Note the color photo (composite image) of South America at the bottom. Note the color variations, where the vegetation shown green maps to the infrared in the MESSENGER image (especially the higher res version). Note also the low infrared matches the brown colorations on the South America photo, especially along the Western coast, but also in Argentina, Paraguay, and Brazil. Finally note the political map higher on that page, and see that the boundary does NOT align with the Chilean border, but rather with the geographical feature of the Andes Mountains. In fact, lower Chile is green (covered by clouds on the MESSENGER image), and the brown arid territory in the north extends into Bolivia and Peru.

Also, if you look at the MESSENGER image in “true color” as opposed to infrared, you will note that the coloration pattern falls along the exact same borders, with the “red” of the infrared mapping to dark coloration on the Amazon forest.

I know that gravity is the only force needed to explain the circular/elliptical motion of orbits of the planets about the stars and the stars about the galactic centers. It might seem that the attractive force of gravity would just cause everything to collapse into a big ball, so a second force is needed to push the objects out from the center. But the planets are not being held away from the sun by any opposing force, they are just moving too fast to ever hit the sun. In a very real sense, the planets are trying to fall into the sun, but they are forever missing it.

It might be easier to picture this if you think of an object orbiting the Earth. If you stand on the top of a tall tower and drop a baseball off the edge, it will fall more-or-less straight down and land at the tower’s base. If you toss it horizontally from the top of the tower, it will fall a little farther away. Throw it faster, and it will land still farther away. If you could throw it fast enough, and the tower were tall enough, you could make the ball hit the ground several miles away. In fact, you can imagine that Superman might even be able to throw it so hard that it would travel halfway around the world before it landed. In this case, the baseball is just barely hitting the Earth at all… any faster, and the ball would miss the planet’s edge and fall past it to the other side. But of course, if there were no air resistance, it would miss the other side too, so it would never land at all! The ball would always be falling towards a point which is just over the horizon: always falling, but never landing – that’s an orbit!

(You might want to visit NASA’s Space Place to play the “Shoot a Cannonball Into Orbit” game. It’s intended for kids, so don’t be offended that the graphics are kinda’ juvenile, I just think the animation might be more clear than my written explanation.)

This was Newton’s great discovery in the apple orchard. He didn’t discover gravity, everyone already knew about that, he discovered that gravity was the only force needed to account for the orbital motion of the moon.

Now, as for your other questions, well, Newton himself never tried to explain why there is any gravity in the first place (though he did develop an equation to predict its magnitude). Einstein accounted for gravity as a curvature in space-time* caused by an object’s mass. He said that the moon falls towards the Earth ’cause the Earth’s mass makes a sort of dimple in the “surface” of space, and the moon is sliding down the curved surface of that dimple, like a ball rolling down a hill. Of course, like all good answers in science, this just pushes the real answer farther away by bringing up more questions. Like: why do masses curve space-time, and why does a ball roll down a hill anyway? (In fact, this is just the sort of “explanation” which Fineman used to poke fun at. Because, in an effort to explain gravity, I’ve used an analogy which only makes sense if you think you already understand gravity so, as he would say, “I’ve cheated very badly.”)

If there is a better explanation, or an answer to those two questions, they are past my depth. Maybe someone else could help us both there.

Also, the whole “falling past the horizon” explanation can only account for the orbit of the planets if they were already moving fast enough to miss the sun the first time. The question as to why the matter in the planets was moving in the first place is a tricky one. The short answer is “the big bang got them going”, but that’s not a very good answer, really. In point of fact, in the early days of our solar system, most of the matter in this area was not moving fast enough, so it did fall in towards the center, where it coalesced to form our sun. (Can you have “days”, or even a “solar system” before your have a sun?) Anyway, most of the solar system did hit the “sun” – that’s why the sun is so big today. But the real question isn’t “why didn’t the matter that made up our planet fall into the center also.” The real question, as you’ve implied, is “what do we mean by ‘center.’”

If all there were to get the system going was a big bang, all the matter in the universe would be evenly distributed into a smooth, uniform, bubble expanding out* from the original explosion. No area would be any more dense than any other area, so none of the matter would have been attracted in one direction any more than the other, and there wouldn’t be a sun to fall past. The only point which could really be considered a center is the spot/moment* at which the “bang” occurred. If the bang weren’t big enough, everything might eventually slow down, stop, and fall back towards the place/time* where it came from (the so-called “Big Crunch”). But that wouldn’t explain why some matter clumped together to form our sun (or any of the other big, glowing lumps of stuff we see when we look at the night sky).

So the three big questions in cosmology are:

- “Why isn’t the universe uniformly dense?”

- “Will it ever stop expanding?”

and

- “If it does, what will happen after* that?”

‘Last I heard, no one really knows the answer to any of these, though there are a few very promising theories in the works.

Again, maybe someone more in the know than I will chime in at this point.

* Einstein’s theory of relativity holds that the universe is not just a collection of points, but also a collection of moments, and that the two are inextricably linked. This is what is meant by “space-time”. It is also why, when you talk about things like the Big Bang and “End of the Universe”, you cannot make a meaningful distinction between a spatial place and a temporal moment. I think I kind’ get relativity, in a general sort of way (no pun intended), but I wouldn’t presume to try to explain it to you. Here again, maybe the blogosphere will help us both out.

In any case, I think the phenomenon is a genuine artifact of the geographic barrier of the mountains. I’d be surprised if there is anything in the image processing software which is even aware of the geopolitical boundaries.

Really, I guess that’s a compliment to the CGI guys, huh?

This is precisely the case in a circular orbit. Because the gravitational force is centripetal, it is perpendicular to the tangential velocity in a circular orbit (and at the instant of aphelion and perihelion in an elliptical orbit). Therefore, the force and the direction of motion are perpendicular, and no work is done.

Consider this: while work must be done to lift an object off the ground(to move it in the direction of the applied force) and get the object moving forward (to change its kinetic energy by accelerating it), no additional energy is needed to carry the object forward at a constant velocity and constant height. Because the direction of motion (forward) is perpendicular to the direction of the lifting force (upward), the work done is zero. (In mathematical terms, work is a dot-product: it takes two vector arguments and returns a scalar answer depending on the degree to which the two vectors are collinear.)

To put it another way, the fact that kinetic energy is based on the square of the velocity makes it direction-independent. In a one-dimensional system, this is a simple as saying

(-v)^2 = (v)^2

In a 2-dimesional sense, remember that the resultant velocity is the hypotenuse of the triangle made from the perpendicular component legs. So

(1/2)m(Vx)^2 + (1/2)m(Vy)^2 = (1/2)m(Vr)^2

reduces to

(Vx)^2 + (Vy)^2 = (Vr)^2

– the Pythagorean theorem!

Therefore, the resultant (i.e. overall) velocity will remain constant even as the component lengths change. (This also holds true for 3- and even n-dimensional motion.)

Of course, when an object is not at one of the “-helions” in an elliptical orbit, the force of gravity is not perpendicular to the tangential velocity, so this non-perpendicular force of gravity does change the overall velocity, and therefore the kinetic energy. But this change is caused in the component of the velocity vector which is collinear to the force, which is to say, the radial component. Therefore, the change in kinetic energy is exactly offset by the change in potential energy as the object moves to a different distance from the sun. (Indeed, you can argue that the work done by the force in that direction is “used” to change the energy form one form to the other.) Any way you look at it, the total mechanical energy of the system remains constant. (At least in a Newtonian/Keplerian an system.)

(Note: I know that “V” is not the correct abbreviation for “velocity”, but I don’t know if this blog supports the sub-script tag, and I wanted to use an upper-case letter to make my sub-scripts look small.)

But don’t forget, cardoso, to say that all orbits are elliptical does not rule out the possibility that an orbit may be circular: a circle is a special-case solution of the ellipse. Just as a square is a rectangle with equal-length sides, a circle is an ellipse with equal-length semimajor and semiminor axes (and both foci in the same place).

To get to Mercury, you need to shed energy, or the spacecraft won’t start to fall inward towards the sun. But once you get there, you need higher velocity, since Mercury is traveling faster than the earth. That’s kind of weird!

The issue of eliptical orbits also interests me. As far as I know, all planets, and moons for that matter, have eliptical orbits of verious degrees of eccentricity.

What I wonder is this: is a perfectly circular orbit possible in theory? I would think that even if it is, such an orbit is extremely unlikely simply because any orbit must, of necessity, have a history. In order to achieve a perfectly circular orbit, you’d have to start out with exactly the right conditions of velocity and direction, and it seems to me that in a natural system, the chances are very slim that bodies condensing out of a preplanetary disk will ever happen to have just the right velocities to ensure that they end up with a perfectly cicular orbit.

But don’t know. I wonder if anyone else here can tell me. Is a circular orbit possible in principle, and real orbits elliptical simply because of historical contingencies, or must an orbit always be elliptical?

It does seem a bit odd that the launch date was August 3rd 2004 and the first planetary swingby was with Earth on August 2nd 2005. That’s almost exactly one year later, so Earth was in almost the same position. It seems to me that launch could have been delayed until August 2nd 2005 if the weather cooperated and safety margins were still good.

Rock, really… eh… Rocks!