臨七夕雜談

今日被媽叫去救火——乞巧演出要個人現場揮毫。說實話,本來我不想去的,風頭我是不愿意出的,但是請我幫忙的是媽,不好拒絕,於是硬著頭皮去了。

坐535路巴士去,誰知司機東川路不停直接開到總站,我憑著感覺兜兜轉轉,不料竟然越走越遠,一直走到了越秀南。此時天色漸昏沈,須臾大雨傾盆,加之雨具未攜,行走不得。一小時後雨止,雨過天晴……又走到文明路,搭上了媽單位同事的車才去到英雄廣場。

演出到到一半我上臺。那宣紙因為之前下雨之故而潤濕了,我手一撥欲撫平皺紋不意宣紙爛掉大半,囧……旁邊的靚女趕忙幫忙換了一張,她一撥,又爛多次……我不管,照寫。寫完感覺馬馬虎虎,氣勢還算是有的,還算沒丟架。就是那墨汁溝水太多,化得厲害,後面被我吃透便無再有事。

遙想小時候曾立有大志,言此生必要超過書聖。今觀之,仍去之甚遠,人生雖無常多舛,算來應已逾五分之一的人生。勤奮恐不遜於書聖,倘也有一池水供我洗筆,水亦已黑了。恐是「悟」劣。

書無性情而死,寫死字者,百年不得真諦。書聖云:

「夫書者,玄妙之伎也,若非通人志士,學無及之。大抵書須存思,余覽李斯等論筆勢,及鐘繇書,骨甚是不輕,恐子孫不記,故敘而論之。
「夫 書,不貴平正安穩。先須用筆,有偃有仰,有欹有斜,或小或大,或長或短。凡作一字,或類篆籀,或似鵠頭;或如散,或近八分;或如蟲食木葉,或如水中科 斗;或如壯士佩劍,或似婦女纖麗。欲書先構筋力,然後裝束,必注意詳雅起發,綿密疏闊相間。每作一點,必須懸手作之,或作一波,抑而後曳。每作一字,須用 數種意:或橫畫似八分,而發如篆籀;或豎牽如深林之喬木,而屈折如鋼鉤;或上尖如枯桿,或下細如針芒;或轉側之勢似飛鳥空墜,或稜側之形如流水激來。作一 字,橫豎相向;作一行,明媚相承。第一須存筋藏鋒,滅跡隱端。用尖筆須落鋒混成,無使毫露浮怯;舉新筆爽爽若神,即不求於點畫瑕玷也。若作一紙之書,須字 字意別,勿使相同。若書虛紙,用強筆;若書強紙,用弱筆:強弱不等,則蹉跌不入。
「凡書貴乎沉靜,令意在筆前,字居心後,未作之 始,結思成矣。仍下筆不用急,故須遲。何也?筆是將軍,故須遲重。心欲急不宜遲,何也?心是箭鋒,箭不欲遲,遲則中物不入。夫字有緩急,一字之中何者有緩 急?至如「烏」字,下手一點,點須急,橫直即須遲,欲「烏」之腳急,斯乃取形勢也。每書欲十遲五急,十曲五直,十藏五出,十起五伏,方可謂書。若直筆急牽 裹,此暫視似書,久味無力。仍須用筆著墨,不過三分,不得深浸,毛弱無力。墨用松節同研,久久不動彌佳矣。」

幸好知自己問題,為時未晚!

昨日深夜久雨初晴,然本欲凌晨起身尋彗,故置相機於戶外自動拍攝,目標為牛郎織女。今日檢視圖片,竟發現幸運地捕獲一顆約莫-6等的火流星,大致由牛郎飛嚮織女。不由地想起了秦觀的那首詞——《鵲橋仙》:

「纖雲巧弄,飛星傳恨,銀漢迢迢暗度。金風玉露一相逢,便勝卻人間無數。

「柔情似水,佳期如夢,忍顧鵲橋歸路。兩情若是久長時,又豈在朝朝暮暮。」

天有情,未見天老。而今未到七夕,牛郎早已按耐不住先送秋波與織女。

我?傷不起,再都不敢送咯,哈哈……

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臨七夕雜談

Calculation Orbit for C/2011 L4 (III)

As MPEC 2011-N34 released the latest astrometric observations of comet C/2011 L4, I again calculated an orbital solution for this promising vagabond in our solar system:

My solution is too quite close to which was published in MPEC 2011-N34. To obtain my solution I set perturbers including Jupiter, Saturn, Uranus and Neptune, i.e. the four planets with the greatest masses in our solar system. We can see that there’s no great shift from what I acquired based upon previous astrometric observations, which suggests that the original prediction won’t change too much, which favors observers in southern hemisphere more. For me any comets brighter than mag. 13 should be called bright comets within my capability of observing it. Therefore it’s likely that I’ll be able to pick it up as early as Aug in 2011, if it behaves normally in accord with the lightcurve prediction.

Calculation Orbit for C/2011 L4 (III)

Calculation Orbit for C/2011 L4 (II)

MPEC 2011-N13 pulished new astrometric observations of comet C/2011 L4 so I feed these new data into FindOrb to verify if there will be great changes in orbital elements. Different from the last calcualtion, I added several perturbers, including Jupiter, Saturn, Uranus and Neptune, the four Jovial planets with the heaviest masses in our solar system, which will exert gravitation on the small body. Overall 15 observations are rejected as their residuals are larger than 1.0 arcsec based upon my calculation.

Seems there’re no much changes compared to previous results, meaning that observations condition won’t improve much. According to the solution, the comet should favor observers in southern hemisphere before perihelion.

Calculation Orbit for C/2011 L4 (II)

Comet Hunt

Having consulted with the reverent comet hunter, Don Machholz, from Colfax, the US, I decide to start comet hunt from this month.

Comet hunt, it has been my perpetual  dream since my early childhood yet has been obstackled by the sky condition where I live as it’s frequently hazy and teemed with severe light pollution. By no means can I see the should-have-be spectacular summer milky way even though at predawn when many people go to bed and the majority of lights are off.

Under such unfavorable circumstances, I can only focus mainly on planetary observations. At times when there’re some bright comets in nightskies, I’ll train my 10cm-refractor that I purchased in 2003 to have a look at them. But in many cases, I can only observe comets faint to 8 mag, condensed no less than DC=2, which obviously can’t suffice my ambition.

Luckily, some ten kilometers away northeast to the downtown lies my maternal grandparents’ house, where the sky condition is much better. During my primary school I often went there to have nightsky observations of DSOs through my first scope — a small 8cm-refractor, now already obsolete. The sky there spellbound me deeply. Countless stars resembled the glimmering jewelry placed in front of a mighty black velvet. M13 used to be a very easy object to naked eye, so did M31 and various DSOs ancored in the fabulous summer milky way. Furthermore, every spring night when it was clear, which is yet rare owing to influence from the monsoon, I could well see the southern Cross as well as Rigil Kent and Hadar to its east above the south horizon by naked eye.

It would have been a wonderful place for me to comet hunt as seen from today. But, it’s a great pity, I must confess that I didn’t have any ability to conduct comet hunt at that time in that, weirdly, formatively from the habit I formed in urban area that I still firmly sticked to planetary observations even under such superb circumstances, paying little attention to comets, as an inertia. Therefore I intensely lacked experience of comets, let alone to begin comet hunt! It was not until the new year’s day in 2005 when I observed C/2004 Q2 (Machholz) in the chillest atmosphere I had ever experienced, the first comet I have ever seen, albeit several attempts had taken before but vainly, did I start to concentrate on cometary observations.

Unfortunately now my precious foundation, at least for me, has been stained — the municipality authorities widened a road not far from my site and a lot of bright road lights have been come into use since 2007. To make matters worse, a new avenue was finished in 2010 freight with powerful road lights on at nights, despite some kilometers away to the south, yet leading to a fairly bright southern sky… People quite second to these promotions as they observe that they needn’t so be scare when walking along the road in eerie darkness as in the past. So my sound is weak.

It’s fatal to me. And I have no idea stop the trend. Dark sky is a rare estate now. My new 8″ Dob from Mr. Tin from Amoi made in 1995 gives me some piteous compensation to fight against the brighter and brighter nightskies. My faintest comet that has ever seen was 103P/Hartley in early August last year, whose brightness is then estimated as 12.8. I’m sure my eyes have been well trained during these years that I’m so proud of myself that no any other observer around me can detect objects as faint as I can. When I point out that something, for example, a comet or a galaxy of 9 mag is quite obvious through the eyepiece to me under light polluted condition, other people, however, need to exert themselves to attempt a tiny glimpse of the blotch of light, or, in most cases, see nothing whatsoever; it’s a great luck to me! Thereby I have some confidence in my future comet hunt.

I clearly remember the order in importance suggested by Don, that it’s the eye, the conditions, and finally the scope that decides how faint one sees. I totally agree wih him in accord with my own experience. My eyes are actually the best weapon!

I frequently dream of discovering a new comet, but now I decide to set off to conduct real comet hunts in nightskies. The opportunity is always there, however small it is, and the key to success is whether you give it a try. During the approaching summer vacation, I’ll put my dream into practice. I need to find out the best means for me to sweep the sky, the rate and the way to recognize DSOs as fast as I can against a printed star atlas. I need to form my own pattern.

Undoubtedly I know there’s no much opportunity for me to make my dream come true this life, but I won’t get repentent with any complain when mortibund in that I’ve been trying my best. In fact, varieties and myriad of DSOs will satisfy me already through the eyepiece; they’ll awe me deeply, and delight me philosophically, as I’m seeing the mighty universe through my own eyes by myself. We human often speak highly of ourselves, busy seeking reputation and vainglory. Every time when faced with the heaven, I calm down and retrospect myself, therebyunhappiness away. The heaven is my real friend; it rejoices me when I’m overwhelmed with sadness; it relieves me when I’m distressed.

If I become as miserable as Robert Burnham Jr. in the future, I won’t complaint a bit. Instead, I’ll enjoy myself.

Hmm, I must to put many trifles aside, and I’ll keep this way. It’s also so great that I don’t have any loveship that blocks my way at the moment. I mustn’t get entangled by this quackmire in the future, because this along with other trivia may well distract my concentration. It’s well known that a very negative fluctuation in emotion results in a smaller LM, i.e. I’m likely to lose faint objects that should have been within my ability. All of these must get away from me!

As Don suggested, I need to go to bed as early, so I’d love to take his advice. I’ll go to bed before 9 p.m. and get up at around 2:30 a.m. in summertime and about 3:30 a.m. in winter at every clear predawn, regardless of however hot or cold. I’ll apply for my driving liscence too, for the reason that with a car I myself can drive out to seek for more favorable sites to comet hunt with ease at predawn as what Shigeki Murakami, my great mentor, have been doing. I’ll learn to be as perseverent and patient as those esteemed hunters like Murakami san, Don, Kaoru Ikeya, and Tsutomu Seki. In fact I have been influenced by these figures directly or indirectly for long. Last year Murakami san sent me two books by Seki san, ホウキ星が呼んでいる, 未知の星を求めて, from which, although I can’t understand much Japanese, I’m still able to read out an industrious hunter who impact upon my heart deeply.

Best wishes to myself! Toast!

Comet Hunt

On Conditions of Rocket Lift-off

I’ve encountered with a post in a forum asking that what the conditions would change if a rocket is lift off on the moon rather than on Earth. It’s an intriguing question and therefore I spent some time attempting to solve the problem. And now the solution which I believe is correct is shown as follows.

LetFdenotes the gravity, whileMand\mu

respectively denote the mass of the rocket itself and the one of fuel at a moment. After a moment of\mathrm{d}t, the combustion engine exhausts\mathrm{d}\mumass of the fuel.

To simplify the problem, I ignore the details how a rocket lift off from the origin stationary status otherwise the force from the ground is likely to complicate the scenario, i.e. somehow the rocket now has already left the ground but I need to consider the conditions of the force that can drive the rocket up. Let the rocket’s velocity right at this moment be\vec{u_{0}}, and the gush-out fuel’s velocity with respect to the rocket’s be, supposingly, a constant\vec{u_{0}}.

Then according to momentum law, we can yield the following equation:

\vec{F}{\mathrm{d}t}=(M+\mu-{\mathrm{d}\mu})\vec{u}+{\mathrm{d}\mu}(\vec{u}+\vec{v}_{rel})-(M+\mu)\vec{u}_0

Now supposing that the rocket’s motion is parallel to the gravity, so all of the vectors can be introduced into scalar quantity easily. Let the gravitation to be a negative value, hereby yielding

-F{\mathrm{d}t}=(M+\mu-{\mathrm{d}\mu})u+{\mathrm{d}\mu}(u-v_{rel})-(M+\mu)u_0

Step further, we have

-F{\mathrm{d}t}=(M+\mu){\mathrm{d}u}-{\mathrm{d}\mu}(u_0+v_{rel})

or

F+(M+\mu)\dot{u}=\dot{\mu}(u_0+v_{rel})

Introducing gravitational acceleration, hence the gravity becomesF=(M+\mu)g, which then substitutes the equation above, yielding the final equation as following:

\huge g=\frac{\dot{\mu}(u_0+v_{rel})}{(M+\mu)}

Now we can draw conclusions from this equation that compared to lift-off on the earth as g is smaller, there’s no need for the rocket covering so swiftly as on Earth, the gushing fuel’s speed with respect to the rocket itself doesn’t have to be so fast as well, and furthermore, the mass of fuel exhausted per unit time is unnecessarily so larger as on Earth.

Despite that there’s a omission of the detailed discussion about how a rocket can leave the ground, I think these conclusions are quite reasonable.

On Conditions of Rocket Lift-off