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'''Nodal precession''' is the precession of an orbital plane around the rotation axis of an astronomical body such as the Earth. This precession is due to the non-spherical nature of a spinning body, which creates a non-uniform gravitational field.
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Around a spherical body, an orbital plane would remain fixed in space around the central body. However, most bodies rotate, which causes an equatorial bulge. This bulge creates a gravitational effect that causes orbits to [[precess]] around the rotational axis of the central body.
 
The direction of precession is opposite the direction of revolution. For a typical prograde (in the direction of central body rotation) satellite orbit in an about the Earth, the [[longitude of the ascending node]] decreases, i.e. node precesses westward. If the orbit is retrograde, this increases the longitude of the ascending node i.e. node precesses eastward. This nodal progression enables [[sun-synchronous orbit]]s to maintain approximately constant [[Beta angle|angle relative to the Sun]].
 
==Description==
 
[[File:Nodal precession2.png|thumb|Equatorial bulge torques a satellite orbit, leading to nodal precession]]
 
A non-rotating body of planetary scale or larger would be pulled by gravity into a sphere. Virtually all bodies rotate, however. The centrifugal force deforms the body so that it has an [[equatorial bulge]]. Because of the bulge the gravitational force on the satellite is not directly toward the center of the central body, but is offset toward the equator. Whichever hemisphere the satellite is in it is preferentially pulled slightly toward the equator. This creates a torque on the orbit. This torque does not reduce the inclination; rather, it causes a torque-induced gyroscopic [[precession]], which causes the [[orbital nodes]] to drift with time.
 
==Equation==
 
The rate of precession depends on the [[inclination]] of the orbital plane to the equatorial plane, as well as the orbital eccentricity.
 
For a satellite in a [[prograde orbit]] about the Earth, the precession is westward (nodal regression), the node and satellite move in opposite directions.<ref>{{cite book|last=Brown|first=Charles|title=Elements of spacecraft design|pages=106|url=http://books.google.com/books?id=mTSSMhcmVbkC&lpg=PA95&ots=hkARYnIy9h&dq=ascending%20node%20regression&pg=PA121#v=onepage&q=ascending%20node%20regression&f=false}}</ref> A good approximation of the precession rate is
 
: <math>\omega_p = -\frac{3}{2}\frac{R_E^2}{(a(1-e^2))^2} J_2 \omega \cos i</math>
 
where
:<math>\omega_p \,</math> is the precession rate ([[radian|rad]]/s)
:<math>R_E \,</math> is the body's equatorial radius (6 378 137 m for Earth)
:<math>a \,</math> is the semi-major axis of the satellite orbit
:<math>e \,</math> is the eccentricity of the satellite orbit
:<math>\omega \,</math> is its angular frequency of the satellite's motion (<math>2\pi</math> radians divided by its period)
:<math>i \,</math> its inclination
:<math>J_2 \,</math> is the body's ''second dynamic form factor'' (<math> \scriptstyle -\sqrt{5}C_{20}=1.08262668\times10^{-3}</math> for Earth.)
 
This last quantity is related to the [[oblateness]] as follows:
 
: <math>J_2 = \frac{2 \varepsilon_E}{3} - \frac{R_E^3 \omega_E^2}{3 G M_E}</math>
 
where
:<math>\varepsilon_E \,</math> is the central body's oblateness
:<math>R_E \,</math> is central body's equatorial radius
:<math>\omega_E \,</math> is the central body's rotation rate (7.292115&times;10<sup>&minus;5</sup> rad/s for Earth)
:<math>G M_E \,</math> is the product of the universal [[gravitational constant|constant of gravitation]] and the central body's mass (3.986004418&times;10<sup>14</sup> m<sup>3</sup>/s<sup>2</sup> for Earth.)
 
The nodal progression of low earth orbits is typically a few degrees per day to the west (negative). For a satellite in a circular 800&nbsp;km altitude orbit at 56° inclination about the earth
 
: <math>R_E = 6.378 137 \times10^{6}m</math>
: <math>J_2 = 1.08262668\times10^{-3}</math>
 
The orbital period is 6052.4 s, so the angular velocity is 0.001038 rad/s. The precession is therefore
 
:<math>\omega_p = -\frac{3}{2}\frac{6 378 137^2}{(7 178 137(1-0^2))^2}\ 1.08262668\times10^{-3}\ 0.001038\ \cos 56^{\circ}</math>
 
:<math>\omega_p = -7.44\times10^{-7}\ rad/s</math>
 
This is equivalent to -3.683 degrees/day, so the orbit plane will make one complete turn (in inertial space) in 98 days.
 
The apparent motion of the sun is approximately +1° per day (360° per year / 365.2422 days per tropical year ≈ 0.9856473° per day), so apparent motion of the sun relative to the orbit plane is about 2.8° per day, resulting in a complete cycle in about 127 days. For retrograde orbits <math>\omega</math> is negative, so the precession becomes positive. (Alternatively, <math>\omega</math> can be thought of as positive but the inclination is greater than 90°, so the cosine of the inclination is negative.) In this case it is possible to make the precession approximately match the apparent motion of the sun, resulting in a [[sun-synchronous orbit]].
 
==See also==
* [[Axial precession (astronomy)|Axial precession]] or precession of the equinoxes in astronomy (same kind)
* [[Apsidal precession]], the other kind of precession ([[argument of periapsis]] change)
 
==References==
{{Reflist}}
 
==External links==
*[http://yarchive.net/space/orbits/nodal_regression.html Nodal regression description from USENET]
*[http://www.agi.com/resources/academic-resources/astro-primer/primer91.htm Discussion of nodal regression from Analytical Graphics]
 
[[Category:Astrodynamics]]

Latest revision as of 14:09, 3 January 2015

The lockback's blade locking mechanism is a refinement of the slipjoint design; each utilize a powerful backspring located along the again of the knife. However, the lockback design incorporates a hook or lug on the backspring, which snaps right into a corresponding notch on the blade's heel when the blade is fully best fixed Blade knife opened, locking the blade into place. 18 Closing the blade requires the person releasing the blade to use strain to the bar spring located towards the rear of the knife deal with to disengage the hook from the notch and thus launch the blade. 19

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Machetes are a type of survival, or tactical knife They typically have one edge, with a blade that widens at the tip. They are used extensively in many tropical areas for clearing brush, and cutting by means of jungle growth. Many cultures rely on them for farming purposes. Having said that, there are those that do use them for weapons. I took the pocket knife with me as I took Tuck to the occasion, and I quietly slipped it to Coach. Of course, he knew exactly easy methods to close it, and he immediately engaged Tucker in the first guidelines of pocket knife safety. Equally important, Tyler got to hold it, too.

True normally, but some areas like gov buildings, airports have them however for those who're good you will not be carrying any knives into these places toavoid the hassel. For the rest of the state simply bear in mind to check out your native ordinaces and Municipal Codes they might have size laws you might need to comply with. This is just merely information to maintain your self a Legal Knife carrying Citizen of California. This video has the Laws you need to know and some definitions for phrases for with in the legal guidelines. Remember these movies are for strictly informational purposes provided that you want legal recommendation search a Prison Lawyer.

As a part of their Magnum line, Boker has created an reasonably priced yet eye-catching pocket knife in the Bulldog. The naming is suitable – this one is solid, chunky and reliable identical to the canine! It carries a 440C stainless-steel blade about three and a quarter inches lengthy and overall the knife is about 4 and half inches long when closed. It’s just a little heavy at just over six ounces however feels downright sturdy in your hand. The deal with is pretty nice too – it’s textured G-10 which affords an effective grip and is pleasing on the attention. What’s more it’s an actual discount at often beneath $20 online!

If you're still just a little fearful or query your child’s functionality then that is all right. I am reminded of a story posted on the Outfitted to Survive Foundation’s boards on this subject. The father selected, at first, to maintain the knife with him and not with the boy all the time. He wanted to see if the boy was able to the task and did not want to thrust it upon him and to guantee that his son didn't think it was a toy. This is what I would do. Do what works for you and your spouse.

Schrade has been offering knives for civilians and troopers alike for the final century. Nonetheless, they have not at all times achieved it below the dad or mum firm they're now below. They was an independent company and have been doing so out of Ellenville, New York since 1904. About thirty years in the past, they joined up with Smith and Wesson beneath the parent company Taylor Manufacturers, from the Appalachian mountains of Kingsport, TN. Reading the buyer testimonials of Case Pocket Knives 379 Fastened Blade With Leather-based Sheath Fixed Blade – Each prior to buy. It gives you a much fuller understanding of the great attributes and cons from it.

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