# Is the earth flat?

1. Aug 4, 2006

### markintheworld

This is a bit of a lark, but i'm just wondering if i've understood correctly to draw my conclusion....

It is my understanding that the curvature of spacetime postulated by GR is what causes orbits which appear elliptical. An orbiting body is following its inertial path which might otherwise be a straight line, but due to the curvature of spacetime caused by a nearby massive object, that straight line appears curved, as if the orbiting body were traveling around the edge of a depression. So the moon is traveling in a straight line (its inertial tendency), but because it is near the earth, a massive gravitational object, it APPEARS to be traveling a curved path. Am i correct so far?

Assuming the above is true, that a straight path can appear curved due to the distorting effects of gravity, couldn't it also figure that a flat plane could appear similarly curved? Couldn't it be true that the surface of the earth is a flat plane, but the curvature of space-time caused by its own gravity is the reason that it appears spherical? Is this why large gravitational objects generally appear to be spherical? Or is there some flaw in my logic?

Insight would be appreciated....

2. Aug 4, 2006

### Thrice

Inertial path doesn't automatically mean straight line. The straight line is a special case. When something follows an inertial path/geodesic/maximizes proper time & all that it may be going straight or not depending on the geometry.

3. Aug 4, 2006

### MeJennifer

No in GR theory this is not the case!
An orbiting body is traveling on a geodesic but a geodesic is not necessarily a straight line!
See for a detailed discussion on this subject see the last few pages of: Real frame (strong issue)

Last edited: Aug 4, 2006
4. Aug 4, 2006

### pervect

Staff Emeritus
Using standard rulers, the surface of the Earth cannot be flat, because it has a non-zero "curvature tensor".

Similarly, space-tme cannot be flat around the Earth, either, because space-time has a non-zero "curvature tensor".

This is assuming that one defines the rather fuzzy English word "flat" with the mathematical defintion "zero Riemann curvature tensor".

The longish quote from Einstein in the thread