SPC Ramuel Mendoza Raagas for Teaching Fellow Tri A. Nguyen

Physics E-1a
Classical Mechanics
Experiment #1:
Measuring from a Distance
Fall Term 2003
Submitted October 28, 2003
8. The size of the earth perhaps snugly fits right under Lovell's thumb.

I've seen only snatches of the movie Apollo 13 when it was featured on Direct TV this summer--- I didn't get to the thumb sequences.

Serway tells us that the mean radius for [the oblate spheroid that is our planet] Earth measures to like 6.37 million meters. That would make for a 12.7 thousand kilometer diameter. The moon has a diameter 3.66 times smaller--- almost a percent, however, of its distance from us. The moon is not that far, considering its size. Hence, we know how it works on the ebb and flow of ocean tides.


9. The moon is
L = 3.84 x 108 meters = three hundred eighty-four million meters away.

small angle b = D/R = .5 cm/R = .005 meter / (distance from paper quadrette straight to the wall of my right eyeglass lens) = five millimeters / (less than sixty centmeters)

We need to use the sector formula s = rq, that is the Sector = the product of how faR our eye (situated on the Eart's biosphere) is from the moon and the angle b.


It took some time after getting the lab handout before I got to spot the moon. It was half-crescent (not an upright crescent, but illuminated towards the lower right leaving dark and unseen the upper left moiety) come Friday October 3, 2003. When I distended my arm (some sixty-six-and a bit more centimeters, or 0.66 meters, which I measured with a tape measure, shortly after having eclipsed the halfmoon), I could not cover the half-moon except excessively with the half-centimeter wide paper strip prescribed in the handout.

I had to use a fourth of a centimeter strip, and extend this 50.5 centimeters away from eye.


66.3 centimeters is my maximum reach. I could not have performed the moon diameter measurement properly if my paper quadrette had more than six millimeters as its consequential width.

With the 5 millimeter paper strip I used (I used the lower portion tip of a sheet of graphing paper which no longer formed complete squares.), I could not properly fit-eclipse a portion of the moon with much less than 2.9 million meters girth visible.

I used the 5 millimeter paper strip for the moon's full and full-looking states beginning the second week of October.


On Saturday October 4, I could not do a measurement of the moon, as it was drizzling and the sky had an overcast of clouds.


What error do we consider? The Earth itself is a margin of error. It's radius, in fact. The apparence of the moon itself lends to some error. I admit that even during the months I had savoured an orange summer moon in the Philippines, I could not ascertain which night the moon was indeed full---- I'd give or take a night or two.

There are some principles of Earth-moon behavior.
http://www.infoplease.com/ce6/sci/A0859764.html
Ignoring such and so several factors, we get s = rq = 3.84 x 108 meters *

The bigger the portion of the moon is illuminated, the nearer so may the half-centimeter wide paper rectangle (or cigarette, or thumb, or snub antenna of low-end Nokia cellphone) be drawn into the observer's eye so as to eclipse the moon to a reasonable fit, rather than to eclipse in excess. Whereas, on the contrary, one would be harder put to eclipse any one of the stars with the such a foreground (of thumb or cigarette) except with such excess of foreground at hand.


Because I did not see a full moon on Friday. I had to distend my arm farther out to eclipse the slice of moon. The smaller the image of a celestial body on the night sky, the farther must the observer stretch out his arms and fingers to eclipse such a celestial body not too grossly.


Beauty may be in the eye of the beholder. So too is distance. The hand is not quicker in the eye in detecting far-out objects. In fact, the hand must be slowly and carefully measured.
In part, our value for L is affected by the Earth's radius. Where does Cambridge, MA fall away from the moon? L +- portion of Earth's radius, depending on how we're rotating.

10.

Whereas for the door measurement and the dome measurement I had preferred to use the Anglo-imperial measurement system, I go metric for the moon measurement, because the meter indeed was conceived as a planet thing, just as Imperial length started out as a king thing.

Doctor Sarah (in the website http://mathforum.org/library/drmath/view/57566.html ) is one of many who recounts that our Earth's girth was orginally construed as being neatly forty million meters. Each of Earth's four corners perhaps poetically conceived as being ten million meters.

The earth is around 40070 kilometers in circumference. That's 40,070,00 meters.

(http://math.rice.edu/~ddonovan/Lessons/eratos.html)

Could not the diameter of the moon be derived even from a crescent? Obviously, a new moon can't tell us anything, and the stars of the transition from September to October didn't point to any considerable portion of a moon, but I don't know why the first time I first saw the moon after getting the lab hand-out , the moon was already a half-moon. How did the first quarter of the moon phase pass me by? It might have been some due to some inclement weather. I did not procrastinate!

The earth's diameter is 12742 kilometers.

0.54 meters±.005 meters is the distance by which I put the little quadrette of paper away from my eye to fit reasonably snug such quadrette of paper's foreground over the moon.

.005 meter (the quadrette's consequential width) divided by my .54 distension gave me b = .00925925925... radians = .00926 radians.

Multiplying such b value by L (the distance to the moon) so as to get a sector the arc length of which we'd approximate-interchange with a cord representing the moon's diameter. I get 3.5555... x 106 meters = 3.5555... x 106 meters = 4 x 106 meters, which is what the moon any way is if we were to slur its diameter into a single significant figure. I can't have three significant figures to the fashion of 3.48 x 106 meters, the official table value of the moon's diameter. I can't report neither 3.55 x 106 meters nor 3.56 x 106 meters, because my quadrette's width was measured using only a single significant figure, being 5 millimeters, that is.

Just this Saturday, October 11, elsewhere in America a Florida vs. Chicago baseball game telecast featured an orange moon in between playtime. I did not catch the moon orange over Cambridge this week, because I have not been in windowview or outdoors when sunset turns into early evening (considering the onset hours of my weekday Extension School classes)

Although using old, crumpled, springless, caseless, paper tape measures were OK for doing my pre-Range Finder mesasurements of my seven-foot door at home, since like Galileo and his piano inclinato, there were ideal values to lapse to within arms' reach (Galileo in publishing his law of odd numbers as to the steadily-accelerated descent of a rolling ball, cared not so much for intricately recording any significant digits of experimental error. Tenth of a human pulse was all he noted down.)--- in measuring my arm's distension towards the moon way beyond my reach, I had deemed it necessary to utilize a brand-new, five-dollar button-spring cased tapes measure from a pretty stationery store.

56.75 centimeters (.5675 meter) was the reading I got for the full-enough looking moon quarter past seven in the evening on October 9, 2003. This gave me a small angle of .00881 radians, which gave me a (full?) moon diameter of 3.38 x 106 meters, although going by the single significant digit solely warranted by my 5 millimeter paper quadrette edge measurement.

I have never been good at pinning down myself just when the moon really is full. Was October 11 the night? That may seem plausible as I checked the http://weather.boston.com/ website tonight on October 11. Unfortunately, I could not archive my way a few days back to check whether the ninth or the tenth of October had a fuller moon. On the average, I have some idea of when the moon is full, give or take a day or two.

We definitely do not want to have the strip of paper's measuring edge too wide. If the strip of paper is so much as a full centimeter wide, then you better have the reach of the boxing champion Evander Holyfield!

55.2 centimeres gives a good value for the moon's diameter.

10. The number I came up with for the moon's diameter looked pretty good. The only draw-back was that I couldn't report more than one significant figure, limited as I was by my graphing paper tail's accuracy. It's not even a matter of getting more precise scissors to excise the hem of graphing paper I took to be half a centimeter wide. Since I was using no lens or telescope to look, but just my bare, I was limited by the resolution that is inherent in the visible frequency of light. I could not resolve a sixth of a micrometer, and I could not pretend to discern a discrepancy of width amount to just a tenth of a millimeter, or even three-tenths of a millimeter, for that matter.

Epilogue

I missed the horizon thing. My Biology 100 Vertebrate class starts at 5:30 p.m. My Chemistry and Physics start at 6 p.m., so I haven't made it to the prime time of a full moon rising. I have not caught any vistas of any big orange moons. Today, October 12, 2003, it's been lightly raining with the clouds shutting out any blue in the sky, so I haven't checked to see if the moon's visible part did recede from that on October 11. On October 11, around 10 p.m. to 11 p.m., I watched the moon from a bench fronting the main entrance of the Science Center. The moon did advance from just off Loker and Annenberg slightly towards the Yard's gates. I came to realize then that whatever path of displacement the moon would draw on the apparent the night sky amounting to a perceived shift of several meters (as if the moon were a walker on an invisible industrial park skyway getting from the dozensth floor of one tower jutting above and beside Annenberg and the School of Interior Design to a corresponding mouth of another imaginary tower jutting above and beside the Fire Department and Museum buildings (Sackler and that other building fronting Sever Hall)--- if I actually set about eclipsing the moon (with either a cigarette or my cellular phone antenna) from point A to point B more than hour later, I would hardly be shifting my ownstandpoint, in fact pivoting by less than a foot would do---- the is to say, no matter how many hundreds or thousands of meters the moon man pull towards Massachusetts Avenue area, my feet need not go so far away from those benches just in front if the Science Center's main entrance. My eyes, arms and hands could expeditiously re-adjust to re-focus an eclipsing of the moon without burdening my feet. Although my feet seem to determine my Cartesian coordinates on the surface of the Earth, it is the hands, arms and eyes, hovering on a z-axis normal to the Harvard asphalt, which best secure a quantifiable measurement.