Yes, astronauts do experience time dilation. When astronauts travel at high velocities or spend time in gravitational fields that differ from those on Earth, they will encounter time dilation effects as predicted by Einstein's theory of relativity.
Velocity-related time dilation occurs when astronauts travel at significant fractions of the speed of light. For example, during space missions where spacecraft travel at high speeds relative to Earth, time dilation effects become noticeable. As the velocity of the spacecraft increases, the time experienced by the astronauts on board will appear to pass more slowly relative to observers on Earth.
Gravitational time dilation also affects astronauts during space missions. As they move away from the Earth's surface and experience weaker gravitational fields, time will pass slightly faster for them compared to observers on the surface of the Earth. Conversely, when astronauts approach massive objects such as planets or black holes, where the gravitational field is stronger, time will pass more slowly for them relative to observers in weaker gravitational fields.
The combined effect of velocity-related and gravitational time dilation may result in measurable differences in the aging of astronauts compared to people on Earth. However, the magnitude of these effects would typically be small for most space missions. Only for extremely high velocities or strong gravitational fields, such as those near black holes, would the time dilation effects become more significant.
It's worth noting that these time dilation effects have been taken into account in space missions and are considered during the planning and execution of astronaut activities, including the synchronization of clocks and communication with mission control.