Why does the motion of the planet around a star cause a centrifugal force?

Please consider the differences in Newtonian physics and general relativity.

Newtonian physics

In Newtonian physics it makes sense that objects placed on a planets surface facing away from the planets star weight less than objects placed on a planets surface facing to the star due to a "centrifugal force"/ the objects inertia.

General relativity

Considering (my understanding of) general relativity, a planet follows a straight line and the space itself is bend into an orbit. As there is no change in velocity of objects on the surface of the planet there shouldn't be a centrifugal force. Objects on both sides of the planets should have the same weight.

Is there a way to understand this difference and why is there a centrifugal force?

• Only the center of mass of the planet moves on a geodesic line, objects on its surface do not and they do experience tidal forces. The same is true for the ISS. True microgravity experiments can only be performed at the center of mass of the station, which, of course, keeps shifting all the time as people are moving around, air circulates trough the modules, thermal expansion changes from orbit to orbit. The ISS is therefor actually a pretty poor microgravity lab. – CuriousOne Dec 22 '14 at 22:39
• @CuriousOne : Why don't you post you comment as an answer? – Sofia Dec 23 '14 at 10:50
• @Sofia: Five votes? Wow... and I thought that was too trivial for an answer. OK, will do. – CuriousOne Dec 23 '14 at 10:52
• @CuriousOne : 6 votes. Post your answer, what you wait for? – Sofia Dec 23 '14 at 10:55

Only the center of mass of the planet moves on a geodesic line, objects on its surface do not and they do experience tidal forces. The same is true for the ISS. True microgravity experiments can only be performed at the center of mass of the station, which, of course, keeps shifting all the time as people are moving around, air circulates trough the modules, thermal expansion changes from orbit to orbit. The ISS is therefor actually a pretty poor microgravity lab. The Wikipedia article http://en.wikipedia.org/wiki/Micro-g_environment claims that the tidal forces in low Earth orbit amount to $0.33\mu g/m$.