This looks suspiciously similar to post #4. Except I numbered possibilities 1 & 2 the opposite of how you did. 
The old, “throw a baseball” analogy.
Throw a baseball into the air, what happens? It falls back down and hits the ground, because gravity pulls it back. Throw it harder and it travels farther, but eventually hits the ground still, because on Earth there is a lot of gravity.
But if you could throw the baseball really really hard you could throw it into the air and it would never hit the ground, it would just fly off into space. This speed is what we call “escape velocity”.
So things either fall to the ground, or they fly off into space. But there’s a third possibility. You throw it really hard, over the horizon. You notice that the Earth is curved? What if you could throw it so hard that by the time it fell five feet, it was so far in the distance over the horizon that the ground had curved five feet lower?
In this case, the ball is falling five feet, but the ground has curved five feet lower, and so the ball is still five feet above the ground. And now the ball will circle the entire Earth this way, and smack you in the back of the head after orbiting the Earth once.
Of course on Earth this couldn’t happen, because air will cause the ball to slow down via friction. And there are hills in the way, and valleys and mass concentrations and so on that will cause the ball to impact the Earth pretty soon, even if there was no air in the way. So even on the Moon where there is no air a baseball orbiting at 5 feet above the ground is going to have problems and will probably smack into the Lunar surface sooner or later.
But if we orbit higher up, above the air, above the hills, and where all the variation tends to cancel out, the baseball could orbit the Earth over and over. And this is how artificial satellites and space stations keep going orbiting the Earth.
I found it easiest to understand the explanation that planets in orbit are falling in, but keep missing the sun by thinking of comet orbits rather than planets. Planet orbits are so close to circular that the “falling and missing” idea is hard to see.
Comets, on the other hand, have a highly eliptical orbit. You can see how they’re headed almost straight at the sun during certain times of their travel. But, again, they just miss it. They get pulled back toward it and just miss it again. Then they have all this excess speed that shoots them away from the sun, but it’s not enough speed to escape entirely. They slow down and start to fall back… but, again, they just miss it.
Throwing a baseball up follows much the same motion as a comet. So if you can start your thought experiment with baseballs that hit the ground, then extend it to baseballs that operate like comets, you should be able to extend the thought experiment until the baseball has a more or less circular orbit.
More bees.
It’s bees all the way out to infinity.
And the giant ones shoot barking dogs out of their mouths.
Newton’s laws of motion:
First law: When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.[2][3]
Second law: F = ma. The vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration vector a of the object.
Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.
So unless there is some force acting on the planets to make them change their path, they will continue on their path.
Note that general relativity supersedes Newton’s laws in explaining variances in them, such as the procession of the orbit of Mercury (the planet, not the car) but we aren’t going to be able to explain general relativity in a SD thread. Newton’s laws are a good explanation to start.
precession
The precession usually proceeds according to precedent.
I can’t say that I’m a fan of that analogy, especially as an explanation for gravity (it’s ok as a simulation of gravity). It only works if you already have gravity–that’s what causes the rubber sheet to dimple.
If I were trying to teach how gravity worked to some kids, I’d start by exploring what it means to have a force law at all. Play around with strings, rubber bands, springs, magnets, and so on. These objects do not have the 1/r[sup]2[/sup] force law that gravity has, but they do have force laws, and with enough examples the students can understand their general nature. It is not a great leap from a mass oscillating on a spring–where potential and kinetic energy are repeatedly exchanged–to that of a stable orbit, where the same thing happens, but with a different force law.
That’s why it’s an analogy, not an “explanation”.
The rubber sheet with a bowling ball deforming it is actually quite a good two-dimensional analogy of gravity, and a great way of showing by analogy how it’s not really a force so much as a deformation of space. You can demonstrate, for instance, how the “attraction” of a billiard ball varies with distance to the bowling ball. You can shoot the billiard ball into the gravity well and show how it starts to “orbit” the bowling ball, and were it not for rolling friction and air resistance, it really would go into orbit. And if the orbit was elliptical it would exhibit all the expected dynamics of a real 3D orbit in space.
I found myself pondering this thought just the other day. I accept the explanation that the Earth is moving in a straight line through spacetime. I have a lot of trouble visualizing it.
I understand that a light beam defines a straight line in space (I guess that when we say that the sun “bends” a beam of light, this is a colloquialism). I guess it is straight in space, because the “time” part of space-time is zero for a photon.
I guess the Earth’s orbit is curved-looking to me because I’m visualizing its course through space rather than through space-time. But here is where my brain kind of gives out.
Any help?
It doesn’t really work as that, though. In general relativity, objects moving in straight lines nevertheless experience attraction due to the curvature of space. With the rubber sheet analogy, that’s not happening; actual gravity keeps the balls moving on curved trajectories. All that you get out of it is the ability to simulate a 1/r[sup]2[/sup] force law (gravity at large scales) with one that is basically constant (gravity at small scales).
I really don’t see any way to usefully convey the nature of curved space with analogies like this. GR is just… too complicated. Better to stick with Newton, where we just have to assert that it’s reasonable for a force law to exist at all. From there on it’s pretty straightforward to see what happens.
While we’re at it, I get very confused when physiscists say that gravity is a manifestation of spacetime geometry AND that there ought to be a graviton with spin=2.
Isn’t a geometric explanation and a particle explanation mutually contradictory?
Also, how important is it that the Earth is also dimpling the sheet?
Isn’t this actually unhelpful? The challenge in understanding orbital mechanics is that there is a force (gravity) continually acting on the motion of the planets. Without that force, the planet would move in a straight line, not a circular/elliptical orbit. Furthermore, it’s not a simple F=ma kind of equation except at any single instant, because the vector and quantity of the force are continually changing, as is the velocity and position of the planet. To use Newton’s laws to get the whole orbit means pulling out calculus.
The earth isn’t moving in a straight line from any perspective. The earth returns to any given point in its orbit every year, and it’s not because the sun’s gravity is so strong that space has “curved in on itself”!
I think we’re conflating two different concepts here. Mass deforms space in such a way as to create the appearance of a gravitational force, and the apparent magnitude of that force defines the orbital parameters associated with a pair of masses – in particular, the orbital velocity associated with any given distance from a mass. IOW, the earth travels in a circle around the sun because its speed is just right for the relatively slight amount that the sun’s mass has deformed the space around itself, not because the space around it has been deformed into a circle!
Yes, I suppose this is all true. But it’s a bunch of pedantic bullshit, too. If you’re trying to explain something in relatively simple terms - for the purpose of answering a basic question that is posed on a simple and simplistic level, then going into detail about the space-time continuum, the curvature of space, or any other counter-intuitive and non-rational gobbledy-gook may make you feel great and superior, but it’s not teaching anyone anything. Look again at the OP. Do you detect a thirst for the type of information you provided? Puleeze. Not unlike the guy who gets asked for the time and spends the next 20 minutes explaining the way a watch works.
:smack:Of course Newton’s laws of motion are unhelpful! What was I thinking? Get a textbook on general relativity, some shrooms’ put on Inna Gadda Davida and grok that an orbit is a straight line, now spin in your chair and go right through frame dragging. :eek:
Reality, what a concept. – Robin Williams
Sure it is. Like all objects in freefall, Earth moves along a geodesic. Geodesics are straight lines in spacetime. Their projection back to 3D space is curved. It was one of Einstein’s great insights that gravity was not a exception to Newton’s First Law (“objects in motion stay in motion unless acted on by an outside force”); instead, gravity is the result of the relative motions of objects moving in straight lines in spacetime.
OK, I see your point now. I can accept that if one is talking about the curvature of spacetime (which you were) and I was thinking about space. The key difference being that in a curved spacetime different velocities define different geodesics, which deals with the objection that orbital trajectories are affected by velocity, and a beam of light, say, emitted tangentially to the earth’s orbit would follow quite a different path.
Simple–Because bees can’t fly!