Here's Your Chance to Help LISA Happen!

A depiction of a LISA satellite with its lasers.

I've written about LISA several times on this blog and most of those times the news hasn't been good.  Today I have a bit of encouraging news and a way for you to help!

For readers who've recently found Living LIGO, LISA is a space-based gravitational wave detector that will be sensitive to lower frequency gravitational waves than any Earth-based counterpart ever will be.  Gathering gravitational-wave information from low frequencies will help complete the picture that gravitational-wave astronomy can paint; Earth-based detectors are really only sensitive to the "death throes" of violent astrophysical interactions while LISA will be sensitive to these same sources in their youth.  This youth stage is so long that the predominant noise source for LISA is continually measuring the gravitational waves from these young sources coming from all over the sky at the same time.  This is called the "confusion limit" and it is like trying to listen to a conversation on the other side of the room at a busy party.  This can be overcome, but what a wonderful problem to have! The noise you measure is really just measuring so many gravitational waves at the same time that they mix together!

You can follow the unfolding of the LISA drama through these Living LIGO posts:

• News on LISA  [25 May 2012]
• More on LISA/NGO  [3 May 2012]
• The Likely End to a Space-Based GW Detector  [19 April 2012]  (The title turned out to be over dramatic - I'm glad!)

In the "News on LISA" (25 May 2012) post, the statement from the eLISA Consortium was that they were going to push for the next launch opportunity.  The European Space Agency has initiated the process to choose candidate missions for the next launch.  The eLISA mission team is looking for your support! 


HOW YOU CAN HELP...

Please go to the eLISA - Make History page and sign your name as a supporter.  Anyone from around the would can lend their support.  If you are a scientist, you can also opt to have your name and institution listed in the eLISA white paper.  (You can see the ESA's call for white papers here.)

If you support gravitational-wave science at any level, please consider putting your name on the list!  Let's show the world that there is true support for this science!

HURRY!  There are only 2 days (or less) to add your name to the list of supporters! 
eLISA - Make History

NEW LISA YOUTUBE CHANNEL

The LISA Mission has also created their own YouTube channel and is starting to post some truly exceptional animated educational videos.  Right now, two are available:

Gravity Ink. - Einstein's Gravity (Episode 1)

Gravity Ink. - The Future of Astronomy (Episode 2)

Consider subscribing to their YouTube channel to keep up on new installments (I will most likely feature them here too!). 

Black Holes 101

Most of what I discuss on this blog has to do directly with gravitational waves.  This time I'd like to talk about one of their most talked about exotic sources: black holes.  Black holes are an exemplary source because they are highly concentrated mass.  Just add a touch of accelerated motion and gravitational waves are emitted in abundance (well, it's not quite that simple and "abundance" is a relative term, but you get the idea).  But what are the fundamental concepts that add up to the existence of black holes?  That's what we are focusing on now.


1.  Escape velocity

You've probably noticed that the harder you throw an ball straight up in the air, the higher it goes.  We also know that the farther away the ball gets from the Earth, the lower the gravitational attraction is between the ball and the Earth.  When you connect these two concepts, you can imagine that there is a speed at which you can throw the ball up and it will never come back down.  This is called the escape velocity:

We have discussed escape velocity before on this blog (specifically when discussing the conditions an object must have to be 'eaten' by a black hole).  In this equation, G is the gravitational constant, M is the mass of the 'thing' you are trying to escape, and r is the distance you are from the center of the 'thing'.  The bigger the mass of the 'thing', M, is, the faster the object must be thrown to escape it, v_e.

Going back to throwing a ball up in the air from the Earth's surface, you would need to throw that ball about 25,000 mph so that the ball would not come back to the Earth (good luck with that)!


2.  The speed of light is the universal 'speed limit'

Nothing can travel faster than the speed of light (in a vacuum), represented by c.  No matter, energy, or information about the Universe can travel faster than that.  That is pretty much the long and the short of this concept.

[Source: Knight Science Journalism at MIT blog]

This 'speed limit' comes from Einstein's special relativity and the effect of simultaneity.  Perhaps I will write a longer post about this in the future, but all that is important now is to recognize that if something needed to travel faster than the speed of light to communicate information to you, then you are never going to know about it.


3.  Light is affected by gravity

Light is both a particle and a wave.  As a particle, it has no mass.  Since gravity acts between two masses, it may be surprising that light can be affected by gravity at all!  But it does.  This effect is called gravitational lensing and I've written about this previously here. 


CONCLUSION:  How these concepts form a black hole

The simplest black hole is called a Schwarzschild black hole.  This is a black hole that has no electrical charge and is not rotating - it's just "there" meaning that there won't be anything to complicate our black hole situation.  For now, let us think of our black hole as having mass but no volume.  You can think of this as being the ultimate implosion.  Since this mass has no volume, there isn't any surface to it.  Eventually, as we get closer and closer to where the mass is centered, the escape velocity will become so large that the escape velocity will be greater than the speed of light.  And since light is indeed affected by gravity, that means that nothing will be able to escape the black hole.  We can even figure out what this distance is from the equation for escape velocity by setting v_e to the speed of light, c, and solving for r (the distance away from the mass where the escape velocity equals the speed of light):

This distance from a black hole where light will not be able to emerge from a black hole is also called the event horizon and this sphere around the black hole is what is being referred to when we talk about the size of the back hole.  For this simple Schwarzschild black hole, it is also known as the Schwarzschild radius.  You can also think of this radius as how small a mass would have to be to become a black hole.

So, how big would the Schwarzschild radius be for some things we are familiar with?  Well, for a black hole with the mass of our Sun it would be just about 3 km or about 1.9 miles.  For a black hole with the mass of the Earth it would be 8.87 mm or a little under 11/32" (0.349 in).

Lessons From My Childhood on How to Teach

One of the best parts of my job is getting to do outreach.  This is going out and teaching the public about the research that I do.  Since I love what I do and those that I encounter are usually interested in what I have to say or they wouldn't be there (like you wouldn't be reading this if you didn't want to), it is almost always a rewarding experience all around.  However, I had some childhood experiences with outreach that were, well, a little traumatic.  However, they have taught me lessons that I use every time I teach whether in the classroom, engaging the public at LIGO, or writing for you.

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"HAIR-RAISING" TRAUMA

Ever since I was a young child, I've always known that where I am now is where I wanted to be.  That is, I've always known that I wanted to be a physicist or an astronomer.  Of course, that's not what I said; I wanted to be an astronaut since that is the hero job for the physical sciences.  My family has also been supportive of me and one of my favorite things to do was go to the planetarium.  At the time, I lived outside of Pittsburgh, PA and we would go to the Buhl Planetarium (before it became part of the newer Carnegie Science Center - the building is now part of the Children's Museum of Pittsburgh).

Front entrance of the Buhl Planetarium in Pittsburgh, PA. [Source: Wikipedia]

On the fateful trip in question, I was no more than 7 or 8 years old and I was watching a demonstration in between planetarium shows with my father.  The presenter asked for a volunteer from the crowd, preferably with long fine hair.  The next thing I felt is my father's hand on my back pushing me forward.  I wasn't interested in being the center of attention, but the presenter thought that I would be perfect for the role.

She called me forward and had me stand on a plastic milk crate beside a metal dome that was bigger than my head.  She told me that I was going to have to hold on the the metal dome with one hand but I was not to do a list of things or I would get hurt.  Then I was worried.  She had me put one hand on the dome and turned the machine on.  It made a lot noise and I feel an odd tingling over my skin.  Then I was scared.  The presenter was very happy about everything and told me to shake my head.  I did so timidly.  Then she encouraged me to shake my head with more vigor.  I shook the heck out of my head so she would leave me alone and I could be done with all of this.  Then EVERYONE who is watching this demonstration WAS LAUGHING AT ME.  Then they applauded as the machine was turned off and I was helped down from my perch and left to think I was being laughed at.

The machine with the big metal dome attached to the top.  I later discovered that this is a Van de Graaff generator.  [Source: UMN Physics department]

It wasn't until I was in middle school that I figured out why everyone was laughing at me.  That machine was a Van de Graaff generator and it deposited static electricity on me.  The warnings that worried me were to prevent me from getting "zapped" and everyone was laughing at me because my hair was standing on end.  The harder I shook my head, the more the static electricity made my hair stand out.  A lot like this:

WHAT WENT WRONG?:  The presenter didn't show me what I looked like in a mirror (as is featured in the clip above) or tell me what I looked like.  I had no idea why everyone was laughing at me or what the point of the "hair raising" demonstration was.  Without this knowledge, I walked away from the experience thinking that everyone was really laughing at ME and not the effects of static electricity.

LESSON LEARNED:  If you use a volunteer in a demonstration, make sure that they understand what is happening.

I don't have many occasions where I need a volunteer for a demonstration, but when I do I make the volunteer the focus of the demonstration so that, at the very least, they walk away understanding what happened. 

Read more about how Van de Graaff generators work.

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SWINGING FOR A "BREAKTHROUGH"

When I was too young for school, I wanted to be a big girl and play school.  Even then I loved science.  One day I convinced my father to play school with me.  Using the sliding green chalk board doors on my toy box, my father taught me about the layers of the Earth.

A toy box much like the one my father used to play school with me.  [Source: It's Still Life blog]

The Earth's layers can be generalized into 4 main layers: the crust at the surface where we live, then the mantle, and finally the outer and inner cores.

Diagram showing the layers of the Earth.  [Source: About Earth blog]

I was told that the crust was very thin and the mantle is hot molten rock (magma) [note: only the mantle near the outer core is molten but the mantle under the crust is about 1000^oF so I equated that to "molten" too as a child].  I'd seen documentaries about volcanoes on television and knew what "molten rock" meant.  This completely changed the way I saw the swing set in my back yard.  Why?  Well, have you noticed the divot under the swings where you drag your feet to slow the swing to a stop?  I saw that as eating away at the crust and I was afraid that I would break through to the mantle and sink my feet into molten rock!  I know that it really isn't logical since I'd seen deeper holes before and there was nothing but dirt at the bottom, but I was a little kid and didn't think like that.  Anyway, I then was afraid of breaking through the crust if I dragged my feet and I was too chicken to jump off.  That left me sitting on the swing waiting for it to slow down on its own.  The wait took a lot of the fun out of swinging!

WHAT WENT WRONG?:  The scale of "thick" and "thin" was not established.  When I heard that the crust was thin, I defined for myself what "thin" was.  I assumed it was only as deep as I could dig through it.  What "thin" really meant is compared to the size (radius) of the Earth.

For the record, the radius of the Earth is almost 4,000 miles and the crust is up to about 22 miles.  Since 22 miles is much, much less than 4,000 miles, the crust is indeed "thin" compared to the size of the Earth!

LESSON LEARNED:  When you tell someone that something is "big" or "small", make sure you establish what you are comparing that something to, i.e. make sure you set the scale for your comparison.

I sometimes tell this story after I admonish people to always ask a scientist how big or small they think "big" or "small" are.  I tell them that I think a "big" gravitational wave, one that we would only expect to see every 10 years or so, would change the length of LIGO's 4 km (2.5 mile) long arms less than 1/1000^th the diameter of a proton (10^-18 m).   That may be "big" to me now, but to a 5-year-old me something smaller than an atom would be most certainly be considered "small". 

Q: What's the Difference Between a "Gravitational Wave" and a "Gravity Wave"?

The things that LIGO looks for are called gravitational waves (which are discussed in depth here on my blog and on the LIGO website).  That can be a mouthful, especially when having a conversation about them.  People, including us professionals, realize this and often take the shortcut of calling them "gravity waves".  It sounds so similar that this must mean the same thing, right?  Well, no!


GRAVITY WAVES ARE NOT GRAVITATIONAL WAVES

The proper technical use of gravity wave refers to waves on the interface of two fluids, which can be liquid and/or gas.  Where this boundary is disturbed, gravity will pull it down and buoyancy will push it up.  This combination of opposite push and pull creates a wave that moves out over the surface.  You can make your own interface of two fluids by filling a glass with some water and oil:

A glass containing oil and water.  Oil settles at the top because it is less dense (more buoyant).  [Source: Wikipedia]

Water and oil will separate if left alone.  This separation creates a boundary between the oil and water with the oil on top since it is less dense.  Now imagine gently tapping on the side of the glass.  The vibration from your tap will transfer into the separated oil and water which will produce a gravity wave on their boundary.  If you actually do this carefully enough, you can produce a gravity wave ONLY on the oil/water boundary and not on the surface of the oil (though a surface wave on the oil is technically a gravity wave too since that is a liquid/gas fluid boundary).

While the oil and water example technically illustrates a gravity wave, the term is usually applied to gravity waves that occur in nature.  Examples include:

• The waves on water caused by wind from large ocean waves to ripples in a puddle; these are examples of gravity waves on an gas/liquid boundary.  
• Waves of different density waters under the oceans' surface (like warm/cool water, or fresh/salt water); these are examples of a liquid/liquid boundary.
• The rippling of clouds, like in the movie below; this is an example of a gravity wave on a gas/gas boundary.

CAN A GRAVITATIONAL WAVE DETECTOR DETECT GRAVITY WAVES TOO?

We've now established that a gravity wave is very different from the gravitational waves that LIGO is looking for.  But can LIGO detect them anyway?  Indirectly, yes!  Almost three-quarters of the Earth is covered by oceans.  These oceans are roiling with gravity waves both within the water and on top of it.  When these waves encounter solid earth, much of the wave is reflected but some of the energy is absorbed.  This absorbed energy can then create surface waves on the remaining part of the Earth's surface that is solid.  These ground vibrations are called microseism.

Since LIGO lives on the Earth's surface (many people think that LIGO is underground but it really is built above ground), these vibrations shake the detector and contribute to the measured detector noise.  So much so that, compared to the gravitational waves we seek, we don't expect to be able to detect low frequency (less than about 10 Hz or so) gravitational waves.  And it doesn't matter that both LIGO detectors are near shores since the microseism shakes the entire Earth - we could have built LIGO in the middle of Nebraska and the microseism would still negatively affect us. 

In order to detect low frequency gravitational waves, we need to get away from the microseism.  The proposed gravitational wave detector that can do this is the space-based eLISA satellites.  (I've also discussed eLISA and associated drama on this blog previously.)  eLISA would be exclusively sensitive to low frequency gravitational wave and would compliment LIGO well: there are many young systems producing low frequency gravitational waves all the time while there are few producing the high frequency death throes that LIGO can detect.  Together, LIGO and eLISA will provide a more complete gravitational-wave picture of the life cycle of some of the most energetic, violent objects in the Universe.


CONCLUSION

"Gravitational waves" and "gravity waves" are very different entities.  However, you may hear us refer to a gravitational wave as a "gravity wave".  This is a personal pet peeve of mine (can't you tell?).  While I work hard to use the term "gravitational wave" correctly, I am often hesitant to say anything to colleagues I hear using "gravity wave" instead.  Watch the NSF documentary Einstein's Messengers (also on the "Viewing Fun" page on this blog) and you will see some highly respected LIGO scientists refer to "gravity waves"; it makes me cringe a little every time but I'm not one to gainsay my betters.  Now that you've read this, you'll know what we really mean ;)


Read more:

• Another explanation of the difference between gravitational waves and gravity waves (this is correct but a little outdated on its discussion of gravitational waves)

SNEWS and LIGO: Neutrinos Tell of Possible Gravitational Wave

When I start off a tour at the LIGO Observatory, I usually start by talking about how gravitational waves will open a new window to view the Universe.  I've done this so many times that I have the talking point pretty much memorized:

"Up until recently, we've only been able to observe the Universe using light and its different forms.  Visible light, X-rays, and microwaves are just a few different kinds of light and every time we have looked at the Universe in a new way, we discovered something unexpected that revolutionized our understanding of the Universe.

Well, light has the inconvenient property of being fairly easily absorbed or reflected away from its path.  However, the Universe is transparent to gravitational waves; meaning that they can go through matter and come out the other side unchanged.  There is no such thing as a gravitational-wave shadow!"

Note that I start by saying that until recently all of astronomy has used light as its tool.  This is because there is another medium that has been used: neutrinos.  I've talked a bit about neutrinos previously here, namely when I discussed the debunking of the "faster-than-light neutrino" claim last year and how neutrinos are used in multi-messenger astronomy.  Quoting the important part from the multi-messenger astronomy post:

"Today, we can do astronomy with means other than light.  For example, neutrinos.  These are subatomic particles that have no electric charge, have nearly no mass, travel very near the speed of light and are able to pass through matter almost undisturbed.  However, these properties add up to make it very hard to detect neutrinos (did you know that there are billions of neutrinos from the Sun passing through your body every second?!).  Neutrinos are also emitted when a star dies in an explosion called a supernova.  That means we may observe the optical burst of light AND the neutrinos from a single supernova.  Any time that you can observe the same event in multiple ways, you almost always learn more than if you only observed it one way."

- 14 October 2010

What I didn't go into is that LIGO is working to detect gravitational waves from a supernova as well.  While we can do this without complementary detections from traditional and neutrino observatories, having that information from them will make it easier for us to find the signal buried under the detector noise that dominates what LIGO records.  This is done through the Supernova Early Warning System (SNEWS).

SNEWS

Yes, this is pronounced just like you pronounce "snooze".  A SNEWS alert is sent out shortly after neutrinos from a supernova (as opposed to neutrinos from the Sun) are detected.  Since neutrinos and travel through matter with very little disturbance just like gravitational waves, that means that if we saw neutrinos, there is also a good chance that we may see the gravitational waves from that event.  Even more compelling for us in the gravitational wave community is that SNEWS only really expects to see neutrinos from a supernova if it came from within the Milky Way galaxy (or the Magellanic Clouds that are two small galaxies that orbit the Milky Way).  As far as gravitational waves are concerned, that is in our own backyard so any accompanying gravitational waves would likely be large enough for us to detect!   (When searching for gravitational waves in general, we expect that almost all of our sources will come from galaxies outside of the Milky Way.)


EARLY WARNING SYSTEM?

The reason that the detection of neutrinos is considered an "early warning system" for a supernova is that the processes that produce these neutrinos happen hours to days before the optical explosion that traditional observatories would be able to see.  The supernova explosion occurs after the mass of the star collapses in on itself; this is called a core collapse.  Neutrinos are normally produced by the nuclear fusions inside the star (our Sun produces MANY all the time), but during the core collapse many more are produced (it is estimated that over 90% of the energy in the collapse is expended as neutrinos).  It is also during the core collapse, when so much of the star's mass is in motion, that gravitational waves are produced.  If there is a SNEWS alert, that means that there is a higher probability of a gravitational wave detection at that time.


WHAT HAPPENS AT LIGO DURING A SNEWS ALERT?

First off, let me say that there has not been a SNEWS alert yet since these supernovae in our galaxy are rare (they happen about every 50 years or so that we are aware of).  But if a SNEWS alert comes through while LIGO is looking for gravitational waves, the protocol is quite simple: don't do anything that would cause the quality of the data to be degraded.  More specifically, don't create vibrations.  Don't walk close to the detector (your footsteps appear to be little earthquakes to the detector), don't leave the site in an automobile (any acceleration by that a car or larger vehicle will create a little wave in the ground that will affect the detector).  This has brought up the question of what to do with the FedEx guy if he is on site making a delivery...  While we cannot hold anyone against their will, I am sure that he would be asked to stick around for a while. 

This may sound a little harsh, but considering the rarity of these events and what is to be gained, sitting around isn't all that bad!


WHAT IS TO BE GAINED?

First, to the traditional astronomy community (telescopes detecting light), it is exceedingly rare to see a supernova from its beginning and doing so can tell astronomers more about what kind of supernova it is (see this Wikipedia page for more information about the different types of supernovae).

Also, if the gravitational waves from the core collapse of a star were to be detected, this will allow us to "see" what went on inside the star - something that can never be done with traditional astronomy.  Knowing what goes on inside the star will allow us to use the dying star as a nuclear reactor unlike any we could ever create on Earth.  This may be able to tell us more about nuclear physics which could have implications for technology in the future (I have no idea what those may be).


NEUTRINOS AND SUPERNOVA IN THE PAST

So far, there are only two detected sources of neutrinos other than those produced by nuclear reactions on Earth: those from the Sun and those from the supernova known as SN 1987A.

NASA image of 1987A supernova remnant near the center.  Inset: a close up of the supernova  [Source: Wikipedia]

SN 1987A happened on 23 February 1987 (hence the name) and was located in the (relatively) nearby Large Magellanic Cloud and could be seen from the Southern Hemisphere.  About 2-3 hours before the star exploded (as seen from Earth), neutrinos were detected at 3 different neutrino detectors.  This detection not only was the birth of neutrino astronomy, but also allowed for the early observation of the light from the supernova.

Also, this supernova is thought by some to be the instigator of the LIGO concept.  This was when Joseph Weber made his claims of the first detection of gravitational waves (which was debunked - but that is a discussion for another blog post).  Weber used a method of looking for gravitational waves called a resonant bar gravitational-wave detector (a.k.a. Weber Bar).  Even though there wasn't a gravitational-wave detection, his claims and SN 1987A made scientists begin to consider other way to look for gravitational waves and that the technology needed was within reach.  So, that February day in 1987 was also the birth of LIGO in a way!

Happy New Year!

I can't believe how long it's been since I've last blogged - I've had so many ideas of stories to post, but I've also had some life issues that have kept me away.  Not to worry!  My most important resolution for 2013 is to write blog posts a few weeks ahead of time so that I can still post weekly even when life gets in the way.  I will be back in full force in 2013!  Expect posts on Thursdays, unless there is something timely I want to share before then.  I will make sure to post on Twitter when I a new post is available so if you don't follow me already, please follow @livingligo.

This is a smiley face the deicing crew at the Pittsburgh International Airport made in the snow.  As seen through the deicing fluid on the window of my plane on the evening of 29 December 2012.

2012

This year has been a year of many changes for me.  My days as a postdoc have come to an end and I now hold a dual position with Caltech as a scientist at the LIGO Livingston Observatory and as a physics instructor at LSU.  It is great being back in the classroom but that is also something that has kept me from posting as much as I would like.  It takes a lot of time to create interesting lectures for a class of 150 students and handle all of the class administration myself (office hours, grading, etc.).  This semester I am teaching the second semester of physical science (astronomy, chemistry, earth science) and will only have a 30 students.  I am very excited about the more personal instruction I will be able to do!

There have also been many changes at LIGO.  When I first started working at the Livingston observatory in 2007, there were about 25-30 people who worked there on a daily basis.  Starting with the Advanced LIGO preparations in 2010, we nearly doubled the number of daily staff.  Since the installation is well underway, we no longer need to have so many people on site (having too many people on site while we are looking for gravitational waves will cause ground vibrations that will decrease our sensitivity).  The parking lots are noticeably less full and it is starting to feel a little lonely even though we still have more people working on site than when I started.

As far as my personal life is concerned, I'm glad that 2012 is over.  It has been full of drama and uncertainty and it is one of the things that have been getting in the way of keeping up with this blog and my career in general.  But I wouldn't change a moment of it since I have so many great people around me, at home and at work, who care for me. 


2013

This coming year will prove to be exciting!  The installation of Advanced LIGO should be completed and the first commissioning (use of the detector to fine tune it to its best sensitivity) started.  This is always an interesting time when you get to use the detector for the first time and solve novel problems.  I will be sure to tell you all about them here! 

I will also continue teaching at LSU.  As I mentioned above, I will be teaching the second semester of physical science with about 30 students.  I also expect to teach a masters degree class on inquiry learning for in-service teachers this summer (I've done this class twice before with LSU).  

Of course, the most exciting events are usually the unexpected.  I look forward to sharing the professional and personal excitement with you here.

Thank you to all of my readers, followers on Twitter, and those who found me through a search engine!  Keep coming back for more!

What are you looking forward to this year?

Gravity - The Love Story II: Starstruck!

So, where was I when I last posted...  Ahh... The great corny love story between two objects bound together by gravity.  I started that post asking what would happen to the Earth if the Sun were to suddenly become a black hole.  Many people think that the Earth would be sucked in because they assume that a black hole will suck everything into it like water going down a drain.  But, from careful examination of the universal law of gravitation and the story it tells, we see that isn't the case and the Earth will stay in the same orbit that is it now - no closer and no farther away.

But what about an object flying by a black hole (or any other massive object) instead of being in a nice stable orbit (like the Earth is in the previous example)?  This makes things a little more complicated, so I am going to let go of telling a love story.  That being said, there will be more equations here, but like the previous love story post the equations will only serve to help tell the story and we will not be using any numbers.


THE FATE OF A COSMIC WANDERER

Instead of looking at the universal gravitation law, we are going to look at how a passing object comes to be in orbit, or not, around another object (this governed by Kepler's laws of planetary motion).  To keep things simple, let's assume that the moving object has much, much less mass than the object it's passing (this is so that we can ignore the motion of the big object due to its gravitational attraction to the passing object).  Basically, picture something small whizzing through space (I'll call this the small object) that passes by a star or black hole (I'll call this the big object).  It is now safe to assume that any motion caused by gravity is going to be seen in the small object.


IT'S ALL ABOUT THE SPEED

The one factor that completely determines the fate of the small object is its speed.  If this speed is great enough, then the small object will be able to escape the big object, though its speed and direction will have changed.  The minimum speed at which the small object will not be captured into an orbit is called the escape velocity:

Here, we see that the escape velocity, v_e, changes as the square root of 1/distance (1/r) between the objects' centers.  That means that the closer the small object is to the big object, the more speed it must have in order not to get caught by it; the farther away, the less speed it needs to escape.  2GM is a constant value and never changes; G being the universal gravitational constant and M being the mass of our big object.


ORBITS AND ELLIPSES

Any speed less than the escape speed and the small object will be captured by the big object and will likely start orbiting the big object (or collide with it, we'll get to that later).  Let's say that we are traveling at a speed less than the escape velocity.  Kepler's laws of planetary motion (which are a consequence of gravitation) provide that the shape of the orbit is an ellipse (an oval shape).  Instead of having one center like a circle does, an ellipse has 2 each called a focus.  A classic way to draw an ellipse for yourself is to put two pins into a piece of paper, put a loop of string around the pins, place a pen in the loop and pull the loop taut.  The shape that you draw doing this is an ellipse:

[Image from: Wikipedia]

Here, each pin is a focus.  This is what having 2 "centers" means - if you were to draw a shape using this same method but using only one pin, then you would draw a circle (the pin being the true center).  When talking about an orbit of a very massive object and much smaller object (like we have in this example, or like the Earth orbiting the Sun), the more massive object will be located at a focus and there isn't anything at the other focus.

The speed of the object determines the shape of orbit:

Here v is the speed of the orbiting object (which is less than the escape velocity), μ is a constant (G times the mass of the big object), r is the distance from the objects' centers when the velocity is measured, and a is the semi-major axis of the ellipse (the distance between the midpoint of the foci and the farthest point of the ellipse). 

[Image from: Wikipedia]

STARSTRUCK!

Under what conditions does the small object collide with the big object?  So far it sounds like the small object is either going to escape the gravitational pull of the big object or start orbiting it.  Can a black hole (assuming it's our big object) ever "swallow" anything?  Yes, indeed, but only under certain conditions...

To determine the conditions for an object to be swallowed by a black hole or collide with a star, we need to realize that neither of these objects is a nice point as we have been treating them (well, the singularity inside the black hole is a nice point, but more on that below).  Instead, objects occupy a volume and the points we were considering were really the center of mass of the object (approximately the actual center for a spherical object).  So, the small object will collide with the big object if the radius of the big object is more than the distance of closest approach of the small object's orbit.  This distance is called periapsis and is the distance along the red line (the semi-major axis) between the ellipse (orbit) and the focus (the big object) in the previous figure.  If a star has a radius of this or more, then the small object will slam into it.

NOTE:  This scenario for collision (and the one for merger with a black hole below) assumes that the objects only interact through gravity.  That means that there is no consideration here for other forces like the interactions of the objects' magnetic fields (if they have them) or resistance from the matter and radiation that stars tend to spew out.


HUNGRY, HUNGRY, BLACK HOLES

But what about the specific case of a black hole?  I mention that there is a point-like singularity in the black hole where all the mass is located.  How do we determine the shape of the whole black hole?  First, consider why a black hole is called "black"; because the gravity inside of it is so strong that the speed of light is less than the escape velocity (now you can think of our small object as a photon of light).  Since nothing can travel faster than the speed of light, nothing can escape a black hole.  So we define the edges of the black hole to be the radius at which the escape velocity equals the speed of light.  This radius is called the event horizon.  Therefore, an object (even a photon) will merge with a black hole when the distance of closest approach of its orbit is equal to or less than the event horizon.

Now that's what I call "starstruck" lovers!  Get it?  The small object strikes the big object which could be a star...  Okay, I know it's lame, but that's why I'm a physicist and not a comedian (though I do try!).

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♥  Speaking of love, happy anniversary to my husband, Derek, who is always nice enough to proofread these posts.  We've been together for 16 years, married for 9 and looking forward to many more!  ♥