Yes, time dilation caused by gravity is similar in concept to gravity affecting your motion. In general relativity, the theory of gravity proposed by Albert Einstein, the presence of mass or energy curves the fabric of spacetime, causing objects to move along curved paths. This curvature is what we perceive as the force of gravity.
In the context of time dilation, the curvature of spacetime near massive objects like planets, stars, or black holes affects the passage of time. The greater the curvature, the more significant the time dilation effects.
When you jump on Earth, you experience the force of gravity pulling you downwards. This force opposes your upward motion and slows you down, eventually causing you to fall back to the ground. Similarly, the presence of a massive object curves the fabric of spacetime, and this curvature affects the flow of time.
As you move closer to a massive object, the gravitational field becomes stronger, and the curvature of spacetime increases. This leads to a dilation of time, where time appears to pass more slowly for an observer in a stronger gravitational field compared to an observer in a weaker gravitational field.
An extreme example of time dilation caused by gravity is near a black hole. The intense gravitational pull near a black hole creates a significant curvature of spacetime, resulting in profound time dilation. An observer far from the black hole would perceive time passing much more rapidly for themselves compared to an observer near the black hole.
So, in summary, both gravity affecting your motion and time dilation caused by gravity are consequences of the curvature of spacetime near massive objects.