Neutron star spin-up: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older editNewer edit →
en>Hqb
ubsubst navbox
en>Jni
mNo edit summary
Line 1: Line 1:
The '''free-fall time''' is the characteristic [[time]] that would take a body to collapse under its own [[gravity|gravitational attraction]], if no other forces existed to oppose the collapse. As such, it plays a fundamental role in setting the timescale for a wide variety of astrophysical processes—from [[star formation]] to [[helioseismology]] to [[supernova]]e—in which gravity plays a dominant role.
== ' in the woods ==


==Derivation==
Yan smile: 'In recent years, it really is to live up to the expectations of the mother ...'<br><br>deep breath, Xiao [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-7.html カシオ 腕時計 gps] Yan suddenly swing too far toward the dark [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-11.html カシオ腕時計 g-shock] woods warm smiles: '? Father, you have come.'<br>While the bucket of gas<br>only three paragraphs, but Xiao Yan soul perception, Que Shibi a five stars who have a lot of sharp, talking about his mother in a previous time, he noticed [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-11.html カシオ 電波時計] a hint of movement in the woods.<br><br>'Oh, Yan children, so late, how still stay above this it?' in the woods, in the quiet moments, the outgoing concern laughter men.<br><br>branches burst of swing, a middle-aged man jumped out with a smile on the [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-15.html カシオ gps 時計] face, looked at his son standing in the moonlight that.<br><br>middle-aged man dressed in luxurious gray 'color' clothes, among [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-6.html 腕時計 メンズ casio] quite a few Dragon Tiger step majesty, his face a pair of bushy eyebrows add a little more to their pride, he is currently xiaojia
相关的主题文章：
<ul>
 
  <li>[http://www.bxyyyy.com/home.php?mod=space&uid=4299 http://www.bxyyyy.com/home.php?mod=space&uid=4299]</li>
 
  <li>[http://www.bjmm.info/home.php?mod=space&uid=54388 http://www.bjmm.info/home.php?mod=space&uid=54388]</li>
 
  <li>[http://www.sxtongxiang.com/home.php?mod=space&uid=16868 http://www.sxtongxiang.com/home.php?mod=space&uid=16868]</li>
 
</ul>


===Infall to a point source of gravity===
== a storm surge of overwhelming Road flame out ==
It is relatively simple to derive the free-fall time by applying nothing more than [[Kepler's laws of planetary motion|Kepler's Third Law]] of planetary motion to a [[degenerate elliptic orbit]]. Consider a point mass <math>m</math> a distance <math>R</math> from a [[point source]] of mass <math>M</math> which falls radially inward to it. Crucially, [[Kepler's laws of planetary motion|Kepler's Third Law]] depends only on the [[semi-major axis]] of the orbit, and does not depend on the [[Eccentricity (orbit)|eccentricity]]. A purely radial trajectory is an example of a degenerate ellipse with an eccentricity of 1 and semi-major axis <math>R/2</math>. Therefore, the time it would take a body to fall inward, turn around, and return to its original position is the same as the period of a circular orbit of radius <math>R/2</math>, or


:<math>t_{orbit} = \frac{2 \pi}{\sqrt {G(M+m)}} \left(\frac{R}{2}\right)^{3/2}=\frac{\pi R^{3/2}}{\sqrt{2 G(M+m)}}.</math>
Sounded, and soon the magic that surrounds the poison spots around the green flame, rotating at high speed away suddenly, a storm [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-4.html casio 腕時計 g-shock] surge of overwhelming Road flame out, like countless FireWire-like, life will be cut into many parts of the magic drug spots.<br><br>toxic plaques associated with obsession [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-10.html カシオ 腕時計 スタンダード] and split open, Xiao Yan mind a move, glass lotus is the differentiation [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-15.html 電波時計 casio] and opened fire, the poison that magic spot numerous small parcels and into the points and then start the refinery!<br><br>cubicles, Xiao Yan eyes closed, a plume of green flame sailed since grazing the [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-10.html casio電波腕時計] skin, so that was within the room temperature gradually increased.<br><br>With sustained period of time, Xiao Yan spots of the body's inherent magic poisonous toxins, but also in the glass lotus fire refining, gradually into nothingness, but possessed toxic plaques associated with refining, within which the Unit contains a pure vindictiveness, but also the emergence of [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-3.html カシオ gps 時計] a steady stream out, and then like a flood flowing in the meridians of Xiao Yan, so obtaining in vivo
相关的主题文章：
<ul>
 
  <li>[http://crcc4.com/forum.php?mod=viewthread&tid=6900 http://crcc4.com/forum.php?mod=viewthread&tid=6900]</li>
 
  <li>[http://www3.kcn.ne.jp/~azrite/cgi-bin/fantasy2/fantasy.cgi http://www3.kcn.ne.jp/~azrite/cgi-bin/fantasy2/fantasy.cgi]</li>
 
  <li>[http://api.open.tenunion.com/home.php?mod=space&uid=125131 http://api.open.tenunion.com/home.php?mod=space&uid=125131]</li>
 
</ul>


To see that the semi-major axis is <math>R/2</math>, we must examine properties of orbits as they become increasingly elliptical. Kepler's First Law states that an orbit is an ellipse with the center of mass as one focus. In the case of a very small mass falling toward a very large mass <math>M</math>, the center of mass is within the larger mass.  The focus of an ellipse is increasingly off-center with increasing ellipticity. In the limiting case of a degenerate ellipse with an eccentricity of 1, the orbit extends from the initial position of the infalling object (<math>R</math>) to the point source of mass <math>M</math>. In other words, the ellipse becomes a line of length <math>R</math>. The semi-major axis is half the width of the ellipse along the long axis, which in the degenerate case becomes <math>R/2</math>.
== partial ==


If the free-falling body completed a full orbit, it would begin at distance <math>R</math> from the point source mass <math>M</math>, fall inward until it reached that point source, then turn around and journey back to its original position. In real systems, the point source mass isn't truly a point source and the infalling body eventually collides with some surface. Thus, it only completes half the orbit. But since the infalling part of the orbit is symmetric to the hypothetical outgoing portion of the orbit, we can simply divide the period of the full orbit by two to attain the free-fall time (the time along the infalling portion of the orbit).
Then slowly raised his arm, slender TANSEI 'color' on the sword, glaucoma increasingly rich, eyes staring at Xiao Yan: 'However, now I, on behalf of the cloud-lan, to its reputation, therefore, I will not stay the hand '<br><br>with Nalan sweet voice slowly falling, his body and his head above the robes and black hair, suddenly no wind automatically into the sky, forceful momentum, gradually rising into the sky from its body, and the powerful sense of momentum degree of Let get around those cloud-lan apprentice surprised [http://www.nnyagdev.org/sitemap.xml http://www.nnyagdev.org/sitemap.xml] Zhang played a mouth, a road whispered exclaimed, could not help but rang: 'This stock momentum Nalan senior sister apprentice turned Jin into a large bucket division of?'<br><br>look around those cloud-lan apprentice's face, it seems that [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-7.html カシオ 腕時計 gps] even they are [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-6.html 電波腕時計 カシオ] not very clear real strength Nalan sweet.<br><br>'I did not expect Nalan young niece is the big bucket division level, [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-10.html casio 腕時計 データバンク] people really admire ah.' Chen looked at the field of wood that exudes [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-15.html カシオ 腕時計 激安] a strong momentum of Nalan sweet, partial
相关的主题文章：
<ul>
 
  <li>[http://www.p2peye.com/home.php?mod=space&uid=117660 http://www.p2peye.com/home.php?mod=space&uid=117660]</li>
 
  <li>[http://www.ecoolr.com/plus/feedback.php?aid=458 http://www.ecoolr.com/plus/feedback.php?aid=458]</li>
 
  <li>[http://www.wmcc.cc/tw/bbs/forum.php?mod=viewthread&tid=124187 http://www.wmcc.cc/tw/bbs/forum.php?mod=viewthread&tid=124187]</li>
 
</ul>


:<math>t_{ff}=t_{orbit}/2 = \frac{\pi}{2} \frac{R^{3/2}}{ \sqrt{2 G(M+m)}}</math>
== you should be able to avoid the other person is blocked ==


This formula also follows from the [[Free_fall#Inverse-square_law_gravitational_field|formula for the falling time as a function of position]].
Speed ​​flashing, after a moment, then filled from the body's overbearing bloody breath, turned out to [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-14.html カシオ 時計 電波 ソーラー] be sailed a lot of convergence, palm flash, that is Kito sword disappeared, he looked at Xiao go far, quite unwilling said: 'Come on, this time even if you good luck!'<br><br>seeing, Xiao go far people are surprised a moment, looked at each other one, are all [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-5.html カシオ 腕時計 スタンダード] somewhat understand how this guy suddenly changed his mind.<br><br>'go west from here, this caught among the many strong junction, [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-6.html casio 電波時計] since you walk, you should be able to avoid the other person is blocked, and finally reach your place to go.' to see some daze the crowd, that some impatience Xuedao Holy Road.<br><br>'Thank you, seniors.'<br><br>Xiao Yan Gu Qingyang with others as the one, then quickly Xuedao Holy respectful toward a Baoquan, then a pedestrian slowly backwards, the body is [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-0.html カシオ 腕時計 チタン] still in with a [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-10.html casio電波腕時計] grudge
相关的主题文章：
<ul>
 
  <li>[http://cgi.www5b.biglobe.ne.jp/~pousan/bbs/yybbs.cgi http://cgi.www5b.biglobe.ne.jp/~pousan/bbs/yybbs.cgi]</li>
 
  <li>[http://bbs.m.1799.com/home.php?mod=space&uid=2034114 http://bbs.m.1799.com/home.php?mod=space&uid=2034114]</li>
 
  <li>[http://www.llxd688.com/forum.php?mod=viewthread&tid=742039 http://www.llxd688.com/forum.php?mod=viewthread&tid=742039]</li>
 
</ul>


Note that <math>t_{orbit}</math> in the above equation, is the time for the mass to fall in a highly eccentric orbit, make a "hairpin" turn at the central mass at nearly zero radius distance, and then returns to '''R''' when it repeats the very sharp turn. This orbit corresponds to nearly linear motion back and from distance '''R''' to distance 0. As noted above, this orbit has only '''half''' as long a semimajor axis ('''R/2''') as a circular orbit with radius '''R''' (where the semimajor axis is '''R'''), and thus the period for the shorter high-eccentricity "orbit" is that for one with an axis of '''R/2''' and a total orbital pathlength of only twice the infall distance. Thus, by Kepler's third law, with half the semimajor axis radius it thus takes only (1/2)<sup>3/2</sup> = (1/8)<sup>1/2</sup> as long a time period, as the "corresponding" circular orbit that has a constant radius the same as the maximal radius of the eccentric orbit (which goes to essentially zero radius from the primary at its other extreme).
== good tone mad ==


The time to traverse half the distance '''R''', which is the infall time from '''R''' along an eccentric orbit, is the Kepler time for a circular orbit of '''R/2''' (not R), which is (1/32)<sup>1/2</sup> times the period '''P''' of the circular orbit at '''R'''. For example, the time for an object in the orbit of the Earth around the Sun, to fall into the Sun if it were suddenly stopped in orbit, would be <math>P/\sqrt{32}</math>, where '''P''' is one year. This is about 64.6 days.
'Well, good tone mad, do not think that has a body and soul stars were puppets, there will be a qualification to compete with glacial valley, my strength, in glacial valley among the elders, it [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-2.html カシオ腕時計 g-shock] is only ranked at the end, but even Ice breaks and ice yuan, which is still ranked in [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-8.html casio 腕時計 スタンダード] the middle position, if I come out real strong glacial valley, what are you proud of the capital, will be immediately worth mentioning! 'heard, even if the situation somewhat wrong, but That still could not resist the ice crane sneered.<br><br>Xiao Yan eyes slightly narrowed, glacial valley is one of the three valleys, presumably strength is not [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-1.html カシオ 腕時計 チタン] weaker than 焚炎 Valley, and that 焚炎 Valley, just three elders, is about the strength of the star, and [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-15.html カシオ gps 時計] that two elders is reached the bucket peak levels were, [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-2.html 腕時計 casio] of course, is undoubtedly the most terrible natural 焚炎 Valley Tang Zhen, who with Xiao Yan eyesight, can only evaluate unfathomable given four words, and although the order for fighting respect other strong, Xiao Yan is difficult to accurately determine the strength, but instinct told him that Tang Zhen
相关的主题文章：
<ul>
 
  <li>[http://www.dgzhuangxiu.cn/plus/view.php?aid=484411 http://www.dgzhuangxiu.cn/plus/view.php?aid=484411]</li>
 
  <li>[http://yirenyiren.com/forum.php/forum.php?mod=viewthread&tid=603462 http://yirenyiren.com/forum.php/forum.php?mod=viewthread&tid=603462]</li>
 
  <li>[http://www.crackerbluesband.com/cgi-bin/guestbook/guestbook.cgi http://www.crackerbluesband.com/cgi-bin/guestbook/guestbook.cgi]</li>
 
</ul>


===Infall of a spherically-symmetric distribution of mass===
== storm surge vast majestic soul ==
Now, consider a case where the mass <math>M</math> is not a point mass, but is distributed in a spherically-symmetric distribution about the center, with an average mass density of <math>\rho</math>,


:<math> \rho = \frac{3 M}{4 \pi R^3}</math> ,
Halo, also could not resist a blood spray out.<br><br>sudden vomiting blood is so small medical cents Xiao Yan surprised, quickly will the live arm, looked a blowing shells can be broken goes pale cheeks, dark Mouzhong, [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-13.html カシオ腕時計 メンズ] intended to kill suddenly Dasheng,<br><br>amount deep breath, turned his head and looked at Xiao Yan Skyfire Venerable, voice, reveals a sub awe-inspiring: 'The trouble Yao gentleman, please resolve this as soon as possible, a small medical cents was seriously injured, did not sustain long.'<br><br>'ten minutes.'<br><br>Skyfire Venerable saw a live arm [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-11.html 腕時計 メンズ casio] that was Xiao Yan small medical cents, with his eyesight naturally be able to [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-13.html カシオ 腕時計 ソーラー 電波] see who suffered [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-10.html カシオ腕時計 価格] light injuries, [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-9.html 電波時計 casio] the current face of 'color' is seriously a lot, nodded slightly, immediately turned to look that face, 'color', who alarmed the ice breaks, the pace slowly step forward, storm surge vast majestic soul, suddenly its center, swept out!<br><br>soul in that storm burst
 
相关的主题文章：
where the volume of a sphere is:<math> {(4/3) \pi R^3}.</math>
<ul>
 
 
Let us assume that the only force acting is gravity. Then, as first demonstrated by [[Isaac Newton|Newton]], and can easily be demonstrated using the [[divergence theorem]], the acceleration of gravity at any given distance <math>R</math> from the center of the sphere depends only upon the total mass contained within <math>R</math>. The consequence of this result is that if one imagined breaking the sphere up into a series of concentric shells, each shell would collapse only subsequent to the shells interior to it, and no shells cross during collapse. As a result, the free-fall time of a massless particle at <math>R</math> can be expressed solely in terms of the total mass <math>M</math> interior to it. In terms of the average density interior to <math>R</math>,
  <li>[http://www.greenfiltering.com/plus/feedback.php?aid=138 http://www.greenfiltering.com/plus/feedback.php?aid=138]</li>
 
 
:<math>t_{ff} = \frac{1}{4}\sqrt {\frac{3 \pi}{2 G \rho}}\simeq 0.5427 \frac{1}{ \sqrt {G \rho}}\simeq 66430\,{\rm s} \frac{1}{ \sqrt {\rho}}</math>
  <li>[http://51glg.com/plus/view.php?aid=10224 http://51glg.com/plus/view.php?aid=10224]</li>
 
 
where the latter is in [[SI]] units.
  <li>[http://www.dhyqw.com/plus/feedback.php?aid=5167 http://www.dhyqw.com/plus/feedback.php?aid=5167]</li>
 
 
This result is exactly the same as from the previous section when :<math>M \gg m</math>.
</ul>
 
==Applications==
The free-fall time is a very useful estimate of the relevant timescale for a number of astrophysical processes. To get a sense of its application, we may write
 
:<math>t_{ff} \simeq \frac{35 \, \mbox{min}}{\sqrt{\rho}} \cdot \sqrt{\frac{\mbox{g}}{\mbox{cm}^3}}.</math>
 
Here we have estimated the numerical value for the free-fall time as roughly 35 minutes for a body of mean density 1 g/cm<sup>3</sup>.
 
==Comparison==
For an object falling from infinity in a [[capture orbit]], the time it takes from a given position to fall to the central point mass is the same as the free-fall time, except for a constant <math>\frac{4}{3\pi}</math> ≈ 0.42.
 
==References==
* [http://adsabs.harvard.edu/abs/1987gady.book.....B  Galactic dynamics] Binney, James; Tremaine, Scott. Princeton University Press, 1987.
 
{{DEFAULTSORT:Free-Fall Time}}
[[Category:Celestial mechanics]]

Revision as of 19:05, 2 March 2014

' in the woods

Yan smile: 'In recent years, it really is to live up to the expectations of the mother ...'

deep breath, Xiao カシオ 腕時計 gps Yan suddenly swing too far toward the dark カシオ腕時計 g-shock woods warm smiles: '? Father, you have come.'
While the bucket of gas
only three paragraphs, but Xiao Yan soul perception, Que Shibi a five stars who have a lot of sharp, talking about his mother in a previous time, he noticed カシオ 電波時計 a hint of movement in the woods.

'Oh, Yan children, so late, how still stay above this it?' in the woods, in the quiet moments, the outgoing concern laughter men.

branches burst of swing, a middle-aged man jumped out with a smile on the カシオ gps 時計 face, looked at his son standing in the moonlight that.

middle-aged man dressed in luxurious gray 'color' clothes, among 腕時計 メンズ casio quite a few Dragon Tiger step majesty, his face a pair of bushy eyebrows add a little more to their pride, he is currently xiaojia 相关的主题文章：

a storm surge of overwhelming Road flame out

Sounded, and soon the magic that surrounds the poison spots around the green flame, rotating at high speed away suddenly, a storm casio 腕時計 g-shock surge of overwhelming Road flame out, like countless FireWire-like, life will be cut into many parts of the magic drug spots.

toxic plaques associated with obsession カシオ 腕時計 スタンダード and split open, Xiao Yan mind a move, glass lotus is the differentiation 電波時計 casio and opened fire, the poison that magic spot numerous small parcels and into the points and then start the refinery!

cubicles, Xiao Yan eyes closed, a plume of green flame sailed since grazing the casio電波腕時計 skin, so that was within the room temperature gradually increased.

With sustained period of time, Xiao Yan spots of the body's inherent magic poisonous toxins, but also in the glass lotus fire refining, gradually into nothingness, but possessed toxic plaques associated with refining, within which the Unit contains a pure vindictiveness, but also the emergence of カシオ gps 時計 a steady stream out, and then like a flood flowing in the meridians of Xiao Yan, so obtaining in vivo 相关的主题文章：

partial

Then slowly raised his arm, slender TANSEI 'color' on the sword, glaucoma increasingly rich, eyes staring at Xiao Yan: 'However, now I, on behalf of the cloud-lan, to its reputation, therefore, I will not stay the hand '

with Nalan sweet voice slowly falling, his body and his head above the robes and black hair, suddenly no wind automatically into the sky, forceful momentum, gradually rising into the sky from its body, and the powerful sense of momentum degree of Let get around those cloud-lan apprentice surprised http://www.nnyagdev.org/sitemap.xml Zhang played a mouth, a road whispered exclaimed, could not help but rang: 'This stock momentum Nalan senior sister apprentice turned Jin into a large bucket division of?'

look around those cloud-lan apprentice's face, it seems that カシオ 腕時計 gps even they are 電波腕時計 カシオ not very clear real strength Nalan sweet.

'I did not expect Nalan young niece is the big bucket division level, casio 腕時計 データバンク people really admire ah.' Chen looked at the field of wood that exudes カシオ 腕時計 激安 a strong momentum of Nalan sweet, partial 相关的主题文章：

you should be able to avoid the other person is blocked

Speed ​​flashing, after a moment, then filled from the body's overbearing bloody breath, turned out to カシオ 時計 電波 ソーラー be sailed a lot of convergence, palm flash, that is Kito sword disappeared, he looked at Xiao go far, quite unwilling said: 'Come on, this time even if you good luck!'

seeing, Xiao go far people are surprised a moment, looked at each other one, are all カシオ 腕時計 スタンダード somewhat understand how this guy suddenly changed his mind.

'go west from here, this caught among the many strong junction, casio 電波時計 since you walk, you should be able to avoid the other person is blocked, and finally reach your place to go.' to see some daze the crowd, that some impatience Xuedao Holy Road.

'Thank you, seniors.'

Xiao Yan Gu Qingyang with others as the one, then quickly Xuedao Holy respectful toward a Baoquan, then a pedestrian slowly backwards, the body is カシオ 腕時計 チタン still in with a casio電波腕時計 grudge 相关的主题文章：

good tone mad

'Well, good tone mad, do not think that has a body and soul stars were puppets, there will be a qualification to compete with glacial valley, my strength, in glacial valley among the elders, it カシオ腕時計 g-shock is only ranked at the end, but even Ice breaks and ice yuan, which is still ranked in casio 腕時計 スタンダード the middle position, if I come out real strong glacial valley, what are you proud of the capital, will be immediately worth mentioning! 'heard, even if the situation somewhat wrong, but That still could not resist the ice crane sneered.

Xiao Yan eyes slightly narrowed, glacial valley is one of the three valleys, presumably strength is not カシオ 腕時計 チタン weaker than 焚炎 Valley, and that 焚炎 Valley, just three elders, is about the strength of the star, and カシオ gps 時計 that two elders is reached the bucket peak levels were, 腕時計 casio of course, is undoubtedly the most terrible natural 焚炎 Valley Tang Zhen, who with Xiao Yan eyesight, can only evaluate unfathomable given four words, and although the order for fighting respect other strong, Xiao Yan is difficult to accurately determine the strength, but instinct told him that Tang Zhen 相关的主题文章：

storm surge vast majestic soul

Halo, also could not resist a blood spray out.

sudden vomiting blood is so small medical cents Xiao Yan surprised, quickly will the live arm, looked a blowing shells can be broken goes pale cheeks, dark Mouzhong, カシオ腕時計 メンズ intended to kill suddenly Dasheng,

amount deep breath, turned his head and looked at Xiao Yan Skyfire Venerable, voice, reveals a sub awe-inspiring: 'The trouble Yao gentleman, please resolve this as soon as possible, a small medical cents was seriously injured, did not sustain long.'

'ten minutes.'

Skyfire Venerable saw a live arm 腕時計 メンズ casio that was Xiao Yan small medical cents, with his eyesight naturally be able to カシオ 腕時計 ソーラー 電波 see who suffered カシオ腕時計 価格 light injuries, 電波時計 casio the current face of 'color' is seriously a lot, nodded slightly, immediately turned to look that face, 'color', who alarmed the ice breaks, the pace slowly step forward, storm surge vast majestic soul, suddenly its center, swept out!

soul in that storm burst 相关的主题文章：

Retrieved from "https://en.formulasearchengine.com/index.php?title=Neutron_star_spin-up&oldid=240026"