Retrograde Asteroids and TNOs

Of the 793,918 asteroids and trans-Neptunian objects (TNOs) currently catalogued, only 98 are in retrograde orbits around the Sun. That’s just 0.01%.

By “retrograde” we mean that the object orbits the Sun in the opposite sense of all the major planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. From a vantage point above the north pole of the Earth, all of the major planets orbit in a counterclockwise direction around the Sun.

Source: https://community.dur.ac.uk/john.lucey/users/inner.html

But a retrograde object would be seen to orbit in a clockwise direction around the Sun, as is shown in the animation below for Jupiter retrograde co-orbital asteroid 514107 (2015 BZ509), with respect to Jupiter and its two “clouds” of trojan asteroids.

Source: https://www.sciencenews.org/article/asteroid-jupiters-orbit-goes-its-own-way

Of these 98 retrograde objects, only 14 have orbits well-enough determined to have received a minor planet number, and only one has yet received an official name (20461 Dioretsa).

Semimajor Axis (a) between…Number of Retrograde Minor Planets
Mars – Jupiter3
Jupiter – Saturn*20
Saturn – Uranus*15
Uranus – Neptune*20
TNOs40

*asteroids between the orbits of Jupiter and Neptune are often referred to as centaurs

At least some of these objects may be captured interstellar objects.

Let’s now take a look at some of these 98 retrograde objects in greater detail.

20461 Dioretsa
The first retrograde asteroid to be discovered was 20461 Dioretsa, in 1999. The only named retrograde asteroid to date, Dioretsa is an anadrome of the word “asteroid”. It is a centaur in a highly eccentric orbit (0.90), ranging between the orbits of Mars and Jupiter out to beyond the orbit of Neptune. Objects in cometlike orbits that show no evidence of cometary activity are often referred to as damocloids. Dioretsa is both a centaur and a damocloid. Its orbital inclination (relative to the ecliptic) is 160°, which is a 20° tilt from an anti-ecliptic orbit. It takes nearly 117 years to orbit the Sun once. It is a dark object with a reflectivity only around 3% and is estimated to be about 9 miles across.

2010 EQ169
This retrograde asteroid holds the distinction (at least temporarily) of being the most highly-inclined main-belt asteroid (91.6°), relative to the ecliptic plane. It is also the retrograde asteroid with the smallest semimajor axis (2.05 AU) and lowest orbital eccentricity (0.10). Unfortunately, it was discovered after the fact by analyzing past data from the Wide-field Infrared Survey Explorer (WISE) space telescope, and has not been seen since. We have only a three-day arc of 17 astrometric observations of 2010 EQ169 between March 7-9, 2010 from which to determine its orbit. Nominally, 2010 EQ169 orbits the Sun at nearly a right angle to the ecliptic plane once every 2.9 years, between the orbits of Mars and Jupiter. However, our knowledge of its orbit is extremely uncertain, as shown below, and it has been lost. Our only hope will be to back-calculate the positions of future asteroids discovered to these dates to see if it matches the WISE positions.

ElementValue1σ Uncertainty
Inclination (i)91.606°18.177°
Semimajor Axis (a)2.0518 AU2.2176
Orbital Eccentricity (e)0.101530.90213
Orbital Period (P)2.94y4.765

2013 BL76
This retrograde TNO has the largest known semi-major axis of any of the retrograde non-cometary objects: 966.4274 ± 2.2149 AU. In a highly eccentric cometlike orbit (e = 0.99135), its perihelion is in the realm of the centaurs between the orbits of Jupiter and Saturn (8.35 AU), and its aphelion is way out around 1,924 AU. It takes about 30,000 years to orbit the Sun. Its orbit is inclined 98.6° with respect to the ecliptic.

2013 LA2
This retrograde centaur is in an orbit closest to the ecliptic plane (i = 175.2°), tilted 4.8° with respect to the ecliptic. It orbits the Sun about once every 21 years between the orbits of Mars and Uranus.

2017 UX51
The distinction for this retrograde TNO is that it has the highest orbital eccentricity of any non-cometary solar system object (e = 0.9967). Or is it an old inactive comet? 2017 UX51 orbits the Sun every 7,419 ± 2,883 years as close in as between the orbits of Earth and Mars (perihelion q = 1.24 AU)—classifying it as an Amor object—out to far beyond the orbit of Neptune (aphelion Q = 759.54 ± 196.77 AU). Its orbital inclination is 108.2°.

343158 (2009 HC82)
An Apollo asteroid, 343158 is the only known retrograde near-Earth asteroid (NEA), with an orbital inclination of 154.4°. It orbits the Sun every 4.0 years, between 0.49 AU (almost as close in as the aphelion of Mercury) out to 4.57 AU (between the orbits of Mars and Jupiter).

References
Conover, E., 2017. Science News, 191, 9, 5.

JPL Small-Body Database Browser, https://ssd.jpl.nasa.gov/sbdb.cgi, retrieved 31 March 2019.

Kankiewicz, P., Włodarczyk, I., 2018. Planetary and Space Science, 154, 72-76.

Minor Planet Center, https://minorplanetcenter.net/iau/MPCORB.html, retrieved 28 March 2019.

Namouni F., Morais M. H. M., 2018. MNRAS, 477, L117.

Wiegert, P., Connors, M., Veillet, C., 2017. Nature, 543, 687–689.

Year-Round Daylight Saving Time?

I’ve never been a fan of daylight saving time. During the warmest months for stargazing and other astronomy activities, daylight saving time (DST) puts the end of twilight (and every other astronomical event) an hour later: near, at, or past bedtime for children and early-rising adults.

The last time we tinkered with DST in the U.S. was to extend it in 2007 to begin the second Sunday in March and end the first Sunday in November (previously it was the first Sunday in April to the last Sunday in October). We currently observe daylight saving time 65.4% of the year (almost ⅔) and standard time the remaining 34.6% of the year (a little over ⅓).

DST is a zero-sum game. Getting that extra hour the first weekend in November sure is nice, but we pay for it when we lose an hour the second weekend in March. For a few days in November, we feel like we’re sleeping in an extra hour, but for a few days in March, we feel like we’re getting up an hour earlier than usual.

While I would much prefer to stay on standard time all year long nationwide, there doesn’t appear to be much public support for that. On the other hand, there is a groundswell of support for going to year-round DST. Even this would be preferable to our current system, in my opinion.

We have toyed with the idea of year-round DST once before: from January 6, 1974 to October 27, 1974. During the winter months in early 1974, there was a lot of public outcry about schoolchildren going to school in the dark, and I’m sure the pre-sunrise cold was a factor, too. So, the year-round DST experiment was terminated early (it was supposed to last until April 27, 1975). Would it be any different this time around?

Northern states (where the winter nights are longest) would be most affected by year-round DST, as would areas in the far-western reaches of each of the time zones. Here in Wisconsin, we would see something like the following:

Some Highlights of Year-Round Daylight Saving Time in Wisconsin (times are for Dodgeville, WI)
  • Earliest End of Evening Twilight: 7:08 p.m. (around December 6)
  • Earliest Sunset: 5:26 p.m. (around December 9)
  • Latest Sunrise: 8:32 a.m. (around January 3)
  • Latest Onset of Morning Twilight: 6:50 a.m. (around January 6)
DateSunriseSunset
November 17:35 a.m.5:53 p.m.
November 157:53 a.m.5:37 p.m.
December 18:12 a.m.5:27 p.m.
December 158:25 a.m.5:27 p.m.
January 18:32 a.m.5:36 p.m.
January 158:29 a.m.5:51 p.m.
February 18:16 a.m.6:13 p.m.
February 157:59 a.m.6:31 p.m.
March 17:36 a.m.6:51 p.m.
March 157:12 a.m.7:08 p.m.

I have an idea. If we extend DST to year-round, why not also start the school day an hour later? There are studies that show that most students would benefit from a later start of the school day. Of course, that would also mean that many parents would probably want to start their work day an hour later, too. But if we do that, then what’s the point in going to year-round DST in the first place?

Many states are currently considering and some have even passed legislation extending DST to year-round, but federal law will have to change to allow any of these states to do this. Right now, states only have the right to opt out of DST altogether, as Arizona and Hawaii currently do.

Gas Tax and Road Maintenance

State and local roads and city streets have been in a downward spiral of deterioration for the past several years and something needs to be done. You have no doubt noticed this driving, but try riding a bicycle and you will really notice how bad things have gotten.

Here in Dodgeville, Wisconsin, many of the city streets are in such bad shape they are becoming dangerous for bicyclists. And more difficult, too. Ever try riding up one of our many hills on pavement that is badly cracked? No wonder I hardly ever see anyone else biking here.

I think the best way to fund road resurfacing and reconstruction projects is to increase fuel taxes. These taxes should not only fund maintenance of state roads, but local roads and city streets as well.

The current gasoline tax in Wisconsin is 51.3¢ per gallon. This includes the following components:

  • Federal tax: 18.4¢ per gallon
  • State tax: 30.9¢ per gallon
  • Petroleum inspection fee: 2.0¢ per gallon

Let’s increase gas taxes in Wisconsin by a minimum of 8¢ to 10¢ per gallon (more would be better) and use all of that revenue to resurface and reconstruct roads throughout the state. Small communities and rural areas are most in need of assistance.

The Laws of Physics and the Existence of Life

George F. R. Ellis writes in Issues in the Philosophy of Cosmology:

The first requirement is the existence of laws of physics that guarantee the kind of regularities that can underlie the existence of life.  These laws as we know them are based on variational and symmetry principles; we do not know if other kinds of laws could produce complexity.  If the laws are in broad terms what we presently take them to be, the following inter alia need to be right, for life of the general kind we know to exist:

  • Quantization that stabilizes matter and allows chemistry to exist through the Pauli exclusion principle.

  • The neutron-proton mass differential must be highly constrained.  If the neutron mass were just a little less than it is, proton decay could have taken place so that by now no atoms would be left at all.

  • Electron-proton charge equality is required to prevent massive electrostatic forces overwhelming the weaker electromagnetic forces that govern chemistry.

  • The strong nuclear force must be strong enough that stable nuclei exist; indeed complex matter exists only if the properties of the nuclear strong force lies in a tightly constrained domain relative to the electromagnetic force.

  • The chemistry on which the human body depends involves intricate folding and bonding patterns that would be destroyed if the fine structure constant (which controls the nature of chemical bonding) were a little bit different.

  • The number D of large spatial dimensions must be just 3 for complexity to exist.

It should not be too surprising that we find ourselves in a universe whose laws of physics are conducive to the existence of semi-intelligent life.  After all, we are here.  What we do not know—and will probably never know: Is this the only universe that exists?  This is an important question, because if there are many universes with different laws of physics, our existence in one of them may be inevitable.  If, on the other hand, this is the only universe, then the fantastic claims of the theists, or at least the deists, become more plausible.

You may wonder why I call the human race semi-intelligent.  Rest assured, I am not being sarcastic or sardonic.  I say “semi-intelligent” to call attention to humanity’s remarkable technological and scientific achievements while also noting our incredible ineptness at eradicating war, violence, greed, and poverty from the world.  What is wrong with us?

References
G.F.R. Ellis, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

Les Misérables

There have been many film adaptations of Victor Hugo’s timeless novel, Les Misérables, but after watching the 1935 film starring Fredric March and Charles Laughton last night, I am in no rush to see any of the others. It is, quite simply, perfect.

This movie says more in one hour and forty-eight minutes than most other movies (especially more recent ones) say in two or three hours. A riveting tale of unjust laws, poverty, inhumanity, cruelty, compassion, love, mercy, doubt, and morality, this is one of the most moving and inspiring movies I have ever seen. And just as relevant for us to today as it was in 1935 and when Victor Hugo wrote the book, first published in 1862.

We need movies like this to remind us (and in such complex and jaded times as these we do need constant reminding) that idealism can help each of us navigate through life, and—no matter what burdens we bear—to make the world a better place. Not a single minute in this movie is wasted, so artfully is each and every scene of the movie constructed. If you tire of (and are horrified by) the seemingly endless stream of dystopian prognostications in recent years, this movie is the perfect antidote. There is an alternative to a ruined world, and that change begins with you and me right now.

https://dvd.netflix.com/Movie/Les-Miserables/70073445

https://www.amazon.com/Miserables-Richard-Boleslawski/dp/B076LJ6Y7V/

All of the film adaptations of Les Misérables, including this one, have a number of departures from the original novel by Victor Hugo. Behind every great movie there is usually an even greater book, and I have been remiss in never having read Hugo’s classic. That deficiency will be rectified soon.

Moon and Meteors

Did you know that it is possible to observe a meteor shower when its radiant is below your horizon? When its radiant is too far south (or north, in the southern hemisphere) to ever rise above your horizon? When its radiant is even located near the Sun?

Yes you can! By video recording the Earth-facing night side of the Moon, or during a total or partial lunar eclipse, you have the opportunity to record meteors impacting the surface of the Moon. Those of us who record occultations of stars by asteroids and trans-Neptunian objects already have the equipment necessary to accurately document such events, which typically produce brief flashes of light lasting for a few hundredths of a second.

Leonid meteor lunar impact flashes of +3m to +8m were recorded in 1999 and 2001, and Geminid meteor lunar impact flashes have been recorded that were between +5m and +9m. Meteor impact events have also been recorded during lunar eclipses, such as just after the beginning of the total lunar eclipse of January 20/21, 2019.

Besides during lunar eclipses, the best time to look for meteor impact events on the Moon is when most of the Earth-facing side of the Moon is dark and illuminated only by earthshine. This occurs during the waxing crescent and waning crescent phases.

NASA has twin 14-inch telescopes that observe the nighttime part of the Moon between the phases of New and First Quarter, and between Last Quarter and New. These telescopes have recorded 435 flashes on the Moon from 2005 to April 2018.

On Mt. Kyllini (930 m), Corinthia, Greece, the 1.2 m Kryoneri telescope of the National Observatory of Athens has been employed in a four year project called NELIOTA (Near-Earth Object Lunar Impacts and Optical Transients) to monitor the Moon for lunar flashes using a two camera system (one R-band and one near-IR) at a video rate of 30 frames per second. All candidate flashes are compared against a database of artificial satellites to exclude false positives due to sunglints of satellites passing in front of the Moon. Between February 2017 and January 2019, forty lunar impact events have been detected.

Of course, you’re more likely to capture a lunar meteor impact flash during a major meteor shower.

Peter Zimnikoval in Slovakia has written a wonderful program called MetShow that will present your local circumstances for the Moon at any date and time and for any meteor shower radiant. I’ve reproduced in the gallery below the lunar circumstances for all the major meteor showers (ZHR ≥ 10) for the remainder of 2019.

Not only does the lunar phase have to be favorable, but the meteor shower radiant must be coming from a direction that will impact a nighttime part of the Moon that we can see. If the Moon is located near the radiant of a meteor shower, then most of the meteors will impact the far side of the Moon where they will be unobservable from Earth. If the Moon is located near 180˚ from the meteor shower radiant, then the meteors will favor the near side.

This year, the best meteor showers to monitor are the Eta Aquariids around May 6, the Delta Aquariids around July 30, and the Ursids around December 23.

Most meteor showers have a broad maximum, so the exact time to observe the Moon is not as important. But if the meteor shower has a sharp peak, then one should consider the time offset between the Earth and the Moon. Peter Zimnikoval writes (personal communication, 2019):

“Bombarding of the Moon’s surface is almost the same as on the Earth. The position of the observed radiant is given as the vector sum of the heliocentric motion of the meteoroids and the Earth’s motion. For the Moon, there is only a small difference due to its orbital velocity (1 km/s). Regular meteor showers cross the Earth’s orbit at the same point every year. The angular position of this point is described as solar longitude (J2000). The Moon at 3rd quarter reaches this point about 3.6 hours before the Earth (384,399 km / 29.78 km/s = 12,908 seconds = 3.6 hours). The Moon at 1st quarter reaches this point about 3.6 hours after the Earth.”

“For most of the regular meteor showers (Perseids, Orionids, Geminids) this time shift is not very important. Their maxima are not too sharp and the duration is many hours. The time shift may be important for very narrow meteor streams, where the suspected time of maximum is only a few hours and therefore observed from only a small part of the Earth. When the structure of a shower is very sharp, then small differences in the position of the Earth and the Moon passing through this stream can make a difference. At full moon or new moon, the Moon may reach a higher density of particles than the Earth, but these phases are not suitable for observation of lunar impact flares.”

Lunar Meteor Shower Peak Time Geometry (kindly provided by Peter Zimnikoval on March 8, 2019)

References
King, Bob (2019). A Space Rock Strikes Moon During the Total Lunar Eclipse. Sky & Telescope, January 23, 2019 blog. https://www.skyandtelescope.com/observing/a-space-rock-strikes-moon-during-the-total-lunar-eclipse/ .

Liakos, Alexios et al.(2019). NELIOTA Lunar Impact Flash Detection and Event Validation. Proceedings of the “ESA NEO and Debris Detection Conference -Exploiting Synergies-“, held in ESA/ESOC, Darmstadt, Germany, 22-24 January 2019. arXiv:1901.11414 [astro-ph.EP].

Zimnikoval, Peter (2017). Lunar impact flashes. WGN, Journal of the International Meteor Organization, 45:5.

Infrasound and Meteors

Humans typically can hear sound waves in the range 20 Hz to 20,000 Hz. Frequencies below 20 Hz are called infrasound and frequences above 20 kHz are called ultrasound. The speed of sound in dry air at a temperature of 20˚ C (68˚ F) and an atmospheric pressure of 1 bar (slightly less than the average air pressure at sea level) is 343 m/s. Dividing the speed of sound by the frequency (in Hz) gives us the wavelength of the sound waves: 17 m (56 ft.) at 20 Hz, and 17 mm (0.67 in.) at 20 kHz.

Meteoroids enter the Earth’s atmosphere (thus becoming meteors) at hypersonic velocities, 35 to 270 times the local speed of sound (Mach 35 to Mach 270). Only a small portion of the total energy of the incoming meteoroid is transformed into visible light: most of the energy dissipated goes into acoustic shock waves. If the meteoroid is on the order of a centimeter (0.4 inches) or larger, infrasound waves are generated that can be detected on the ground, albeit after a delay of many seconds to minutes.

Infrasound waves can travel long distances, but higher frequencies are attenuated due to spreading losses and absorption over much shorter distances. There are many natural and man-made sources of infrasound waves, so identifying an incoming meteoroid as the source of the infrasound requires that we also “see” and record the meteoroid optically (the “meteor”), through radar, or VLF radio emissions from the meteoroid’s ionization trail in the Earth’s atmosphere. Ideally, all of these methods should be used at each observing station to best characterize the size and kinetic energy of each incoming meteoroid.

Infrasound detectors are not yet an off-the-shelf commodity. Chapparal Physics (http://chaparralphysics.com/) is one good source, but seeing as they do not list any prices you know the equipment will be expensive.

An infrasound detector is basically an extremely sensitive microphone that can detect tiny changes in air pressure. A peak sensitivity around 1 Hz is probably a good place to start for detecting meteors. Meteors large and/or energetic enough to be detected on the ground are rare, not even one a day for a given station, so automated recording will be necessary.

Finally, it is important to know that louder sounds that we cannot hear (infrasound and even ultrasound) can sometimes have adverse physical and psychological effects on humans. The cause can be as simple as a malfunctioning piece of mechanical or electrical equipment, or as nefarious as a sonic weapon. It would be advantageous to have a readily available and affordable infrasound and ultrasound detector to detect problem emissions.

For example, you might want an

  • Infrasound detector that maps 0.02 Hz – 20 Hz to the 20 Hz – 20 kHz audible range
  • Ultrasound detector that maps 20 kHz – 20 MHz to the 20 Hz – 20 kHz audible range

References
Silber, Elizabeth A. (2018). Infrasound observations of bright meteors: the fundamentals. WGN, Journal of the International Meteor Organization, 46:2.


Retirement Advice?

I’ll be 63 in a couple of months. My the years go fast, faster still of late.

Naturally, I’m beginning to look toward retirement when I can finally devote nearly all my time and energy to astronomy, preservation and restoration of our nighttime environment, and classical music. These three avocations have been my primary interests all of my adult life.

I’m in need of some retirement advice by someone who is not trying to sell me a financial product. I’d like to semi-retire as soon as possible, but want to wait until age 70 to collect Social Security when the monthly benefit reaches a maximum. So, I guess that means gradually cutting back work hours and supplementing the lost income with some retirement benefits.

I’m in a good position in terms of having a marketable work skill for the semi-retirement years. You’d be hard pressed to find a better SAS programmer. I’ll be at SAS Global Forum 2019 in Dallas this spring if you want to talk.

Honestly, I’ve been in a bit of a funk since I started this blog back in December 2016. First, Trump got elected, and that made me realize how bad things have gotten in this country. That someone so boorish and with zero job skills as a public servant got elected as President of the United States is both frightening and depressing. And the national nightmare continues. Then, last fall, my employer moved everyone except for management into an open office environment, which I hate. Throughout my work career, I’ve always had my own office or a cubicle and now I’m in a big open room with lots of distractions and a desk half the size of what I had just a few months ago, and no place to put my books, so I had to bring them all home. No one wants to learn SAS at my company anymore, even though I do amazing things with it every day. I’m in high demand, but they’re not hiring anybody anymore with SAS skills. That’s depressing, because it is a great language and a great company and SAS Institute most definitely continues to innovate. But open source is the name of the game where I work now.

It is easy to feel isolated living in a small town. As my friend Jeff Dilks once said when he was a physics teacher in Shenandoah, Iowa, the chances of finding anyone else in a small town (or rural area) with similar interests and abilities are vanishingly small if you have “big city” interests and a specialized education. That’s true, but where else are you going to live if you want to do observational astronomy and ride a bicycle to and from work? Quality of life issues like that, you know. But loneliness, yes, and I imagine that gets to be more of a challenge in our later years.

For something like 30 years, I’ve wanted to help develop and nurture a science-oriented and education-oriented intentional community where astronomy is a major focus. I even have a name for it: Mirador Astronomy Village. Can’t think of a better way to spend my retirement years, but it takes serious money to get something like this off the ground, and money I don’t have.

With open office and all (which is pretty much ubiquitous nowadays), I’ve soured on the idea of working for “Corporate America” any longer. I’d be much happier as a public servant, trying to make the world a better place and helping to solve the many problems for which Corporate America is not the answer, and has no answers.

Desiderata

The word desideratum has been a part of the English language since at least 1651, according to the Oxford English Dictionary, which provides this definition:

Something for which a desire or longing is felt; something wanting and required or desired.

This word comes from the Latin dēsīderātum “thing desired”, and its plural is desiderata.

The French astronomer Auguste Charlois (1864-1910) discovered the asteroid 344 Desiderata on 15 Nov 1892 at the Nice Observatory, in southeastern France near the border with Italy. Like most of his 99 asteroid discoveries between 1887 and 1904, it is named to honor a woman. In this case, that would be Désirée Clary (1777-1860), French woman who became Queen Desideria of Sweden.

On 25 Feb 2019, I recorded 14.1-magnitude 344 Desiderata passing in front of the 14.6-magnitude star UCAC4 639-020401 in the constellation Auriga. Right before the event, star and asteroid formed a 13.6-magnitude blended image, and when the asteroid covered up the star, the brightness dipped 0.5 magnitude to the brightness of the asteroid alone. This great cover-up event lasted 16.8 seconds. Here’s a light curve of the event as a function of time.

Light curve of asteroid 344 Desiderata passing in front of UCAC4 639-020401 in Auriga

That dip to the right (after) the asteroid covered up the star suggests that a smaller satellite of the asteroid might have also passed in front of the star. Alas, it is only noise. We can tell this by looking at the light curve of a nearby comparison star at the same time.

Wind gust caused a dip in brightness of both stars at the same time after the main occultation event
A view of just the comparison star clearly showing the dip in brightness from a wind gust

Here is the smoothed and fitted light curve of the asteroid occultation event.

Asteroid occultation of the star UCAC4 639-020401 by the asteroid 344 Desiderata on 25 Feb 2019


Max Ehrmann (1872-1945) wrote a prose poem Desiderata (Latin: “things desired”) in 1927 that has since become well known, and for good reason.

Desiderata

Go placidly amid the noise and the haste, and remember what peace there may be in silence.  As far as possible, without surrender, be on good terms with all persons.

Speak your truth quietly and clearly; and listen to others, even to the dull and the ignorant; they too have their story.

Avoid loud and aggressive persons; they are vexatious to the spirit. If you compare yourself with others, you may become vain or bitter, for always there will be greater and lesser persons than yourself.

Enjoy your achievements as well as your plans. Keep interested in your own career, however humble; it is a real possession in the changing fortunes of time.

Exercise caution in your business affairs, for the world is full of trickery. But let this not blind you to what virtue there is; many persons strive for high ideals, and everywhere life is full of heroism.

Be yourself. Especially do not feign affection. Neither be cynical about love; for in the face of all aridity and disenchantment, it is as perennial as the grass.

Take kindly the counsel of the years, gracefully surrendering the things of youth.

Nurture strength of spirit to shield you in sudden misfortune. But do not distress yourself with dark imaginings. Many fears are born of fatigue and loneliness.

Beyond a wholesome discipline, be gentle with yourself. You are a child of the universe no less than the trees and the stars; you have a right to be here.

And whether or not it is clear to you, no doubt the universe is unfolding as it should. Therefore be at peace with God, whatever you conceive Him to be. And whatever your labors and aspirations, in the noisy confusion of life, keep peace in your soul. With all its sham, drudgery and broken dreams, it is still a beautiful world. Be cheerful. Strive to be happy.