# Is spacetime in an ellipse around a massive object, or does it just slope down towards the massive object?

In some discussions, people seem to imply that spacetime is in an actual ellipse around a massive object so that, for example, the planet orbiting a star is actually traveling in a straight line in spacetime as it orbits the star. But my understanding is more that spacetime just curves slightly around the star and that the planet is simply falling down a slope towards the star as the planet attempts to fly off in a straight line.

It seems to me that if spacetime was in an ellipse then everything, including light would get trapped in the ellipse and never escape, just like a planet. Or perhaps the ellipse concept is correct and the result has more to do with the speed of the orbiting object. This would be the time part of spacetime.

• Your (and my own) physical pictures will eventually let us both down, nobody can visualise 4 dimensions. Only mathematics can give you a correct description.
– user198207
Jul 3, 2018 at 17:47
• Is spacetime in an ellipse... What do you mean? Spacetime is 4D. An ellipse is only 1D. Jul 3, 2018 at 19:24
• @Qmechanic: I think my original question explains what I mean. Is a planet, orbiting around a star, traveling in a straight line in spacetime? A straight line that circles around the star. Or, to the planet, is a straight line still outwards from the star but it keeps falling down the spacetime slope towards the star. Jul 3, 2018 at 20:38
• The closest things to straight lines in a curved space are trajectories of light. They are "still outwards", not elipses around a star. Planets on elliptical orbits do not move along straight lines. There is one exception though. When gravity is very strong, such as around a black hole or large neutron star, light can indeed move on an orbit around the star. The sphere of these orbits is called the photon sphere. If our Sun were squeezed to become a neutron star, the diameter of its photon sphere would be 9 km. So a circle 9 km in diameter around the squeezed Sun would be a straight line. Jul 3, 2018 at 21:04
• @safesphere: So we can confidently say that light travels in a straight line in spacetime? Whether that be coming from a distant location and curving between galaxies, or even traveling in an unending circle, trapped around a black hole or neutron star? Jul 3, 2018 at 22:39