Star Formation, Part I

Sorry we’re late, we just had to take the time to evolve this post.  That’s right, we are here to discuss the first step in a star’s evolution!  In one of my many twisted analogies I said that stars are like people.  So, we have the early stages of a star’s life!  Just like how people have baby and teenage years we have the topic of star formation and nebulae (again, twisted analogies…but I think we can all deal with the puns and any bad humor presented here).

Interstellar medium (ISM) is quite literally “the stuff between the stars”. And by stuff, we mean the gas and dust that stars form out of, and often, spew back into space during their lifetimes through stellar winds or supernovae. Unsurprisingly, hydrogen makes up most of the ISM as HI (neutral), HII (ionized), or H2 (molecular), and helium makes up most of the remainder. It’s hard to detect neutral hydrogen because its single electron is in the ground state, so it cannot jump down an energy level to release radiation, and only rarely does a photon of the right energy come along to boost the electron to a higher energy level. However, astronomers can still detect HI using the 21 cm line. This relies on the fact that electrons and protons both have a quantum “spin”. A hydrogen atom has slightly less energy when they are spinning in opposite directions as compared to when they are spinning in the same direction – the photon corresponding to this difference  in energy has a wavelength of, you guessed it, 21 cm.

While it doesn’t make up a large percentage of the ISM, dust blocks light and also reddens it, since longer wavelengths are less likely to interact with dust grains. It is sometimes found in the form of Polycyclic Aromatic Hydrocarbons (PAHs), which are relatively complicated hydrocarbons with ring structures. Why do we mention PAHs? Not for any important reason, they’re just thought to be necessary for life (even though we consider them scary carcinogens down here on Earth).

Thus, we start our evolution with stuff.  What is this stuff?  Oh, various things.  Hydrogen, helium, lithium… Yes, lithium in fact would exist, but we will ignore this until a bit later into the post.  But we just have stuff, what do we need to make a star?  Well, this stuff, at this point forming a nebula, literally meaning cloud, is not condensed.

The Eagle Nebula

Soar like an Eagle Nebula (yes, nebulae are pretty). Credit: Jeff Hester and Paul Scowen (Arizona State University), and NASA. From http://outreach.atnf.csiro.au/education/senior/astrophysics/stellarevolution_formation.html

Before we go further, we should note that there are several kinds of nebulae. Reflection, emission, absorption/dark, planetary, supernova remnants… heck, people used to call galaxies and star clusters “nebulae” as well. Note that this post will deal with star forming regions or cloud complexes, so there won’t be SNRs or planetary nebulae because they don’t really apply to the start of a star. Emission nebulae are formed when gas molecules are excited (yes, you be excited as well) by radiation from a nearby star and release radiation; they are typically red in color because of their hydrogen content. Reflection nebulae occur when starlight doesn’t have enough energy to excite the electrons and just reflects off dust particles instead (typically blue because shorter wavelength light is easier to scatter). Both these types of nebulae signal regions of star formation. Absorption nebulae, or dark nebulae, appear “dark” because they’re made of relatively dense clouds of dust that simply block light from behind them.  And why study these?  Well…they’re dark for one.  So yeah, they block out light, how annoying!  Luckily we have some ideas of how they block out light, but if we didn’t it would be quite the nuisance.  But then what else could they involve (you know, since astronomy just can’t leave something as is)?   Well, there are these things known as Bok globules.  They are smaller dark nebula that are also regions of star formation in HII regions, and they can also hint at some star formation in general since they can be in molecular clouds.

Horsehead Nebula (a dark nebula)

One of the most famous dark nebulae in the sky. Credit: NASA

B68

Barnard 68-the other most famous blotch of black stuff in the sky that is actually stuff. Credit: NASA and cfa.harvard.edu/COMPLETE

Thackeray’s globule-the other OTHER most famous blotch of black stuff in the sky indicating star formation. Yay for Bok globules! Credit: HST and cfa.harvard.edu/COMPLETE/

But back to stars. For a star to form, a chunk of the gas cloud has to increase in density to such a point that it collapses under its own gravity. Either random turbulence within the gas cloud itself may achieve this critical density, or an outside source, such as collision with another gas cloud or shock waves from a nearby supernova, may be involved. Astronomer James Jeans derived an equation to show the minimum mass necessary for a cloud of a certain radius to collapse; we of course know this as the Jeans mass. However, the Jeans mass neglects external gas pressure (which is factored in by the Bonner-Ebert mass) as well as several other factors that may influence collapse. The initial gas cloud fragments into several pieces, for reasons that we don’t quite understand yet, and these pieces may fragment further until their density is so great that they just keep collapsing.  And you guessed it, this is called fragmentation!  These are important because they can form binary stars and relate clusters of many stars, both of which are quite useful.  Fragmentation itself stops and changes due to differences in density and energy radiated as the collapse occurs.  Aside from this, factors influencing protostars are mainly motions (rotational or angular) and magnetic aside from atoms.

And to further the fascination let’s add some more factors.  As we said there is rotation and magnetic fields.  There are also differences in density.  Another factor?  Well, a commonly seen occurrence is to see stellar winds from massive stars blowing at or ionizing the protostar such that they are eroded away.  So, what do we get from these complications?  Birth lines!  Yes, they really are just like humans, well not at all actually, since these are actually lines for the beginning of protostars’ evolution.

Also, massive stars may not form from large amounts of mass collapsing, but from multiple smaller stars coming together because the high temperature, luminosity, and radiation associated with large stars are thought to be hard to achieve by collapse.  But this may not be needed because mass can fall into an accretion disk (an accumulated disk of material) around the star.  This could then make a massive star grow, and it wouldn’t be fully ionized, which could prevent collapse.

bate1.gif (33637 bytes)

“A typical interstellar cloud is supported against collapse by internal turbulent motions.”

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“Once such a cloud is “tipped over the edge” and starts to collapse, it reaches a state where gravity can pull the gas together to form dense “cores”. “

bate8.gif (27444 bytes)

“These cores continue to collapse, often fragmenting further, until they form star – sized clumps.” To show what we have been explaining thus far. Credit for the above three pictures: ircamera.as.arizona.edu and Matthew Bate

So, are we at a star yet?  Nope, we still have a ways to go. You see, like we said stars evolve, like life theoretically, but we can track them much better (see, stars are so much more stellar than other things).  Tracks we say?  Yes, evolutionary tracks in fact!  These curves show major tracks for different mass stars.  The energy produced during this time is created from falling material going so fast that it goes supersonic and has what’s called a shock front, which basically just means that we get this whole mix of really fast moving stuff slowing it down to the point where energy is released.  Another note is that material is accumulating, or accreting (yes, it’s a word that will be used many many times) around the star as it collapses.  In fact, the collapse that occurs appears to be of infrared sources which appear in Bok globules.

Alright, but now what do we have?  Well, we’ll just say by this point we’ve gotten a protostar.  This collapses through the Kelvin-Helmholtz mechanism of gravitational contraction which can release potential energy as heat, explaining the light we see from a protostar.  Moving on we have the oh so important Hayashi Track!  In fact, Hayashi did many things with these early stars, but let’s just start with this.  The Hayashi track shows that for a collapsing protostar the opacity of a star increases from slight ionization of hydrogen.  This results in convection in the envelope, which he managed to show as a vertical line on the H-R diagram.  This line shows that the collapse eventually decreases luminosity and increases temperature.  The best part about this track?  It actually forbids certain types of stars from forming, greatly helping our search for star formation.

Hayashi Track

Credit: David Darling

After all this and some modelling we get what’s called pre-main sequence evolutionary tracks.  These are basically more tracks to see the evolution of stars.  Interestingly, a core and convective zone begins to form at this point, which can allow some slight fusion through the PP chain and the CNO cycle, but not enough to really stop collapse.  This can produce a slight expansion such that luminosity would actually slightly decrease.  In lower mass stars carbon generally can’t be burned, so later in life the CNO cycle wouldn’t really occur as much, but in massive protostars it’s slightly different since the CNO cycle would be more dominant.  So, what does this show?  Basically that mass matters.

We’ll cover types of Pre-Main Sequence objects and more star formation in Part II.

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TL;DR – Stars form out of interstellar medium, massive clouds of gas and dust. A gas cloud becomes denser in one area, which collapses under its own gravity and also fragments to form several protostars. These not-quite-stars follow evolutionary tracks as they evolve towards the main sequence on the H-R diagram.  And what is basically the most important factor?  Mass.  This beginning stage is important to understand where to look for types of stars and events, to understand the processes in stars, and to help make better interpretations of how the universe works.

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Sources:

Nebulae:

Star Formation (these sites cover most of the star formation post in general, which is why this isn’t split up so much)

Carroll and Ostlie, An Introduction to Modern Astrophysics, 2nd edition (pg 398-445)

Coordinates

Coordinates. You have to have them for everything you do (at least in astronomy), they’re a pain in the neck to convert, and you have to learn to read all of them. There are three that we need to discuss—the altitude azimuth coordinate system, the equatorial coordinate system, and the galactic coordinate system. All of these should be written in reference to the J2000 epoch.

First, we’ll discuss the simplest of these—the altitude-azimuth (or horizon) coordinate system. It’s a system based on you (yes, for once, the universe does indeed revolve around you). This system basically takes where you are right now and puts all the stars and whatnot in relation to you. To understand this system, you first must know what a zenith is. For any of you who are slightly literate, you know that “zenith” means that something is at its highest point. So in astronomy, the point that is directly above you is the zenith. Because the heavens are generally referred to as a sphere kind of thing, but you can only see half of it at any given time, the altitude is the angle from the flat horizon line to the height of the star. Now, we have to measure the azimuth. The azimuth is basically the angle that the star is located on in reference to North. Confused? Here’s a diagram:

For reference (although you have doubtless already figured this out), the altitude-azimuth system is measured in degrees, just like our very own latitude/longitude system. This system is difficult to use in practice, purely because it completely depends on where you are. Because of this, the coordinates of everyone in the world are different. For this reason, astronomers hate using this system, preferring instead the equatorial coordinate system, which we’ll talk about next.

The equatorial coordinate system is the one that you all have heard of—the one with the right ascension and declination stuff. (And if you haven’t, then what the heck are you doing in astronomy?!) The system, as its name implies, is based on Earth’s latitude/longitude system, but isn’t affected about the rotations and all. Declination (DEC) is the astronomy version of latitude—and it’s measured from the equator, too! It’s just the degrees north or south of the celestial equator, which has the same plane as Earth’s equator, only more expanded. Right ascension (RA) is—you guessed it—the longitude of astronomy, and this is based on the vernal equinox, which is just astronomy’s version of the Prime Meridian. Right ascension is usually measured in hours, minutes, and seconds, going all the way up to 24 hours. Every 360 degrees equals 24 hours, so 15 degrees equals one hour, and one degree equals 15 minutes. Lovely picture here:

Because this is based on something that doesn’t change as the Earth rotates, the RA/DEC coordinates don’t change on a day to day—or even year to year—basis. This means that whatever the values of RA or DEC are, they remain constant.

Again, this is the coordinate system most often used by astronomers—and it is also the system in common use in Science Olympiad. If you are competing in Astronomy/Reach for the Stars, please know this system better than the back of your hand, and you will have a chance of not failing miserably in these events.

The last system you really need to know is the galactic coordinate system. The thing about the other two coordinate systems is that it’s based off of Earth—and Earth is tilted about 62.87° away from the equator of the Milky Way (henceforth referenced as “the Galaxy”). And that’s a problem (as are our egos, but we won’t go into that). This is really a lot like the equatorial system, only it’s based off the Galaxy midplane, which is the Galaxy’s equator. (Technically, it is based off the Sun drawing a plane parallel to the Galaxy Midplane, but really, the two are so close together that it doesn’t make a difference.) Latitude runs parallel to the Galaxy midplane, and longitude is an angle in reference to the North Galactic Pole (NGP), which is perpendicular to the Galaxy midplane. We measure the latitude and longitude, however, from the Sun. (We design a system so as to not be based off of Earth, so what do we base it off of? Yes, that’s right—the Sun, despite the fact that it’s nowhere near to the centre of the galaxy.) Before we go any further, a diagram to help all of you mind-numbingly confused people.

As you can see from the diagram, there is a line that connects the galactic centre to the Sun. This is where latitude (the universal symbol of which is b) is measured from. It goes from this line until it hits the line where it passes directly beneath the star, and there you have it! Your latitude coordinates.

We measure longitude (the symbol of which is l) very similarly. Since the Sun just happens to be directly beneath the NGP (what a coinkydink, don’t you think?), we use the NGP as a reference point. When we measure the longitude, we measure the angle between the Galaxy midplane and the height of the star in reference to the distance between it and the Sun. (Use your logic and the Pythagorean theorem here—assuming the same height from the Galaxy midplane, the farther out your star is, the smaller the angle. This is why you have to know the distance.)

Or, for a slightly better description, taken from Carroll and Ostlie:

“The Galactic coordinate system exploits the natural symmetry introduced by the existence of the Galactic disk. The intersection of the midplane of the Galaxy with the celestial sphere forms what is very nearly a great circle, known as the Galactic equator. This orientation is depicted in Fig. 24.16. Galactic latitude (b) and Galactic longitude (l) are defined from a vantage point taken to be the Sun, as shown in Fig. 24.17. Galactic latitude is measured in degrees north or south of the Galactic equator along a great circle that passes through the north Galactic pole. Galactic longitude (also in degrees) is measured east along the Galactic equator, beginning near the Galactic center, to the point of intersection with the great circle used to measure Galactic latitude.

By international convention, the J2000.0 equatorial coordinates of the north Galactic pole (b=90°) are:

­a NGP: 12 h 51 m 26.28 s

­d NGP: 27°7′ 41.7”,

­and the origin of the Galactic coordinate system (l0 0°, b0 0°) corresponds to

­a0: 17h 45m 37.20s

­d0: 28°56′ 9.6”.”

Now, for conversions. Brace yourselves for some brutal math rearing its ugly head. If you do not know how to do spherical trigonometry—which is nowhere near nice, normal plane trigonometry—then stay away and keep your sanity. YOU NEED TO HAVE TAKEN PRECALC TO BE ABLE TO UNDERSTAND THIS (or at least advanced trig).

Since the altitude-azimuth system is based on, well, us, we can’t convert it to anything. But equatorial system to the galactic coordinate system and vice versa? Astronomy says yes.

The equations for converting equatorial coordinates to galactic coordinates are as follows:

\sin {b} =\sin { {\delta}_{NGP} } \sin {\delta} +\cos { {\delta}_{NGP} } \cos {\delta} \cos { (\alpha -{\alpha}_{NGP}) } \\ \cos {b} \sin { ({l}_{NCP}-l) } =\cos {\delta } \sin { (\alpha -{a}_{NGP}) } \\ \cos {\delta} \cos { ({l}_{NCP}-l) } =\cos { {\delta}_{NGP} } \sin {\delta} -\sin { {\delta}_{NGP} } \cos {\delta} \cos { (\alpha -{\alpha}_{NGP}) }

The equations for converting galactic coordinates to equatorial coordinates are as follows:

\sin {\delta} =\sin { {\delta}_{NGP} } \sin {b} +\cos { {\delta}_{NGP} } \cos {b} \cos { ({l}_{NCP}-l) } \\ \cos {\delta} \sin { (\alpha -{\alpha}_{NGP}) } =\cos {b} \sin { ({l}_{ NCP }-l) } \\ \cos {\delta} \cos { (\alpha -{\alpha}_{NGP}) } =\cos { {\delta}_{NGP} } \sin {b} -\sin { {\delta}_{NGP} } \cos {b} \cos { ({l}_{NGP}-l) }

The “l” is the same as l –I’m just not good enough with LaTeX to make fancy fonts work. I won’t work examples this time because if you saw the equations that I had to type in…well, suffice it to say you wouldn’t want to either.

And that’s a wrap, folks. Do have fun.

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TL;DR: The altitude-azimuth coordinate system, the equatorial coordinate system, and the galactic coordinate system are the three main coordinate systems seen in astronomy. The altitude-azimuth system is based on where you are standing and is measured in degrees. The equatorial system is based on the orientation of the Earth. Longitude (right ascension) is measured in hours, while latitude (declination) is measured in degrees. The galactic coordinate system is based on the orientation of the Milky Way and the Sun, and measures longitude in hours and latitude in degrees. The math for converting is awful—brutally difficult and takes absolutely forever.

Further Reading:

http://spider.seds.org/spider/ScholarX/coords.html

http://www.shodor.org/refdesk/Resources/Applications/AstronomicalCoordinates/

http://www.physics.uc.edu/~sitko/AdvancedAstro2011/1-TheSky/Sky.pdf

https://dept.astro.lsa.umich.edu/ugactivities/Labs/coords/index.html

http://astronomy.swin.edu.au/cosmos/N/North+Galactic+Pole

http://www.physics.uc.edu/~sitko/Fall2002/1-Sky/sky.html

*Credit for information also goes to Carroll/Ostlie.

Light Curves

First, a bit of housekeeping: we apologize for the fact that this week’s post is slightly late, and unfortunately it will also be somewhat shorter, as we have both been insanely busy this week (we fear this will be a recurring theme), but ’tis a post nevertheless.

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Light curves are almost exactly what they sound like — they plot the brightness of an object over time. They’re typically used with all kinds of variable stars, in particular eclipsing binaries, pulsating variables, and supernovae.

If the light curve seems to repeat itself, like these idealized examples, you’ve got some kind of periodic variable. You can determine the period of the star simply by looking at how long it takes the light curve to start repeating a cycle.

Credit: Davison E. Soper at University of Oregon

If it looks something like this, you’ve got yourself an eclipsing binary — the brightness is mostly constant, except for the dips where one star passes in front of the other and blocks some of the light from it.

Eclipsing Binary light curve

Credit: Institute for Astronomy at the University of Hawaii

If it looks like this, then you’ve got a cataclysmic variable star, more specifically, a supernova. Light curves from Type Ia supernovae are particularly important because they can be calibrated as standard candles to let us determine the distance to the exploded star (as for why this is possible, that is a topic for a future post). Furthermore, Type II supernovae are classified based on their light curves, with Type II-P having a “plateau” of relatively constant brightness shortly after maximum magnitude before decaying away, while Type II-L tend to just fade away in a relatively linear fashion.

SN light curves

Credit: University of Oregon

A very useful astronomy tool based off light curves is the O-C diagram, typically used for periodic variable stars. O-C stands for “observed minus calculated”, and (this seems to be another recurring theme today) it’s exactly what it sounds like. First, you look at collected data for a varstar, and then try to create a model that will be able to predict the future behavior of the star. To create an O-C diagram, you plot Time on the x-axis, just like for a light curve, but you subtract your calculated brightness from your observed brightness and plot that on the y-axis.

O-C diagram for AB And

Credit: AANDA (“Starspots and photometric noise on observed minus calculated (O-C) diagrams” by A. Kalimeris, H. Rovithis-Livaniou and P. Rovithis)

If your O-C diagram shows a straight horizontal line at zero, like in the first half of the diagram above, then your model accurately predicts the behavior of the star, and you should pat yourself on the back. However, as always in science, you can be wrong. If the line has a positive slope (like in the second half of the diagram above), then the real period is longer than what you thought it was; if the line has a negative slope, the real period is shorter than your predicted period. And finally, if the O-C diagram shows a curved line, then the period is changing for some reason, which may warrant further investigation. Of course, there are more complicated ways in which you can be wrong, but we won’t address them here, in order to save time and minimize confusion.

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Sources and links for further reading:

Keeping Time in Astronomy

We are sorry this post was so untimely, but you see it was to show how important keeping time is (okay, just bear with us).  Yes, it’s about time for this post!  But why?  That’s because it’s about time of course!  Time is completely derived from watching the motions or being able to see the light of the Sun, Moon, and other objects.  Things can appear slow, fast, or like nothing in terms of time, it’s all relative of course.  In fact to an extent we can say that these clocks have driven us cuckoo!

The basis of time is the SI unit, the second, a special little s that is the only unit that can’t follow our normal SI system of 10.  Where could this even come from?  It used to be one second of minute of one hour of one solar day, therefore being 1/86,400 of a solar day.  Now we can use the wonders of the atomic clock!  The reason is because of all sorts of interference with complex “leap” times; there is even a leap second along with the leap year.  These leap times were done to correct the calendar due to all sorts of errors.  All these factors have led scientists and astronomers to develop many definitions of time.

To start, we have the year.  On average it is about 365.25 days.  So, where does the decimal come from?  To start we have a few different ways to keep time.  Sidereal time, or sidereal motion, looks to the revolution of the Earth with respect to DISTANT STARS.  This comes from observing the sky.  Solar time, also known as synodic motion, is with respect TO THE SUN, it is a daily observation to see when it rotates to get to the same place.  How much of a difference could this make?  Well, the solar day is about 24 hours.  The sidereal day is 23h 56m 4s.  In addition to the slight error, think about how the stars are moving in space.  We are slowing down/speeding up throughout the year, and on the scale of billions of years, or even a few years, these errors can make a fair amount of difference.  To be direct, the motions of the Earth are quite inaccurate.  That alone is reason to develop more accurate time-keeping.  Also, the sidereal year is an orbit around the sun relative to stars, while the tropical year measures between two successive spring equinoxes.  This alone creates a difference of 20 minutes in the year, so  this too builds up over time.

You can see not only is this revolutionary, but it is also timely (from Prof. Richard Pogge, Astronomy 161: An Introduction to Solar System Astronomy, http://www.astronomy.ohio-state.edu/~pogge/Ast161/Unit2/time.html, listed below ).

What would astronomy or science be without have more than a few ways to do something?  There is also standard time.  This was using railroads and telegraphs to standardize time.  It synchronizes clocks of different locations within a time zone not exactly using solar time.  This goes into time zones, dividing the Earth into zones of 15 degrees of longitude.  But this links into Universal Time (UT).  This was used to develop time offsetting from the Prime Meridian.  It was to replace the Greenwich Mean Time (GMT) which had multiple definitions.  UT is technically closer to a Mean Solar Time, with Greenwich as the reference.

But then there is more of course.  Eventually, with all these errors scientists decided that our definitions were a bit faulty.  So, the second was defined again.  The interesting thing about the second is it’s the only unit that isn’t regularly used with multiples of 10.  So, this develops into atomic time.  By using Cesium-133 (this is a specific isotope, but if you get your hands on cesium in general…well, please be responsible/have fun with the explosion) has a specific number of cycles with decay.  This has developed  into the notable atomic clock.

Another type of advanced time keeping is Ephemeris Time (ET), based on observing the motions of the planets and the sun.  ET was briefly used to define the SI second, but it has since been phased out as we have discovered better ways of timekeeping.  Now we’ll return to something nuclear.  Nuclear time involves an H-3 (tritium) isotope that beta decays to He-3.  When tritium reaches its half life a nuclear time elapses.  Next we have something very astronomical: pulsar time, the use of binary pulsars (yes, massive stars rotating around each other) to find periods varying by less than a second because of their relatively definite motion.

Lastly, we have one of the more important astronomy-related methods of keeping time.  These are Julian Dates (JD).  This is a continuous count of days since noon Universal Time on January 1, 4713 BCE (this would be on our everyday Julian calendar).  This may seem quite arbitrary, but the reasoning was that at the time of its development, there were no known historical events before this year, so as to avoid negative dates or BC/BCE/AD.  It also links to solar and lunar cycles.  About 2.5 million days have occurred since then, and it may not seem obvious, but this calculation has to take into account leap years, days, minutes, seconds, and other inaccuracies.  However, it is much more accurate and can better show second differences in data collection.  To make life easier, below we have these formulas:

a=\frac { 14-month }{ 12 } \\ y=year+4800-a\\ m=month+12a-3

For dates in the Gregorian calendar:

\\ JD=day+\frac { 153m+2 }{ 5 } +365y+\frac { y }{ 4 } -\frac { y }{ 100 } +\frac { y }{ 400 } -32045

For dates in the Julian calendar:

\\ JD=day+\frac { 153m+2 }{ 5 } +365y+\frac { y }{ 4 } -32083

Aside from this we should note what a common notation is-J2000.  This is related to epochs, saying that time is starting from the JD on the date January 1, 2000.

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TL;DR

Time can be taken from keeping track of specific stars in the sky, relative to the sun, from atomic clocks and pulsars, or simply by measuring the amount of time from a specific date.  While time may not seem directly important, but a lot of work has been put into this concept.  It is the basis of a large portion of physics and technology.  Astronomy itself benefits immensely from being able to orderly be able to keep track of time for objects.  So next time your clock wakes you up in the morning, remember to not throw it across the room, because it’s just another way of reminding us how important time is.  Also, it means that you should get the heck out of bed or else you’ll be late.

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Sources:

Time in general

http://physics.nist.gov/cuu/Units/second.html 

http://www.astunit.com/astunit_tutorial.php?topic=time

http://www.maa.mhn.de/Scholar/times.html

http://www.maa.clell.de/Scholar/calendar.html

http://www.astronomy.ohio-state.edu/~pogge/Ast161/Unit2/time.html

http://astronomy.nmsu.edu/nicole/teaching/ASTR505/lectures/lecture08/slide08.html

http://curious.astro.cornell.edu/timekeeping.php

http://www.skyandtelescope.com/howto/basics/3304611.htm

http://www.optcorp.com/edu/articleDetailEDU.aspx?aid=2193

Julian Dates

http://aa.usno.navy.mil/data/docs/JulianDate.php

http://scienceworld.wolfram.com/astronomy/JulianDate.html

http://curious.astro.cornell.edu/question.php?number=88

http://www.tondering.dk/claus/cal/julperiod.php#formula