How does General Relativity explain the orbit of a planet around a star?

[HarryWertM]

The wikipedia article titled "Geodesics & General Relativity" opens with:

"the path of a planet orbiting around a star is the projection of a geodesic of the curved 4-D spacetime geometry around the star onto 3-D space."

Uhhhh... "Real" spacetime has four dimensions - 3 space; 1 time. To map the precession of Mercury in "real" spacetime, GR practitioners MUST be projecting GR's "curved" spacetime onto "real" spacetime.

No?

 

[Dale]

GR practitioners MUST be projecting GR's "curved" spacetime onto "real" spacetime.

What do you mean by '"real" spacetime'? I have never heard such a term.

 

[bapowell]

"the path of a planet orbiting around a star is the projection of a geodesic of the curved 4-D spacetime geometry around the star onto 3-D space."

All they're saying here is that the planet traces out a path in 4D spacetime. The path of the planet -- the spatial route taken by the planet -- is the projection of this 4D geodesic onto the 3D (spatial) hypersurface.

 

[HarryWertM]

What do you mean by '"real" spacetime'? I have never heard such a term.

I likewise never heard the term until I searched for words to understand Wikipedia. Maybe they are just wrong. Curved 4D spacetime maybe is not mapped anywhere because we are actually living in it?

 

[Nabeshin]

I likewise never heard the term until I searched for words to understand Wikipedia. Maybe they are just wrong. Curved 4D spacetime maybe is not mapped anywhere because we are actually living in it?

Right, but we perceive events as a sequence of 3-dimensional slices of 4-dimension spacetime, strung together by observations at different time values. So the 3-d slices we perceive are the projection of the full four-dimensional worldline into the three spatial dimensions.