Time is tight!

[Glom]

Ah.  Thank you.  To the person unfamiliar with much of orbital mechanics, the idea that the orbital period changed probably sounds more ominous than it does to experts.

Remember Kepler's third law: T² = a³, where T is the orbital period and a is the semi-major axis of the orbit (a measure of the orbit's size which is equivalent to the radius if the orbit is circular).  There's also a constant of proportionality in there depending on the units you use.

[ka9q]

The constant of proportionality depends on the mass of the body you're orbiting. It's called the gravitational parameter. It in turn is equal to the body's mass times the gravitational constant G, a constant of nature. The interesting thing is that we know many of these products far more accurately than the actual masses or the gravitational constant. We know the earth's gravitational parameter to 2 parts in a billion, but the earth's mass (and G) to only about 1 part in 7,000.

The semi-major axis (or orbital period, since they're directly related) determines the energy in the orbit. To change them some force must perturb the orbiting object: thrust from a rocket, drag from an atmosphere, gravity of a third body, sunlight, etc.

An interesting thing about the period of a small satellite orbit is that it depends solely on the average density enclosed by the orbit. Mass and size don't matter except as they affect the density. For a "surface skimming" orbit, ignoring any atmosphere, the period depends on the average density of the body itself. The higher the density, the shorter the period.

Since the earth has the highest density of any major object in the solar system, it also has the shortest minimum orbital period. The moon is considerably less dense, so even a very low lunar orbit has a longer period than a low earth orbit.

[gillianren]

Remember Kepler's third law: T² = a³, where T is the orbital period and a is the semi-major axis of the orbit (a measure of the orbit's size which is equivalent to the radius if the orbit is circular).  There's also a constant of proportionality in there depending on the units you use.

To remember it, I would have had to have known it.  Sometimes, you guys have no idea how much more you know than laymen.

[ka9q]

The interesting thing about Kepler and his laws of planetary motion is that when he proposed them circa 1600, even he didn't really know why they worked. He simply deduced them from observations, particularly those of Tycho Brahe.

It took almost another century for Isaac Newton to come along and figure out why Kepler's laws worked.

[gillianren]

Now, that, I did know.  I know quite a lot more about the history of science than I do about equations and things.  (When I was a child, I inherited a book called Pioneer Germ Hunters or some such from my godmother, who had been a teacher.  A few years ago at a library book sale, I think, I found the equivalent book about astronomers!)  To be perfectly honest, this is in no small part because I find the history more interesting.

[Count Zero]

Gillian, I very highly recommend Blind Watchers of the Sky by Rocky Kolb.  It is not only readable, it is entertaining enough to be re-readable (i.e. "a real hoot" - my favorite kind of book!)  This history of astronomical discovery focuses on the personalities involved (Kepler, Newton, etc.) and the struggles they went through overcoming their own myopia.  Along the way you learn a lot of the science.

For example, you learn about the Curtis - Shapley Debate over the size & nature of the universe.  Curtis argued that our sun was part of one small galaxy among many.  Shapley contended that there was only one great galaxy, and we were on the fringe, and that the "spiral nebulae" we see in telescopes were nearby swirls of dust & gas that may be individual stars coalescing.  In Kolb's amusing account, Curtis blew almost every point in the "Great Debate", but eventually turned-out to be vindicated.

In another account, Kolb recounts the discovery of the Cosmic Background Radiation (the 3K echo of the Big Bang) in the 1960s.  Big Bang proponents & theorists predicted that it should exist, and were trying to figure out a way to detect it.  Meanwhile, observational astronomers were detecting it - but did not understand its significance.  For example, physicists & engineers at Princeton were struggling to build a suitable microwave detector for the search, while 50 miles away Penzias & Wilson were cleaning birdshit out of their microwave antenna to try and clear-up this damn 3K interference that was screwing-up their experiment.  When one of them stumbled across an article about the 3K search and made the connection, all they had to do was write it up, publish, and - voilà! - Nobel Prize.

So, in this book you get the science, but as they say, "the journey is where the fun is."  Check it out!

[smartcooky]

Now, that, I did know.  I know quite a lot more about the history of science than I do about equations and things.  (When I was a child, I inherited a book called Pioneer Germ Hunters or some such from my godmother, who had been a teacher.  A few years ago at a library book sale, I think, I found the equivalent book about astronomers!)  To be perfectly honest, this is in no small part because I find the history more interesting.

Back in the 1980's, Carl Sagan's COSMOS contained a number of interesting historical "docudramas" and one of these was about Johannes Kepler, and the torment he endured as he struggled to balance his deep religious beliefs against the raw physical evidence that confronted him, to come to his final conclusions regarding the Laws of Planetary motion.

If you have never seen it, and you are interested in the history of astronomy its well worth taking some time to watch it.

Its in this Episode "Harmony of the Worlds"

The actual docudrama starts at about 22 minutes in, but the whole hour is worth watching.

[Sus_pilot]

@gillianren:  if you're interested in the history of science, another great book is The Day We Found The Universe by Marcia Bartusiak.  It's about the birth of modern astronomy (1870 - 1940, IIRC), including the politics and personalities of the key figures in physics during that era.  Fun read and just the right mix of hard and social science for that type of work, IMO.

[gillianren]

Thanks for the book recommendations!  I saw Cosmos years ago (starts with "C," if for no other reason), but the library does have the other two, and I have put them on hold.

I just feel it bears repeating every once in a while that, you know, a lot of us don't know the math.  The story of "why Gillian didn't learn physics in her physics class" is an entertaining one, but it's worth noting that I still know more physics than the average person.  I've taken as high as precalculus, but not in nearly twenty years.  Graham took prealgebra in the spring, and I couldn't help him with his math, because I didn't remember the stuff he was doing.  I've taken algebra a lot more recently (the last time I took it was in 1998 or '99), and I'm not expecting to be much help with that, either.

[nomuse]

I have somewhere a book I found rather cool; "A History of Astronomy from Thales to Kepler."  Gave a nice tour of several early (classical, medieval et al) views of how the universe was constructed. 

Turns out the book I have is a Dover reprint, and the full text is free online:

http://archive.org/stream/AHistoryOfAstronomyFromThalesToKepler/Dreyer-AHistoryOfAstronomyFromThalesToKepler#page/n9/mode/2up

[BazBear]

I have somewhere a book I found rather cool; "A History of Astronomy from Thales to Kepler."  Gave a nice tour of several early (classical, medieval et al) views of how the universe was constructed. 

Turns out the book I have is a Dover reprint, and the full text is free online:

http://archive.org/stream/AHistoryOfAstronomyFromThalesToKepler/Dreyer-AHistoryOfAstronomyFromThalesToKepler#page/n9/mode/2up

Thanks Nomuse!

[Noldi400]

Ah.  Thank you.  To the person unfamiliar with much of orbital mechanics, the idea that the orbital period changed probably sounds more ominous than it does to experts.

Gillianren, if you have any interest in something that resembles a "computer game", let me recommend 'Orbiter' - it's a real-world-accurate space flight simulator created by Dr. Martin Schweiger of UCL. I've learned more about Orbital Mechanics and related subjects in the past month than I would have ever thought possible, and relatively painlessly.

http://orbit.medphys.ucl.ac.uk/index.html

[nomuse]

Heh.

I first worked with that stuff on the old arcade game "Space Wars" (the Cinematronics commercial port of "Spacewar!"  Although it was a two-player game, you could plug in a quarter and just play around with one ship and the gravity of the central sun.  It was a nice way to bring home some of the lessons of the introduction astronomy class I was taking at the time.