Lunar orbital dynamics

 

 

Student:    Hey professor, I am wondering something about the Moon.  I mean, I know that the Moon moves, but I never seem to see it move in the sky?  But then again, I’ve seen it in everywhere in the sky at some point or another.  It’s almost like the Moon moves when I’m not looking.  And another thought I’ve had on this subject is that sometimes the Moon follows me, or so it seems.

Professor:  Well, you’ve really opened up a can of worms – tell me more about how the Moon seems to follow you.

Student:    Um, well, the other night I was driving down Memphis street and the houses and trees that line the street were whizzing past me as I drove, but no matter how far I drove down Memphis street, the Moon was always there in the sky – it was like I couldn’t get away from it.  It almost seemed as though the Moon was following me, even though I know that’s ridiculous.

Professor:  No, it’s not ridiculous.  What you’re describing is part of a phenomenon that we call parallax.  Let’s say that you’re driving down Memphis street, and that you’re driving away from 19^th street and towards 34^th street.  Because 19^th street is only a half-mile behind you, you probably have no problem observing the stoplight at 19^th street get further and further away from you.  The same goes for the stoplight at 34^th street that you’re heading towards – it’s only ¾ of a mile ahead of you, so it gets bigger and bigger even if you only get 200 or 300 yards closer to it.  But the Moon is tens of thousands of miles away – getting 100 yards closer to or even 4 or 5 miles closer to it doesn’t make the Moon appear to get noticeably bigger or smaller.  The distances that you are traveling down Memphis street aren’t very significant in comparison with the tens of thousands of miles between you and the Moon.

Student:    Oh, I see.  I guess it’s like an airplane flying in the sky.  It’s flying at 300 miles per hour, but because it’s so far away, it doesn’t seem like it’s actually moving that fast.

Professor:  Exactly – that’s another example of parallax.

Student:    So, I do know that the Moon moves in its orbit around the Earth – but I never see this happen in front of me.

Professor:  There again, that’s because the Moon is so far away.  It is actually hurdling through space around the Earth at over ½ mile per second – quite fast.  But just like the airplane, the Moon is so far away that the human eye cannot discern this movement.

Student:    Well, the other night, I came out just after dark and the Moon was in the east, but later that evening the Moon was in the west.  How did it move like that without me noticing it?

Professor:  The Moon (and the stars too, for that matter) all rise in the east and set in the west every night, just like the Sun does – and for the same reason that the Sun does.

Student:    Oh, yeah, that’s because the Earth is rotating.

Professor:  Right.  So the Moon rises and sets just like the Sun does because of the Earth’s rotation.  This would happen even if the Moon were holding a stationary position in space. 

Student:    But sometimes I see the Moon out in the middle of the day.  I thought the Moon only came out at night.

Professor:  The Moon is generally not visible during the day, but sometimes it can be seen in the day if the Moon is in the right place in its orbit.

Student:    How can that be?

Professor:  It might be easier if I draw a diagram for you.

 

                In this diagram, the person standing where the square is on the surface of the Earth would be able to see the Moon, even though he is on the day side of the Earth.

Student:    Oh, so I suppose that I could also see it during the day if it were straight up in the sky like this:

 

Professor:  Actually, no.  If the Moon were in that part of its orbit, you wouldn’t be able to see the Moon.

Student:    Why not?!  I drew the Moon straight up in the sky.

Professor:  I agree, yes the Moon is straight up in the sky, but the bright side of the Moon would be facing away from us – and since the unlit side doesn’t put off any light, we can’t see it.

Student:    You know, I just thought of another question.  When the Moon is in the position that I just drew, then the Moon should block out part of the Sun.  I keep forgetting what they call it when that happens.

Professor:  They call it a solar eclipse.

Student:    Well, if the Moon makes one lap around the Earth every month, why don’t we see a solar eclipse every month?

Professor:  That’s because the Moon’s orbit is a little tilted off-center.  It only happens occasionally that the Moon’s off centeredness lines up just right so that the Moon moves in front of the Sun and blocks it out.

Student:    You know, I’ve never seen that happen in my entire life!

Professor:  Right, a total solar eclipse is a rather rare event to see.  Most people never get the chance in their lives to see one where they live.  Now total solar eclipses happen several times per year.  But it seldom happens that of all people, you happen to be standing in the right place at exactly the right time.

Student:    So I guess the people who have actually seen one are just lucky.

Professor:  Well, I don’t know if I would call it just luck.  Astronomers know when and where they are going to happen.  It’s not unheard of for people to get in an airplane and fly where they need to go solely to see one.  In fact, at the time of this writing, the next total solar eclipse that will be visible from the continental United States will take place on August 21^st 2017.  I hope it’s not cloudy that day!

Student:    How do they know that it’s going to happen.  I mean, do they have some crystal ball that tells them this?

Professor:  Oh of course not!  Astronomers have had the Moon’s orbit calculated very precisely for many centuries.  And it’s not like the Moon ever changes its mind about where it’s goes.

Student:    So if these things happen twice per year, why is it so rare to see one where I live?

Professor:  Well, they are only between 4 and 10 minutes in duration, generally.  And the shadow that falls on the Earth doesn’t cover the entire Earth, it’s actually quite small.  So the end result is that you have to be standing in just the right place at just the right time to see one.

Student:    Have you ever seen total solar eclipse?

Professor:  Actually no, I haven’t.  I did see a partial solar eclipse on the afternoon of July 11, 1991 when I lived in Coppell, Texas.  But from where I was at, it only blocked out about 1/3 of the Sun.  The people in Hawaii and Mexico were the lucky ones that year who actually got to see a total solar eclipse.

Student:    I hope you didn’t look at it directly.  I heard that looking directly at a solar eclipse can blind you.  But I never figured that out – I mean, I know that looking directly at the Sun can damage your vision, but if the Moon is blocking out the Sun entirely, how is it that it can still damage your vision?

Professor:  That’s a really perceptive question!  Actually, you are right – during the few minutes when the Moon is totally blocking out the Sun (we call this the moment of totality), yes you can look at the eclipse directly.  But the problem is that as the Moon moves out of the way, and the Sun begins to become visible again, there is a brief moment in there when there is enough sun visible for the UV rays to damage your eyes, but there isn’t quite enough visible light to make you want to squint.  This is one of the reasons why people can damage their vision by watching a solar eclipse.  The other reason is that sometimes, people go outside several hours before it’s about to take place and they start looking at the Sun, totally forgetting that you’re not supposed to do that.  Generally, in the weeks prior to a solar eclipse, convenience stores and other such places in the area where the solar eclipse will be visible will sell special dark sunglasses so that people can watch the solar eclipse without fear of damaging their vision.  And as for looking at the solar eclipse directly, no I didn’t.  The television stations in that area broadcasted the eclipse on television with a special camera as it was taking place. 

Student:    So, we seem to have gotten off track.  What were we originally talking about?

Professor:  Oh, we were talking about how the Moon moves.  One of the things you will notice is that from night to night, the Moon will change its position in the night sky.

Student:    Why is that?

Professor:  Because the Moon has moved in its orbit around the Earth.

Student:    Oh, okay – I think I get it – the Moon rises in the east and sets in the west every night, because of the Earth’s rotation.  However, from night to night, the Moon appears in different places in the sky because the Moon is gradually moving in its orbit around the Earth.

Professor:  Yeah, that’s basically correct.  Every night, Moonrise and Moonset occurs a few minutes earlier than the night before – because the Moon has moved a little in its orbit since yesterday’s Moonrise (and Moonset).  Eventually, as the Moon completes one orbit around the Earth, the cycle starts over again.

Student:    Yeah, I read that the Moon completes one lap around the Earth every 27 days.

Professor:  That’s basically it, although the amount of time required for the Moon to complete one lap around the Earth depends on how exactly you define “one lap”.

Student:    What do you mean?!  One lap is one lap, period, isn’t it?

Professor:  Actually, no.  If the Earth were stationary then I would agree that one lap is one lap period.  But the thing is that as the Moon make a complete lap around the Earth, the Earth is simultaneously making a lap around the Sun.  Things get complicated.

                The total amount of time that the Moon takes to revolve 360 degrees around the Earth is called the synodic month.  A synodic month ranges between 29.27 to 29.83 days.

Student:    Why does the length of a synodic month change.

Professor:  Well, both the Sun and the Earth are using their gravity to pull on the Moon, so the Moon’s orbit around the Earth gets sloshed around a little.

Student:    So I guess that there are other ways of measuring the amount of time it takes the Moon to go around the Earth once?

Professor:  Yes, there are.  There is also the sidereal month, which is the time from one full Moon to the next.  A sidereal month is 27 days, 7 hours, 43 minutes and 11.5 seconds.

Student:    But how can the amount of time to rotate 360 degrees around the Earth be different than the time from one full Moon to the Next?

Professor:  Because as the Earth makes progress in its orbit around the Sun, the Moon has a slightly different place that it has to get to in order to be a full Moon.

Student:    So what are some of the other types of month’s

Professor:  There are actually lots of different ways you can define a “month”, but I’ll let you read on your own about the others.

Student:    So why is a month on my calendar 30 or 31 days instead of 27.5 days or whatever?

Professor:  Well, the “calendar” is a thing made up by people.  The calendar month is however we define it.  Asking why a calendar month is 30 or 31 days (or 28 or 29 days in the case of February) is like asking why the letter “S” makes the sound that it does – there is no reason, it’s just how we define it.

                Now, a history book might be able to tell you more about why those of old made a month into 30 or 31 days, but I don’t happen to know exactly what that reason is.

Student:    So, then, what causes the phases of the Moon?  Why is it full sometimes and a crescent Moon on other nights?  Is it because of the Earth’s shadow on the Moon?

Professor:  No, the phases of the Moon are not caused by the Earth’s shadow on the Moon.  Now, don’t get me wrong – the Earth does cast a shadow out into empty space, and sometimes the Moon does move into this shadow (it’s called a Lunar eclipse when this happens), but the ordinary phases of the Moon that we see every month are not caused by the Earth’s shadow.

                Since the Moon is out there in space, it has a daytime side and a nighttime side, just like the Earth.  The phases of the Moon are caused by whether or not the daytime side is facing us or the nighttime side is facing us.  This diagram might clarify things:

 

Student:    So basically, the Moon is invisible during a New Moon.  But why doesn’t this create a solar eclipse like we talked about.  It seems from this diagram that the Moon would be getting in the way of the Sun shining on the Earth.

Professor:  Well, yes, I agree that this diagram makes it look that way.  But this diagram is not drawn to scale – because the proportions are so large that the Sun, Moon, and Earth wouldn’t fit on the page.  If I were to draw the Earth and the Moon to scale, with the distance between them to scale, the Earth and the Moon would look like this:

 

 

                In this diagram, the Sun would probably be about as large as a car, and it would be way down the street if it were included in this diagram. 

Student:    Oh, well, in that case, it would be hard to get the Moon to line up just right to get the Moon’s shadow to hit the Earth.

Professor:  Exactly!  That’s why solar eclipses don’t occur every month – only every now and then.

Student:    So what causes a full Moon?

Professor:  A full Moon takes place whenever we have this situation:

 

Student:    But here again, I don’t think that the Moon would have any sunlight hitting it because the big Earth is in the way . . . oh no wait, I forgot, the diagram is not to scale.  In reality, the Moon has to be lined up just right for the Earth’s shadow to fall on the Moon.  Ordinarily, the Moon is just barely outside of the Earth’s shadow – in which case we can see the full Moon.

Professor:  Exactly!

Student:    So what causes a crescent Moon?

Professor:  The other phases of the Moon work like this:

 

Student:    Oh, I see – how much of the Moon we actually see depends on where it’s at in its orbit, and what side is actually receiving daylight.

                So, I have another question – does the Moon rotate on its axis the way the Earth does in order to have day and night?

Professor:  Well, let me ask you this: I’m sure that when you look at the Moon it always looks like this:

 

               

               

                Now, the Moon may not be full – it may be crescent, gibbous, or whatever, but have you ever looked up in the sky and seen this side of the Moon:

 

               

 

Student:    Hmm, no, I don’t think I’ve ever seen that side.  I think that every time I’ve looked up in the sky, it looked like the first picture you showed me.

Professor:  So, essentially, we always see the same side of the Moon all the time.  How is it that the Moon always faces the same side towards us?

Student:    Oh, so if the same side always faces us, I guess it doesn’t rotate on its axis at all.

Professor:  Well, no, actually, the Moon has to rotate in order to keep showing us the same side.  If you look at my head as I walk a circle around you, I have to walk and rotate my body in order for you to always see the front of my face.  If I didn’t rotate my body at all, you would start out seeing my face, but the eventually be looking at the back of my head as I walked around you.  In order to see my face straight-on at all times, I would have to rotate my body as I walked around you.

Student:    Oh, so if the Moon shows us the same side at all times, then the Moon is rotating.

Professor:  Right.  The Moon makes exactly one rotation for every one lap around the Earth.  It’s almost as though the Moon’s rotation on its axis is timed out so that it always points the same side towards us.

Student:    I guess that’s how we know that God put the Moon there – there’s no way that could be a coincidence for it to be timed out like that.

Professor:  Heh, actually, there is a completely scientific explanation for this phenomenon.  I’m not saying that God didn’t play a role in the creation of the universe, I’m just saying there is a natural cause for this phenomenon.  It turns out that the Moon is a little lopsided, like a pear or an egg.  One side is a little heavier than the other.  Over the eons, the Earth’s gravity has dragged the Moon’s rotation down to the point where the heavier side of the Moon always faces us.

Student:    Oh, darn.  I thought I had found proof of God’s existence.

Professor:  Quite frankly, I recommend that if you’re going to believe in God, you should base your belief on faith, not on whether or not scientists can explain a certain phenomenon.  Basing your belief in God on things that scientists can’t explain is called a “God of the gaps”, meaning that your belief in God is based on gaps in our knowledge about how the universe works.  The problem with a “God of the gaps” is that every time some scientist makes some discovery, you have to change your reason for believing in God to some other gap in our knowledge.

Student:    So, getting back to our previous subject, how far is it to the Moon?

Professor:  The center-of-Earth to center-of-Moon distances averages out to be 238,857 miles.  It increases and decreases depending on where the Moon is at in its orbit around the Earth.

Student:    Oh so the Moon gets further away and closer to us at certain times?  How is that?

Professor:  The Moon’s obit is not exactly a circle, even though we generally think of it as one.  Actually the Moon’s orbit around the Earth is slightly elliptical (oval shaped).  Some full Moons are closer to the Earth than others.  On the night of December 22, 1999, the Moon made its closest approach to the Earth in over 100 years! 

Students:   Wow!  That must have been an extraordinary site to see!

Professor:  Well, the full Moon was noticeably brighter than usual that night (I actually went out and looked at it), and photographic analysis did show that it was bigger than usual, but I wouldn’t describe it as dramatically bigger or brighter.

To make things more complicated, the Moon is gradually getting further and further away from us each year.

Student:    It’s getting further away from us?!  Like, it’s going to fly away someday?

Professor:  Probably someday, but certainly not in our lifetime.  In fact, the Sun might burn out before it ever happens.  But at current estimates, the Moon is drifting away from the Earth at a rate of 3.8 centimeters per year. 

Student:    How did they figure that out?  The Moon is awfully far away to be able to pin it down to a few centimeters.

Professor:  The Apollo astronauts that landed on the Moon in the late 1960’s and early 1970’s left big mirrors on the Moon.  Astronomers back on Earth can now use lasers to determine the distance to the Moon.  They can shoot laser beams at the Moon, and then tell by how far away the Moon is by how long it takes for the laser beam to get back.  After many years of careful measurements, they came up with the 3.8 centimeter number.

Student:    Oh, wow!  That’s cool.  I didn’t know that they knew that.  I see that the Moon does move, in many ways actually.  Thank you for helping me learn so much about the Moon.

Professor:  It’s always my pleasure.

               

 

                Links of interest:

www.moonconnection.com -- A very interesting website detailing all sorts of information about the Earth's Moon.

www.mreclipse.com -- An interesting site about solar eclipses, including a calendar that marks future times and locations of solar eclipses.  Excellent photographs of solar eclipses and the solar corona as well.

www.nightskyinfo.com -- Quite a bit of information on astronomy in general. Excellent web page.

nineplanets.org/luna.html -- A miscellany of interesting facts about the Moon, from mythology to science fact. Overall, a site dedicated to the promotion of science and the rejection of pseduoscience in astronomy