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!  ♥

The Two-Body Problem: Relationships and Physicists

THE PROBLEM OF DUAL CAREER RELATIONSHIPS IN ACADEMIA

One of the more difficult things about being a physicist in a relationship is that your partner is usually also a professional in a technical field as well.  Working in specialized fields make finding jobs in the same location as your partner difficult.  So many of us have experienced these issues that we have a special name assigned to it - the two-body problem (re-purposing the phrase referring  to the physics of two masses interacting, say in orbit).

The problem isn't about finding work, but finding work working in our specialties.  For example, I am a skilled physics educator and every college and university teaches physics at some level so there are job opportunities for me in that respect.  Of course, these jobs are still very competitive to earn, but you get the idea that there is work out there.  But many of these jobs would likely be strictly or mostly teaching without much in the way of research opportunities.  I could be employed but I would likely not be able to continue my LIGO research which is important to me.  There are about 80 institutions from across the country and around the world that work in the LIGO Scientific Collaboration (click here for a list of these institutions).  While this sounds like many, the odds of not only landing a job at one of these institutions and having fulfilling job prospects for a spouse isn't great.

My two-body problem was made official in 2003.

MY TWO-BODY PROBLEM

This is usually most difficult for us academics as we finish our degrees (or when an appointment ends if the relationship started when not a student - mine did so this is what I reference).  For me, it was especially stressful since I finished my doctorate before my husband finished his.  My solution to the two-body problem: take a mini retirement.  He was supposed to graduate next semester so I figured that I would wait for him.  Besides, after writing my dissertation, I was quite burned out on research.  Well, next semester turned into the next next semester and I started to quickly lose my mind as I wasn't nearly as burned out as I thought.  I had a small contract teaching job at Penn State, but it was something that I had been doing for years as a graduate student and it wasn't challenging or time consuming.  Then I discovered vampire books and decided to do a normal person job for fun (almost all of my work previously has been in academia).  One of my students gave me tips on where to apply for a waitressing  job.  I was looking for something in the evening, like in a bar, but I ended up with breakfast/lunch service at a hotel restaurant.  Except for the very early start time (I had to be there for 6 AM, which I know isn't that early, but doesn't exist in my universe), I loved the work!  I met lots of new people and none of them treated me like I was odd because I was a physicist (since they didn't know).  This did come at a potentially steep cost professionally since effectively being out of the field for nearly a year (like I was) is usually career suicide.

Finally, there came a job I was willing to suffer a long distance relationship for - the one I have right now.  It was pure serendipity that they were also hiring engineers with my husband's skills at the same time.  We both got jobs and we are both happily employed at LIGO now.  This is EXTREMELY rare.

Now my concern is maintaining the ability to sleep under the same roof with my husband in the future.  My job here is a postdoctoral scholar is temporary, much like a medical doctor's residency.  I've been at this job for almost 5 years now (I did get promoted to senior postdoctoral scholar after my third year) which is a long time to be a postdoc at the same place.  That's not to say that it's unusual to have several postdoc appointments at different places for more than 5 years.

What to do now?  Well, I am trying to work out a new position but I don't want to jinx by talking about it here now.  This solution would let me stay put but definitely mix things up a bit for me.  Fingers crossed!

THE TWO-BODY PROBLEMS OF MY MENTORS

To give you an idea of how lucky I am to live with my husband through our transition from student to scientist, I've had two advisors on my way to getting my Ph.D. who both had extended long-distance relationships due to the two-body problem.  The first was Gabriela Gonzalez who left Penn State to go with her husband (also at Penn State) to LSU where he was offered a prestigious position and she would be able to work much closer to LIGO.  Before they found the Penn State (and then LSU) solution to their two-body problem, they worked for about 6 years hours apart from each other (you can read about their story here - you may need to register, but it's free).  When I turned down the opportunity to go to LSU with her (due to my own relationship), I then worked for Sam Finn at Penn State.  He and his wife also spent about a decade apart before they found their solution.

Conclusion, I am lucky beyond belief to not only have a job that I love but to have the one I love with me as well.

Read More:

A Dual Dilemma  (NatureJobs.com)
Is the Husband Going to be a Problem?  (New York Times)
Women in Academia: The Two Body Problem  (Persephone Magazine)

What I Do When I'm Not Working (and an Anniversary)

Most of the posts I've made to this blog have been almost exclusively about my work even though I want this blog to be about my life, both the scientific and the mundane. 
This passed Thursday, I only worked a half day (I've been working more 6 day weeks than not for a while now) since I had a moderate migraine.  This one wasn't bad as far as all of the headaches I've had in my life, but it was more than enough to make light hurt my eyes and make me want to curl up in bed until it goes away.  So, I took care of the work that had to be done that day (like another conference call) and spent the rest of the day tending to my migraine.  This amounted to the first decent amount of down time I've had in a while.  While I wouldn't wish migraines on anyone, I am sort of glad I have mine since they force me to stop and relax from time to time (they also can hit at times when I simply can't put my life on pause and that is when I curse them).

So, what did I do with my time?  Well, first you have to know a little bit about me...  If I had 3 words to describe myself, they would be 1) physicist, 2) vampires and 3) Halloween.  I adore vampires and have read almost 200 vampire books in the last 4 years.  I also like to get the audiobook versions of books I've already read and liked to go to sleep to; if I have already read them, I won't keep my self awake to find out what happens next.  Since my eyes hurt me too much to read, I rested in bed and listened to my favorite books while I waited for my medication to take effect.  After about 2 hours of this, I felt a little better and proceeded to read a little.

This weekend was Halloween and I ADORE the holiday.  I love all of the dark fun and the idea of getting to be someone else for an evening.  I'm not one to dress up, but since I love vampire books, it is fun to think about what the world would be like if things that went bump in the night were real.

To celebrate, my husband and I went on the haunted trail at the Cajun Country Corn Maze.  (Tip:  If you go around this time of year, just go for the haunted trail since there is no line for this - there was a line almost an 500 feet long just for the maze.  Come back later in November to do the maze.)  Below is me in the pillory at the corn maze.  I think it is just scary how washed out my face looks with a camera flash:

I also love autumn in general!  So much so, that my wedding was autumn themed the day after Halloween.  That's right, today is Derek's and my anniversary!  To celebrate, here is a picture of us just after the ceremony: