## How do we move around the sun?

Okay i want to stir something up....do we earth dwellers move around the sun in a roughly circular path (ellipse) OR are we moving in a straight line in a curved space?

Dave
 The latter is technically correct by the principles of general relativity, but the former is correct to a good approximation.
 Recognitions: Gold Member Science Advisor It's merely a coordinate system thing. Gravity is the curvature of spacetime in the presence of matter so a straight line in GR is a circle/ellipse in a cartesian coordinate system.

## How do we move around the sun?

it depends on your perspective, your point of reference

 Quote by Chronos It's merely a coordinate system thing. Gravity is the curvature of spacetime in the presence of matter so a straight line in GR is a circle/ellipse in a cartesian coordinate system.
Chronos, when you say "GR" are you refering to General Relativity?
 I would have to say we are doing both.
 Scientifically, you would use whichever theory is more helpful to your calculations / prediction making at the time. Which one is really true is a question for a philosopher, not a physicist.

 Quote by spark802 Chronos, when you say "GR" are you refering to General Relativity?
Yes he was. General Relativity encompasses a mathematical description of space time curvature created by mass or acceleration.
 Uh, we are following a free fall trajectory around the sun. This trajectory is a curved one when in the presence of a gravity well, such as the spacetime in the vicinity of the sun, as described by GR. To get into straightness or such you need to understand the difference between a 4-D curvature and the projection of a portion of that curvature onto 3-D space, and well, it all gets a lot more complicated than just "straight or curved".

Mentor
 Quote by spark802 Okay i want to stir something up....do we earth dwellers move around the sun in a roughly circular path (ellipse) OR are we moving in a straight line in a curved space?
We are following a geodesic in curved space time. A geodesic is an extension of the concept of a "straight line" to curved space time. And you can't leave time out of the equation.

It might help you understand by looking at a different non-Euclidean geometry, the geometry of the surface of the Earth. Ignoring the little bumps from mountains, dips from ocean trenches, is the equator a "straight line"? The equator is a circle. How could it possibly be a "straight line"?

The answer is that it is a straight line in the sense that a "straight line" between points A and B is the shortest of all possible paths between A and B. (Better said as "one of the shortest paths". The shortest path is not necessarily unique once you through out the parallel postulate). Consider the problem of going from point A to point B on the surface of the Earth. No tunneling is allowed. Each possible path from A and B must lie entirely on the surface of the Earth. In this sense, the equator is a "straight line" in the non-Euclidean geometry of a spherical surface.

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 Quote by e^(i Pi)+1=0 Scientifically, you would use whichever theory is more helpful to your calculations / prediction making at the time. Which one is really true is a question for a philosopher, not a physicist.
Nonsense. GR is the correct theory and the Newtonian approximation is just that, an approximation. No philosophy required.
 Mentor While Newton is not right (and only an approximation), you cannot say that GR is "right" and "describes how the universe is". Maybe GR is just a better approximation? This is the usual opinion by the way, as it does not include quantum effects. But even if GR is exact, it does not tell you that there is a curved spacetime somewhere. The curved spacetime is a model. It gives the right predictions (at least up to now). But that is all we can get from a theory.

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 Quote by mfb While Newton is not right (and only an approximation), you cannot say that GR is "right" and "describes how the universe is". Maybe GR is just a better approximation? This is the usual opinion by the way, as it does not include quantum effects. But even if GR is exact, it does not tell you that there is a curved spacetime somewhere. The curved spacetime is a model. It gives the right predictions (at least up to now). But that is all we can get from a theory.
Well, yes, GR is probably just a better approximation and incomplete, but that's beyond the scope of what's being discussed. Everything is a model, but some are certainly more accurate than others.

 Quote by Pengwuino Nonsense. GR is the correct theory and the Newtonian approximation is just that, an approximation. No philosophy required.
Could you please show or say how much difference the 'correct theory' shows versus the
'approximation' with regards to, say, the orbital period and velocity of the earth?
And what new information does this give us that pertains to earthly dwelling?
The realm of philosophy may be called upon to determine where we should stop our
decimal places.

Scientific theories are prediction tools. The best & simplest tool for the job is the one that is always chosen. Whether or not they should be anything more is a point of contention. Einstein thought so, Niels Bohr disagreed.

 Quote by Acker Could you please show or say how much difference the 'correct theory' shows versus the 'approximation' with regards to, say, the orbital period and velocity of the earth? And what new information does this give us that pertains to earthly dwelling? The realm of philosophy may be called upon to determine where we should stop our decimal places.
The orbit of Mercury. Frame dragging by the sun causes changes in its orbit that deviate from the predictions made by Newtonian gravity.

edit: apparently Mercury's anomalous orbit is caused by another GR effect other than frame dragging, either way it's still an example of where the theories deviate.
 Philosophy allows you to produce a framework within which one can interpret observations or findings, it doesn't matter one whit whether you prefer philsophical model A or B, the universe functions just the same either way. A particular philosophy might provide useful insight to ask a useful question, or allow one to gain greater insight in general, but the decimal places stop where the limits of our instruments place them. Newtonian physics is not terribly incorrect regarding basic things like a naive prediction of a planetary orbit, but more complex effects such as precession are poorly handled without relativistic calculations included. The term you want to watch for is "weak field approximation" or "low energy", when things are slow and spacetime is nearly flat, there is almost no significant difference, but the difference is there, and it is important. Case in point: calculate what rate the clocks in a GPS satellite should tick at without taking into account both SR and GR effects. The gravitational acceleration varies enough from the surface of the planet to GPS orbits for it to matter, and the velocity of the satellites matters as well. Though both adjustments are measured in nanoseconds, that is the difference between knowing where you are within feet and meters, as I recall.

 Quote by D H We are following a geodesic in curved space time. A geodesic is an extension of the concept of a "straight line" to curved space time. And you can't leave time out of the equation. It might help you understand by looking at a different non-Euclidean geometry, the geometry of the surface of the Earth. Ignoring the little bumps from mountains, dips from ocean trenches, is the equator a "straight line"? The equator is a circle. How could it possibly be a "straight line"? The answer is that it is a straight line in the sense that a "straight line" between points A and B is the shortest of all possible paths between A and B. (Better said as "one of the shortest paths". The shortest path is not necessarily unique once you through out the parallel postulate). Consider the problem of going from point A to point B on the surface of the Earth. No tunneling is allowed. Each possible path from A and B must lie entirely on the surface of the Earth. In this sense, the equator is a "straight line" in the non-Euclidean geometry of a spherical surface.
Thank you DH.