Radar Ranging of Venus for AST 1040

Statement of Purpose:  Determine the distance and diameter of Venus based on radar data and arc seconds recorded on 3 separate dates.

Statement of Procedure:  The data given was in minutes and seconds.  The first step in this procedure was to convert those times into seconds by multiplying the minutes by 60 and adding the remaining seconds.  These were the times of a round-trip to Venus and back on radar beams (which travel at the speed of light).   The time it takes light to travel to and back from Venus can tell us the distance to Venus.  Light travels at 300,000km/s and our first trip took 574s.  So we can find the distance by multiplying our recorded time by the speed of light and dividing by two (for half the round-trip): (574x300000)/2 = 86100000km.  Then using the graphic we can count the apparent arc seconds of Venus at the same time the radar beams were sent.  The arc seconds are then converted into degrees by dividing by 3600 (since there are 3600 arc seconds in a degree).   Using this Angular Size and the Distance, we can find the true size of Venus by multiplying the two and dividing the sum by 57.3 degrees (Radian).  Using the data of 3 dates, we can average our measurements by adding all three and dividing by three.

Data:

Date	One-way Timing (sec)	True Distance (km)	# of ticks	Angular Size in degrees	True Diameter(km)
11/15/2005	574	8.61 x 107	29	0.0080555556	12104
11/30/2005	426	6.39 x 107	36	0.01	11152
12/15/2005	364	5.46 x 107	47	0.0130555556	12440
Average					11899

Statement of Conclusion:  The actual diameter of Venus is 12103.6km.  So my results weren’t too far off (204.6km difference).  Considering I was using data recorded by someone other than myself, I’m not exactly sure what I could have done differently to get a more accurate result.  I did consider rounding the angular size but noticed quickly that my results became further off after rounding.

1)      Could this procedure be used with other astronomical bodies such as the Sun, Mars or Jupiter?  Why or Why not? 

a.       Depending on the body’s composition will determine whether or not this method may or may not work.   If an object has an atmosphere, radar (radio) waves may or may not be able to penetrate the atmosphere depending on its composition and density.   This procedure can only be used if the wavelength of the sent beam will penetrate and return through the atmosphere of the object (if it has one).  This method will almost always work with objects in our solar system which do not have an atmosphere and have a measurable angular size.

2)      Why would this method not be used with distant stars?  (There may be more than one answer here.)

a.       The closest star (Proxima Centauri) is 4.2 light years away.  That means a round trip at the speed of light from Earth to Proxima Centauri would take 8.4 years.  Considering the Earth’s rotation and orbit, this procedure would take precise timing and calculations to send a signal and receive the bounced signal 8.4 years later.  And then only if Proxima Centauri (or another object) has a penetrable atmosphere.

b.      The other problem with this method is getting an accurate reading on the angular size of a distant star.  Even Proxima Centauri is so far away that getting an accurate reading on its angular size would be incredibly difficult if not improbable.

c.       Another problem would be that the signal would gradually lose intensity as it travels further.  The returning echo (if there is a return echo) would be so faint, it would be nearly impossible to detect.

d.      Another problem might be finding an unobstructed direct path to a distant star.  The space between may be filled with particles, gasses, ice, or other objects that may absorb, deflect, scatter or even bend our sent light signal.

3)      What would be different if we used data for different dates?

a.       If the dates were different in this exercise the distance of, and therefore the angular size of Venus would be different.   As both Earth and Venus travel around the Sun in their respective orbits, Venus may appear to have a larger or smaller angular size depending on its respective distance to Earth.  While the angular size might change, the radar beams should also change, respectively.  If Venus is closer to Earth, Venus will have a larger angular size and a shorter radar time.  If Venus is farther from Earth, it will have a smaller angular size and a longer radar time.  The radar time and angular size of Venus will change in proportion to each other.

4)    Would this procedure work with other forms of electromagnetic radiation such as visible light or infrared light?  Why or why not?

a.       This procedure will work with other forms of electromagnetic radiation given the object being measured.  The moon is currently under scrutinous observation with laser beams (visible light).  However, depending on the atmosphere of the object being measured will determine whether this method will or will not work (see question 1).   The wavelength of the light must be able to reflect off of the object’s surface and return to Earth.  Unless, of course, the object’s atmosphere is what is being studied.  If the object has no atmosphere, this method would probably work with most forms of light.

Film Review of We Live in Public for Soc 1010

Personally, I was most attracted to the film’s music selection.  I have seen hundreds (possibly thousands) of documentaries.  In my experience, documentaries generally tell a story from a one-sided perspective, most of them have an agenda (i.e. make the primary character look good, incite anger against “injustices”, etc...) and most of them use music to appeal to the emotion of the audience.  It’s hard to deny that music can intensify or even create the emotion the filmmaker was looking for.  For example, most horror movies are much less suspenseful when on mute; it’s the music that creates an atmosphere of suspense.

We Live in Public used this technique of emotional appeal through music, but in a very choreographed way.  The music selected for the scenes were typically popular songs from the same era as the scene and also had the emotional appeal to compliment the content of the scenes.  This is a brilliant idea to appeal to the audience of the same era while encouraging emotion and at the same time setting a chronological frame of reference.

While music can strongly encourage an emotional connection this can also be a weakness.  To the conscientious observer, music can also expose the motives of the filmmaker.  Throughout the film, when Josh is speaking about himself or when someone is speaking about Josh, there is soft, ambient music in minor keys, which is generally used to incite sympathy or sadness.  In the opening scenes when the film is talking about people losing their identities and becoming a statistic, the music is eerie, strings driven, offset chords, which is generally used to encourage suspense and/or fear.

According to the music, the film was meant to sympathize with Josh Harris as a person and condemn the influence of the internet in our society.  In a way, it seems like an apologetic film as if we (the audience) should forgive Josh Harris for his foresight and contribution to the advancement of technological society.  It urges us to acknowledge the separation between Josh (the person) and the ever advancing internet (the monster).  It’s a little bit like Dr. Frankenstein.

Josh’s “social experiment”, Quiet, fell a bit short of the experimental standards.  Even Josh admitted that he didn’t know what to expect as a result of the experiment.  According to the Scientific Method, an experiment should have a theory, hypothesis, variables, data and an explanation of results.

Quiet had a theory, but that was about it (as far as we understand from this film).  There was no hypothesis, there were no variables, there was a lot of data, but no explanation of results.  From a scientific standpoint, Quiet comes off as more of an eccentric person’s personal party than a true experiment.

That personal party did have some revealing responses, however the responses were never explained and there was seemingly no sociological advancement or understanding as a result.

Quiet did have a very interesting insight on culture.  By creating this isolated group of people (some more exhibitive than others, but all probably had some sort of exhibitionism) Josh’s experiment showed how cultures and/or sub-cultures adapt.

The people in this experiment adapted to their conditions of no privacy and no identity.  While some people seemed to struggle with this more than others, it seemed the majority learned to adapt to the situation.

However, it was stated in the film, “If you ask someone to take off their pants, they won’t do it.  If you have a camera and ask someone to take off their pants, they probably will.”  This suggests that the idea of being watched (or “fame”) causes individuals to act in “unusual” behavior.

So perhaps Quiet was an experiment to see if a culture’s “unusual” behavior can or will adapt and become usual and at what pace.

The Mass of the Earth for AST 1040

Statement of Purpose:  Estimate the total amount of matter which makes up the earth (mass) using a pendulum of one meter under the influence of gravity.

Statement of Procedure:  I created a pendulum of one meter (measured from center of weight (or “bob”) to anchor point).  Using this pendulum I calculated the acceleration of gravity by timing a 15° angle of swing and finding an average time per swing (out of 10 swings).  Taking the (rounded) average time per swing (T) and the length of my pendulum (1 meter) (L), I used the equation T=2π√ (L/g) to find the acceleration of gravity (g) in m/s².  Then using the found acceleration of gravity (g), the known Universal Gravitational Constant (6.673 x 10^-11 m³ kg^-1 s^-2) (G) and the known radius of the Earth (6378km or 6378000m or 6.378 x 10⁶m) (R) I found the mass of the Earth in kilograms (M) using the equation M=g(R²/G).  I repeated this ten times to average my results for the mass of the Earth.

Data:

Trial	Length  in Meters (L)	Time of 10 swings in seconds	Time of 10 swings in seconds (rounded)(t)	Average Time per swing in seconds t/10 (T)	Acceleration of Gravity in m/s2 (g)	Mass of Earth in Kilograms
1	1	19.85	20	2	10	6.02 x 1024
2	1	19.66	19.5	1.9	11	6.67 x 1024
3	1	20.10	20	2	10	6.02 x 1024
4	1	19.93	20	2	10	6.02 x 1024
5	1	19.89	20	2	10	6.02 x 1024
6	1	20.21	20	2	10	6.02 x 1024
7	1	20.24	20	2	10	6.02 x 1024
8	1	20.02	20	2	10	6.02 x 1024
9	1	20.38	20	2	10	6.02 x 1024
10	1	20.26	20	2	10	6.02 x 1024
					Average Mass =	6.08 x 1024

Statement of Conclusion:   My final conclusion is that the Earth has a mass of approximately 6.08 x 10²⁴kg.  After looking up the actual mass of the Earth (5.9722 x 10²⁴) I am fairly pleased with my estimation.  I was estimating 15°, my measured string may not have been precisely one meter and my stop watch times were probably a little off due to response time, plus I rounded them anyways.  If I had more accurately measured 15°, somehow measured exactly one meter of string and somehow automated an instantly reacting stop watch and used those accurate measurements, my final calculations would probably be much closer to the known acceleration of gravity on Earth (9.807m/s²) and mass of the Earth.  Also, using Newton’s Law of Conservation of Angular Momentum (angular momentum(g) = mass x velocity(T) x radius(L)) I was able to find that the mass of my bob was about 5kg, which I had not previously measured but would estimate is accurate.

1)      What is the effect of the length of the string on the period of a pendulum?  That is, how do the periods compare for pendulums of different length?  Would pendulums of different length give the same or different values for the mass of the Earth?

a.       Newton’s Law of Conservation of Angular Momentum (angular momentum = mvr) says that as the length (or radius) of an orbit increases, the mass or velocity must decrease to maintain angular momentum.  Since the mass of the pendulum bob cannot decrease, the velocity must.  So a longer string on the pendulum (radius) must result in a longer period.  The opposite would be true if the pendulum string were shortened, the swing period would be shorter in order to maintain its constant angular momentum.

b.      In this activity pendulums of different length should have the same results for the mass of the Earth.  The equation to find the acceleration of gravity takes the length (L) and the average time per swing (T) into consideration T=2π√ (L/g).  As the length of the pendulum increases, the time should increase proportionately.  Also, the law of conservation of angular momentum (see “a”) states that length is proportional to velocity but not mass.

2)      Is the strength of gravity the same everywhere?  Put another way, does the acceleration of gravity – the rate at which things fall – different on different planets?  Why or why not?

a.       According to the Universal Law of Gravitation (F_g=GM₁M₂/R²), the strength of gravity(F_g) weakens with distance(R) in a squarely inverse proportion (2x distance = ¼ gravitational force) between two objects.  We feel the same pull of gravity because we (average human) generally do not travel a distance far enough from the center (or surface) of the Earth to feel a noticeable change.  So the strength of gravity is the same everywhere on the surface of the Earth, but it does change when there is a notable distance between two objects.

b.      The acceleration of gravity(F_g) will change on another planet that does not have the same mass and radius as Earth.  While all objects (regardless of mass) will accelerate at the same rate (providing no other forces act on it) no matter which planet you are on, the rate of acceleration will be determined by the radius and mass of the planet.

c.       The Gravitational Constant (G) is the attraction between two objects and it is the same everywhere.

3)      Would the period of a one meter pendulum be the same on Earth and the Moon?  Why or why not?

a.       Because the Moon is less massive (7.36 x 10²²kg) this experiment would have very different results.  The lesser mass of the Moon creates a much weaker gravitational pull (1.63m/s²), so a pendulum of one meter would swing (accelerate) much slower on the Moon than it does on the Earth.  Using the same formula as before (T=2π√ (L/g)) but plugging in the moon’s gravitational acceleration, the same experiment would have an approximate swing period (T) of about 5 seconds on the moon as opposed to the swing period (T) of about 2 seconds on the Earth.

4)      Why do you think we refer to the Universal Law of Gravity and the Universal gravitational Constant?  Why “Universal”?

a.       Gravity is everywhere.  It may lose strength over distance, but every object which has mass has gravity and is thusly attracted to and attracts other objects of mass.  This is what we refer to as the Universal Law of Gravity.  This law does not only apply on Earth or in our solar system, it is a Universal Law that applies to all massive objects in the universe.

The Universal Gravitational Constant (big G) is the measure of the attraction between any two (or more) massive objects.  This attraction is constant throughout the universe, however depending on the mass and distance of the objects will determine the acceleration due to gravity (small g).