If there is no gravity then why space curved around the Earth? As I got it from the Veritasium video on YouTube (I know, people told me before that the video isn't perfect and YouTube isn't the best place to get such knowledge): a satellite flies around the Earth not because of gravity (by relativity theory there is no such thing), it files always straight, but space around Earth is curved around it, so it flies around the Earth.
Also it was told that there is not gravity force, but isn't relativity theory told us that the stronger gravity (the bigger planet, star) the slower time goes near/on that planet?
(Probably it's not related to the question, but also interesting how "no gravity" relates to gravity waves?)
 A: It’s just language. Physicists could stop using the word “gravity” and could say “curvature of spacetime” instead. But out of force of habit, we still talk about the “stronger gravity” near a planet or star instead of “more strongly curved spacetime” and we still talk about “gravitational waves” (note that gravity waves are something different) instead of “oscillations in the curvature of spacetime”.
A: Imagine planets to the left and right of your spaceship as in an avenue of trees.

*

*Not feeling any drag, your ship will wiggling to the left and to the right in dependency from the next planet. All the time you will feel weightless and without any acceleration.

*Having at the end a planet direct in front of you, you will freefall to it, again not feeling any acceleration (if no atmosphere slows down).

*A spaceship with different initial speed, driving from the same point and in the same initial direction, will follow a different path.

*The straightest path will have a photon.

Flying tangential to a planet your ship has three possibilities.

*

*With a high enough speed it will be deflected and then escapes.

*With just the right speed it will be bended in a way that it curve around the planet

*With a lower speed it crashes into the planet.

Since in all these cases you not feel acceleration (except the moment of the crash), no force is applied. You remember F = ma? That is why Einstein insists of the formulation of the bending space from gravity.
Of course, gravity plays an important role in all these processes. However, it would be better to speak of gravitational potential. Because, for example, any calculation of the correct speed for orbiting the Earth without taking into account the gravitational potential of the Sun leads to incorrect results.
