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Here is a basic equation for the tilt of the Earth with respect to the 0 degree equator latitude line [more correctly, it ...
Here is a basic equation for the tilt of the Earth with respect to the 0 degree equator latitude line [more correctly, it is the tilt of the equator with respect to the solar plane or orbit around the sun]. You might want to look at my last vid. also.
The upper half of the graph is for the standard Sine of the angle.
Note, for reference and for calculating what day of the year it is (beginning with March 21):
Day 1 = March 21 (where the tilt is 0 deg.)
Day 91.25 = June 21
Day 182.5 = Sept. 21
Day 273.75 = Dec. 21
Notice that 365 is very close to 360 (the angle commonly associated with a full circle), and the tilt equation is a good approximation at:
Angle = 23.5 Sin (Day from March 21)
The value of 23.5 is simply a multiplier to adjust the resulting "output" range from 0 to 23.5; instead of 0 to 1 as for the std. sine (abreviated sin on calculators) equation.
Now for a more correct formula, we will break 365 days into a range of 360 linear (equally distanced-spaced) steps as required for the complete std. sine graph (which has 360 linear steps of the angle). To do this we see that : 360/365 = 0.986301369
.. and that this multiplier value (factor) will be used as a correction for the formula.
So in other words: 365 x 0.986301369 = 360
As a test to see if you are utilizing your calculator right, here is an example to enter:
Ex. Lets say it's April 21 and you want to know the current tilt of the Earth. Since April 21 is 30 days from March 21, these arguments [current data] used in the formula result to:
Tilt Angle = 23.5 sin (0.986301369 x 30)
Tilt Angle = 23.5 sin (29.58904107)
Tilt Angle = 23.5 (0.493775549)
Tilt Angle = 11.604 degrees
Notice [especially visualized on the graph] that at this date that about half of the max. tilt of 23.5 degrees has already occured. The tilt is getting slower in amt. per day and will take nearly two more months to reach 23.5 degrees.
Perhaps this calculation can be used to adjust a sundial so that the time throughout the year is more accurate as the earth tilts. For example, the sundial for New York City is tilted somewhere about 40 degrees on March 21 since that is the latitude of NYC [more correctly, it is the angle NYC is tilted with respect to the solar plane]. On June 21, it is summer and this angle has decreased by 23.5 degrees to a total of only 21.5 degrees. The sundial should only be tilted 21.5 degrees then for correct time. I guess the positions of the "hour lines" would have to be recalculated and positioined on the sundial. I think there is another less common type of sundial where the hour lines need not be recalculated and positioned.
I understand that I could be wrong about the exact equation to utilize, particularly the Sine equation. It appears to me that the tilt is sinusoidal in nature, but could be some other "curve" such as a cycloid maby [maby some astronomer or meteorologist can let me know.. that is if they even know themselves]. I have checked the results with a website that displays the current tilt and it appears to be very close.
As an extra note, the part of the curve above the horizontal line, and below the horizontal line are symetrical, hence basically the same. Now, taking either the part above or below the horizontal line, the curve is symetrical to the extreme points [peaks of the curve]. Knowing this, you only need calculate the tilt for a quarter of the year or 91.25 days and you can then reuse the data if you make a list. You could also say you only need to calculate this part since the earth tilting is periodic or repetative .. and that is what the sin function can describe.
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Added: 9 months ago
Views: 808
Here we are making a homemade cake from scratch. It's not that hard as you will see. It's kind of like making bread. You ...
Here we are making a homemade cake from scratch. It's not that hard as you will see. It's kind of like making bread.
You can call this cake what you want, but we seem to think of this as some form of a "Christmas Cake". We call it this because the cake itself is flavored and colored. Icing on top of it is therefore optional. The cake is sweet enough as is, and you can find a bunch of icing recipes her on YouTube.
This recipe is a small cake and makes 2 good sized servings. If you need more than that than simply double the recipe.
Recipe:
1 cup flour
1/3 cup sugar
1 tablespoon baking powder
1/2 teaspoon salt
1/2 cup milk
1/4 cup soft shortening such as butter
1 egg
Into the wet ingredients you can place the flavors such as:
anise flavor (1/8 teaspoon)
almond flavor(1/8 teaspoon)
lemon flavor (1/2 teaspoon)
vanilla flavor (1 teaspoon real, or 1 tablespoon artificial)
Opt: cinnamon (1/4 teaspoon) and ginger (1/4 teaspoon)
A drop or two of food color can be used in the batter for a colored cake. For ex. 1 drop of red will give a pink cake, and 2 or 3 will give more of a red cake.
[It is also possible to disolve the sugar and salt in the wet ingredients before mixing the wet and dry ingredients]
Mix dry ingredients together in a seperate bowl.
Mix wet ingredients together in a seperate bowl.
Mix wet and dry ingredents together.
"Dust" a cake pan with a coat of oil with a flour dusting over it. This will act as an insulator so that the cake is not burnt on its sides and helps it release from the pan.
Pour cake batter into the pan. Make sure the batter does not go more than about 1/2 up the sides of the pan because the rest will be needed as the batter/cake rises.
Bake at 350 F. degrees for 20 to 25 minutes. Check after 20 min. with a fork or toothpick to see if batter is not wet still.
When cooked, remove from oven and place on a cooling surface.
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Added: 9 months ago
Views: 6,595
Due to my observations and that it is not expressed too much, if at all, in any guitar literature, here is a note about ...
Due to my observations and that it is not expressed too much, if at all, in any guitar literature, here is a note about intonation and bridge saddle compensation. As a slight exageration to express the point of this video: Consider an uncompensated bridge saddle where the lenght of the bass E string is the same length of the high e string. Pressing down the length of the bass E string at the 12th fret will produce about a step higher or an F note. This is not the E note that is wanted. This effect of a raised note is due to the thickness of the string and the increased tension needed to fret a thicker string. Increased tension means a higher note, just as increasing the string tension at the tuners means a higher note. To compensate or adjust for this effect, the bridge saddle is placed back which lengthens the string a bit [of course you must retune the open E string always when adjusting its length with the bridge saddles], the net result is that when the string is fretted at say the 12 fret (or any fret) that the proper note needed is heard.
Due to the length of the bass E string being longer than any other string, in particular the high e string, the center of the string is no longer over the 12th fret, and hence the harmonic of that string is no longer over the 12th fret and can never be; so dont try adjusting the saddle to do it because then your compensation will be off.
Also, because of this, it is perhaps best not to play harmonics when adjusting intonation. [This effect is usually more noticable over acoustic guitars where the bass E string is very thick and the saddle compensation is greater]
How to check intonation: First tune your guitar. Fret the 12th fret of the sting. To make things easy, consider the 12th fret as a new scale or nut. If the note is lower than expected, then the length of the string from the nut (here the 12th fret) to the saddle is too long since longer strings mean reduced frequency (ie. lower note). To correct this, simply shorten the string by bringing the saddle closer to the nut position. You must now retune the open string since you have changed the length and therefore the tone of it. Check the intonation again. If the 12fret note is higher in sound than expected, then simply do the opposite of what was mentioned.
My Father who once worked at Martin helped me develop some ideas when I made a small acoustic guitar.
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Added: 10 months ago
Views: 3,296
This video shows when are the start of the seasons and why. I call this the "21 Rule" since they start of the seasons are ...
This video shows when are the start of the seasons and why. I call this the "21 Rule" since they start of the seasons are the 21st of the specific months.
As the earth spins or orbits around the sun in one year, the earth tilts towards, and then away from the sun. The (axis or rotation) tilt never exceeds about 23.5 degrees from the solar (sun) plane. The speed of this tilt is not constant, or linear as some would say. For example when heading into max. tilt, the tilt is "slowing down" and practically stopped for an instant before the tilt changes direction and gets faster once again.
[This natural speeding up and slowing down in a periodic (repeating) manner is usually called "sinusoidal" motion since it can be described easilly by a sine (of the angle) equation. I will probably make a vid. of how to calculate the tilt of the Earth using this information. The common latitude lines on earth are not in reference to this tilt, but is in reference to the equator, hence a "fixed" latitude position. Longitude is also fixed and is in reference to a town in England called Greenwich; the standard followed sets this and all areas true North and South of this at 0 degrees longitude. In simple terms, latitude and longitude are just imaginary degree lines on the circle of the earth. http://wwp.greenwich2000.com/ ]
Each season is 91.25 (approx. 90) days long, or 3 months.
When a hemisphere (ex. northern part of the earth above the equator that is located in the middle of the poles) is tilted towards the sun or solar plane ("flatlike" orbit position around the sun) the earth is warmer (ie. summer at max. tilt) at that location.
Don't blast me with comments about the season starting on the 20 or 21 of the month. To keep it simple, let it all start either on the 20 or 21.
If you consider both tilts of the equator above and below the solar plane you have a total tilt of earths axis of about: 23.5 + 23.5 = 47 degrees.
Ever here of the word solstice.. well it is usually used as a word describing winter and summer.. as in winter solstice. Sol means sun and stice means halt or stop... as when the earths tilt per day and the sun's path location in the sky seems nearly stopped.
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Added: 10 months ago
Views: 904
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Here I talk about the orbit and "moon phases" of the moon. The Moons orbit around the Earth takes 27.32 days. That means ...
Here I talk about the orbit and "moon phases" of the moon.
The Moons orbit around the Earth takes 27.32 days. That means it moves around the Earth by 13.2 degrees (out of 360 degrees; a full circle) per day:
360 degrees/27.32 days = 13.177 degrees/day
Now, the Earth itself rotates once a day, and it is divided into 24 hours. Therefore, it rotates:
360degrees/24hours = 15 degrees/1hour.
1hour is further defined as 60 minutes.
Using a equation to find out how many minutes on Earth corresponds to 13.2degrees :
60min/15deg = Xmin/13.2deg
Xmin = 52.8 minutes
In other words, as the Earth rotated once, the Moon rotated in its orbit about 13.2 degrees, and it will take the Earth 52.8 minutes to rotate further to observe the moon in the same position as the day before. The total time is therfore 24h + 52.8m = 24h,and 52.8m.
The Moon is locked in perfect sync or timing with the Earth and we only see about 1/2 of it, and always being the same side seen. The Moon does rotate on its own axis, and therefore has its own "day" and "night" just as we do here on Earth. It's day is very long, being 29.5 days. What we call the "dark side" of the moon, just appears that way; it is actually illuminated by the Sun as it rotates.
The Moon is about 238,800 miles from the Earth. The diameter of the Moon is about 2100 miles. Due to Earths Rotation (frome West to East; counter clockise at the north pole), the Sun, Moon and Stars appear to move by 15 degrees per hour in the west direction. [Actually, due to the Moon changing position in its orbit around the Earth, its slightly faster than that and you can notice it "pass" over or "pass by" other stars]. Both the Sun and Moon often appear to be 1/2 degree wide; from horizon to horizon is 180 degrees:
.
.
. | |moon, 2,100M |
E---------------------- 238,800M
sin angle = opp/adj = 2,100/238,800
sin = 0.008793969
Angle = arcsin(0.008793969)
Angle = 0.503864 degrees [about 1/2 degree]
In your imagination, you could line up about 360 suns or moons end to end from horizon to horizon.
Also, if the sun had a larger viewing angle than the moon, their would never be a full eclipse; part of the sun would still shine.
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Added: 10 months ago
Views: 1,088
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