Can you straighten this out for me? (no pun intended) I'm still having trouble thinking of gravity as the curvature of space-time instead of as a force. If it is really curvature, then:

The earth does not orbit around the sun, correct? The earth and moon travel in a straight line, but the curvature of space-time makes it seem like we're going around the sun. Like drawing a line on a piece of paper and then making a cone out of the paper so that both ends of the line touch. The line is still straight based on the 2-dimensional plane on the paper, but is a circle (somewhat) to a three-dimensional observer.

But if we travel in a straight line through curved space-time, then our orbit around the sun should not be affected by velocity.

But if the earth actually orbits in a circle, and not a straight line, that means that there has to be something pulling us toward the center of the circle. How can curvature of space-time "pull" on an object without using a force? It should merely warp the path of a moving object, but not draw it into the center, and at the same rate regardless of the velocity.

What am I missing here?

Thanks in advance!

I tend to think of it as likened to riding a bicycle around a steep ramp, you have to maintain the same velocity to stay in the same "orbit". Go to slow you fall down, to fast and you fly of the ramp like those punks on americas funnest home videos. Now I see it as matter warping space into a sort of conical ramp, that you can not see.

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But, if this be the case, what makes the orbit ellipsoidal rather than circular?

::Going through another relativity brain-fry::

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"As I lay beneath the Southern Cross, the stars tell more than I could" . . . David Meece

Well I guess likening a bicycle to planet can only go so far in resemblance.

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I am so excited about Canadians ruling the world.
- John Diefenbaker

What you are missing here is the fact that the Earth and the rest of the planets SPIRAL around the Sun in their movement in the galaxy/space.
Envision a spiral staircase, the Sun is the central pole with the planets on railings with different slopes, folowing the Sun. The orbits are but a projection on a plane perpendicular to the cetral pole/direction of travel. My beleive is that the bending of space is actualy the bending of a field thrugh which the Sun and the planets move, sort of enveloping them, just like water would envelope a moving object. Space might be empty of matter but not devoid of some sort of field. The so caled force of atraction must be the result/efect of the interacting fields, like magnet's fields do with magnets.

Not to add to the heat (I hope). The curvature of space-time (or gravitational field if you prefer) allows orbits that are conic sections. This includes circles, ellipses, parabolas (parabolae? ) and hyperbolas. This is an effect of the inverse square nature of gravity, that is the strength of the field (or curvature of space-time) drops off as the square of the distance.

FWIW, this is true of any inverse-square law, so trajectories in an electric field also follow conic section paths.

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"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind." - William Thompson, 1st Baron Lord Kelvin

"If it was so, it might be, and if it were so, it would be, but as it isn't, it ain't. That's logic!" - Tweedledee

This isn't right. This isn't even wrong. - Wolfgang Pauli

Or, to simplify back down from the conic section stuff, the "wall" that Beaver is describing isn't elliptical. It has the steeper the closer you get shape that you're probably used to seeing on the diagrams, and people (planets) aren't always cycling exactly perpendicular to it.

Notice how planets orbit faster the closer to the sun they get? The gravity well is steeper there, and you're lower down the well. So you get a buildup of speed from going in, which is useful because that going faster is what (might) stop you falling right into the centre. As you rise back out you slow down again, to the point where, if you're in an orbit you find youself falling back in once more.

Have I stretched the analogy enough now?

No, that is very good. But this does leave open the question of why ellipses and not circles?

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"As I lay beneath the Southern Cross, the stars tell more than I could" . . . David Meece

But circles are ellipses. Just one in which the two foci are at the same point. The point is that the space-time curvature that causes a circular orbit can just as easily cause an elliptical one (or parabolic etc.) because these are the types of orbit that inverse square forces create.

As to why planetary orbits are elliptical and not circular, chalk it up to small variations in the dust cloud the solar system formed from. The orbits are almost circular, so the disturbance wouldn't need to be very large. If you think about it, a perfectly circular orbit would be very odd. That's quite a special case and very few things come out that precisely.

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"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind." - William Thompson, 1st Baron Lord Kelvin

"If it was so, it might be, and if it were so, it would be, but as it isn't, it ain't. That's logic!" - Tweedledee

This isn't right. This isn't even wrong. - Wolfgang Pauli

I would rather ask WHO made the orbits ellipsoidal and the answer is KEPLER. I ploted the orbits of the terestrial planets from the Nautical Almanac data (Rv and longitude) and found that there's hardly any ellipsicity. The orbits are excentric circles, centred along the perihelion line/Sun. Don't just take my word for it, do it. Plot the planetary orbits, at least the terestrial planets, overimpose a circle and call me the naxt morning.

Indeed. Put yourself in the position of a planet. In this particular case, we're going to ignore rotation, as it makes things easier. Feel free to add the spin later if it makes you happy.

The Sun is exactly to your side (left or right doesn't matter, its just a coordinate thing) and you're moving forward. If you're at EXACTLY the right speed, your forward velocity is exactly right for your pull sideways, and you're in a circular orbit.

A teeny bit more, and you'll start to increase your distance from the Sun as you go round. You're at the closest point of an elliptical orbit, unless you've got enough velocity to escape the gravity well completely, in which case nobody round here will be seeing you any time soon.

A teeny bit less, and you'll start to decrease your distance from the Sun. You're at the furthest point of an elliptical orbit, unless your velocity is so low that you're going to crash into it. Again, no-one is going to notice your existence again after a very short while. By the way, where did you get here from?

So, orbits fall into 5 types.

V < Vboom - you're going to crash
Vmin < V <Vperfect - elliptical orbit
Vperfect - circular orbit
Vperfect < V < Vescape - elliptical orbit
Vescape < V - parabolic flypast.

A planet's orbital velocity being absolutely bang on to have a circular orbit is the sort of thing thats really bloomin' impossible to see in a real-life situation, so everything sits in ellipses after a reasonably short while.

From My? observations?/?
I would say ( yeah )
Times do arive
when Space seams to be Curved
----------------------------------------
one example i can think up {with no problem}
is a video i once saw of an Alaskan Earth Quake
the cement side walk undulated up and down ~
==============================
like a rope held firm on one end and moved
vertically on the other
{um standing waves}?
::::::::::::::::::::::::::::::::::::::::
anyway the cruxt of the tails {this}
when the (event) was finished
the cement was not broken
???????????????????????????
and I can think of no other
way to think about that
{um bent concrete}
//tilt\\
THAN to say {yeah}
obviously the underlying
space was what was bending
and not the concrete itself/\/\/\
as had it been just concrete it would have broken apart {Easily}
yeah, YEAH my other {{been there: SAW THAT}} experiances
also cause my thoughts to be ( indeed Times do arive ){when space
doth assume curvature} those times are RARE and are ...
{always is my guess } accompinied by a large & sudden release of
Energy(or Force)
"""""""""""""""""""""
no about the Sun & Solar System : Circles ? Elipises ? cork Screws ? etc
Visualize a Gravity wave Pod ( ping pong ball, Tennis ball, Basket ball )
with only an invisable skin surface.. then picture all the planets & sun
inside of that (Exto_Skeliton) and those points EXIST within the Frame
and are subject to the Frames influence...
''''''''''''''''''
what you should come out of it with
is NOT a Cartisian Cordinate system +
{ that is to say a central point of reference ... to measure from }
what you gets an EXto Skeliton { picture a turtle ? }
and you measure from the wholes in the surface {inwards}
if there is a hole if not then Measure from where the Hole
would be if you knew WHEN the hole would open
.... well enough B. s if you read that its your own fault not mine

Eta C, I invite every body that thinks the orbits are eliptical than rather circular to plot the path of the terestrial planets. The positios are to be found in the Nautical Almanac. You seem to be knowlegable in math and I need help with the orbital velocities- thay drop (or decrease) with the square root of the distance to the Sun.

Did it, found them to be ellipses not circles. Not terribly ellipsoidal, to be fair, but then anything big with a large eccentricity brings itself close enough to other bodies after a while that things go decidedly three-body-problem, three-body like Shoemaker-Levy 9 if they are particularly unlucky.

Apart from anything else, David, are you suggesting that there are different physical laws for the planets than for comets? Because they are rather blatently in ellipsoidal orbits.

The eccentricity of the planets in our solar system tends to be quite low but they do have eccentricity. Even if they had zero eccentricity the orbits are still technically elliptical.
A circle is a special case of an ellipse where the eccentricity is zero. You say that the orbits are eccentric circles. A "circular" path that has eccentricity however small is an ellipse.

As I recall, Mercury, Mars, and Pluto are the only planets with significantly elliptical orbits. Venus and Earth, in particular, have orbits that are very nearly circular. Fortunately, when Kepler was gathering his data on orbits, the planet he started with was Mars.

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Everything I need to know I learned through Googling.

Great explanation - thanks!

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"As I lay beneath the Southern Cross, the stars tell more than I could" . . . David Meece

Isn't that what an ellipse is?

(Click here for definition of "excentric")

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"As I lay beneath the Southern Cross, the stars tell more than I could" . . . David Meece

Thanks Iain. For good measure one could add asteroids. Those outside the belt (such as Toutatis, the official asteroid of the BABB) move in very elliptical orbits.

On a terminology side, there are two meanings to "eccectric" that are being used in this thread. One is a measure of how far apart the foci of an ellipse are. The lower the eccentricity, the closer it is to circular. The other is an eccentric circular orbit. Here the eccentricity is how far from a point the center of a circular orbit is. In addition to epicycles and other tricks, Ptolomy, Tycho, Copernicus, and every other astronomer up to Kepler used eccentric circles to describe planetary orbits. As most have noticed, actual planetary orbits are ellipses with very small eccentricities and, as such, close to circluar. What David fails to realize is that close only counts in horseshoes (and hand grenades )

As to your mathematical question, the orbital velocity varies with the inverse of the square root of the radius. The actual formula is

V = sqrt(G*Ms/R)

Where G is the gravitational constant and Ms is the mass of the sun. You can derive this from Newton's gravitational law and some elementary classical physics, so I'll leave it as a problem for the student as my profs used to say. Notice that it's independent of the mass of the orbiting object.

Now in an acutal orbit, that radius is constantly changing, so the velocity changes around the orbit. The planet speeds up and slows down as it goes around. That's what Kepler's second law points out. What is constant is the period of the orbit. Kepler's third law shows that the square of the period is proportional to the cube of the orbit's semi-major axis.

__________________
"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind." - William Thompson, 1st Baron Lord Kelvin

"If it was so, it might be, and if it were so, it would be, but as it isn't, it ain't. That's logic!" - Tweedledee

This isn't right. This isn't even wrong. - Wolfgang Pauli

WOW! Thanks for the responses. Just going through them now. Forgive me if they have been subsequently answered.

Thanks Beaver. I understand your example (I always use the example of pinching down on a rubber sheet with a marble on it), but we only fall down or fly off because of the Earth's gravity acting on our examples. So if we could somehow think of an example that didn't rely on Earth's gravity to prove its point, I think it would answer the question for me. That's what's throwing me off.

My problem with the ramp (and rubber sheet) example, is that in space, without the effect of the Earth's gravity, you *would* follow the same path regardless of velocity. Obviously, this isn't reality since velocity would affect our path. That's what's confusing me. And in the rubber sheet example, without the effect of Earth's gravity, the marble should not go anywhere because you pinch near it, no matter how hard you pull on the sheet, the marble should never move from it's spot on the sheet. It should always stay still, relative to the rubber sheet, unless you apply a force to it. But we all know that is not the case. What is the attracting "force" (for lack of a better term) that should draw it to the pinched spot? That is what I'm confused about, and is what keeps bringing me back to gravity being a force.