/index.html


Copernican vs. Tychonic worldviews:

http://www.stumbleupon.com/su/2jRGYC/dd.dynamicdiagrams.com/wp-content/uploads/2011/01/orrery_2006.swf/


Cool:




http://www.physics.buffalo.edu/gonsalves/ComPhys/Chapter4/oct8.html

http://www.pas.rochester.edu/~blackman/ast104/newtonkepler.html

http://einstein.stanford.edu/Media/Newtons_Universe_Anima-Flash.html

http://www.physics.purdue.edu/class/applets/phe/keplerlaw1.htm

http://www.physics.purdue.edu/class/applets/phe/keplerlaw2.htm

http://www.cuug.ab.ca/kmcclary/goodjar/image.html

Fun with gravitation:

http://arachnoid.com/gravitation/

http://arachnoid.com/gravitation/small.html




http://www.solarsystemscope.com/

http://arachnoid.com/gravitation/index.html


Kepler's Laws:

http://www.physics.sjsu.edu/tomley/Kepler12.html

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=9.msg55#msg55

http://www.sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/Kepler/kepler.html

http://astro.unl.edu/classaction/animations/renaissance/kepler.html

http://physics.syr.edu/courses/java/mc_html/kepler_frame.html

http://www.physics.sjsu.edu/tomley/Kepler12.html

http://www.walter-fendt.de/ph14e/keplerlaw1.htm

http://www.walter-fendt.de/ph14e/keplerlaw1.htm




Newton and Universal Gravitation:

http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/kepler6.htm


http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

http://www.youtube.com/watch?v=0fKBhvDjuy0

http://www.atlasoftheuniverse.com/

http://sunshine.chpc.utah.edu/labs/cosmic_zoom/cosmic_zoom2.swf

http://physics.weber.edu/schroeder/software/zoomer.html

http://htwins.net/scale2/
WAY COOL

Again, worth seeing:

http://www.essex1.com/people/speer/model.html

http://rense.com/general72/size.htm