# Motion of celestial objects in Spacetime looks circular in 3D how?

1. Jan 5, 2012

### VaibhavP

I am confused, how the motion of the planets we observing is circular?
The motion of the every object in Spacetime is straight, but as we are watching it in 3D, it seems to be circular. What is the reason behind it?
In simple words, how the straight motion of the objects in 4D(spacetime) looks circular in the 3D??

2. Jan 5, 2012

### D H

Staff Emeritus
You are taking the term "straight" too literally, and you are thinking of spacetime as if it were Euclidean. Don't let your Euclidean concept of space straight-jacket your thinking! Spacetime in the vicinity of a massive object is not Euclidean.

A much better term to use than "straight line" is "geodesic". A geodesic generalizes the concept of straightness. Don't think of it as meaning "straight" in the Euclidean sense. In Euclidean geometry, the straight line from point A to point B is the path that minimizes the length of the path per the Euclidean norm. In curved spacetime, a geodesic from point A to point B is a path that minimizes the length of the path per the Riemannian metric tensor.

Note that I said "the straight line" but "a geodesic". There is but one "straight line" from A to B in Euclidean geometry. It is unique. This is no longer true in curved spacetime.