Objects Falling in General Relativity

[d-richard]

Greetings,
I've been learning about special relativity and most of the learning media included a part of general relativity. From that I learned that space-time is curved and orbits are nothing more than an object following a path in 4D. However I do not understand how those objects may rotate, as that requires a centripetal force, which in Newton's case was gravity. Also I do not understand how objects may change their velocity's direction without a force or torque in the case of rotational motion (the objects velocity constantly changes during rotation and its angular velocity increases from 0) I also do not understand how objects fall in straight paths on Earth and accelerate in the absence of a force or what keeps us stuck to the ground. Sorry for being so long and thanks for any answers.
P.S As my maths is pretty basic (linear algebra and Euclidean geometry only) I would appreciate a qualitative, not quantitative answer. However if any points must be shown mathematically, then I won't mind the use of maths. Thanks a lot.

 

[A.T.]

I also do not understand how objects fall in straight paths on Earth and accelerate in the absence of a force

Check out this animation:

https://www.youtube.com/watch?v=DdC0QN6f3G4

Orbits are more difficult to visualize in this way, because they involve 2 spatial dimensions, which together with time require visualizing a curved 3D manifold. An alternative analogy are light rays in a block of varying optical density:

http://www.nature.com/nphoton/journal/v7/n11/full/nphoton.2013.247.html?WT.ec_id=NPHOTON-201311

 

[Cosmobrain]

I had the same doubt OP had and this video is simply perfect. I want to thank you A.T for sharing it! Really.

cb

 

[d-richard]

thanks, that really clarifies things. Great video