lordoftheselands said:
TL;DR Summary: gravity
people say that gravity is not a force, that it's rather a distortion of space-time
so objets that go to a gravitational center are actually just moving through space in linear direction
but there is a problem in this theory
shouldn't objects go to the center in constant speed? why are they being accelerated?
Consider two great circles on the curved surface of the Earth.
The great circles are like straight lines, in that they are the shortest distance between two points.
If you have two ships that follow great circles routes from the north pole to the south pole, they will initially move away from each other as judged by the rate of change of their separation vector. The rate of change of their separation decreases, eventually stopping at the equator, and then they start to approach each other.
This is an example of what is called "geodesic deviation", great circles on the surface of a sphere, and straight lines in the Euclidean plane, are examples of geodesics.
The mathematics of curvature say that geodesics on curved surfaces accelerate away from each other. In fact, that's one of the possible definitions of curvature.
The example of the Earth's surface is an example of a curved spatial surface, which is easier to visualize. One can gain some insight into GR by imagining that one draws space-time diagrams on a curved surface, such as a sphere, though this technique can only handle 2 dimensons, one of space and one of time, and not the 4 dimensions neaded for actual space-time. To really compute results, one needs to go beyond such simple visualizations and treat the topic mathematically.
In our simple great circle example, then, it's better to imagine one of the dimensions as time, say the north-south motion, and the other dimension (east-west) as space.
The great circle example lacks the feature of how matter determines geometry - the geometry of the sphere is just given. In GR, there is a mathematical relationship between the distribution of matter (energy, momentum, and pressure), and the curvature of space-time given by Einstein's field equations.
Sadly, both the term on the left side (related to curvature) and the term on the right hand side (related to matter distribution) are not easy to discuss without a considerable amount of background. The thing on the left hand side is called the "Einstein curvature tensor", and the thing on the right hand side is called "the stress energy tensor", but the names won't mean much without physics and maths that is usually introduced at the graduate level (or sometimes the late undergraduate level).