Time dilation is a phenomenon in which time appears to pass differently for observers in different frames of reference, particularly when there are differences in their relative velocities or gravitational fields. According to the theory of relativity, time dilation occurs when an object is in motion or in a gravitational field.
There are two main types of time dilation: velocity time dilation and gravitational time dilation. Velocity time dilation, also known as relative time dilation, occurs when two observers are moving relative to each other at different velocities. According to the theory of special relativity, time appears to run slower for the moving observer compared to the stationary observer. This effect becomes more significant as the relative velocity between the observers approaches the speed of light.
Gravitational time dilation, on the other hand, is caused by differences in gravitational fields. According to the theory of general relativity, time runs slower in regions of stronger gravitational fields. This means that an observer in a stronger gravitational field, such as near a massive object like a planet or a black hole, will experience time passing more slowly compared to an observer in a weaker gravitational field.
Regarding the Apollo astronauts, they did experience time dilation during their missions. However, the effect was extremely small due to the relatively low velocities involved and the weak gravitational fields in the vicinity of the Moon. The velocity time dilation experienced by the Apollo astronauts was on the order of microseconds, while the gravitational time dilation was even smaller.
In practical terms, the time dilation experienced by the Apollo astronauts was not noticeable during their missions. The effects of time dilation become more significant at extremely high speeds or in the vicinity of very massive objects. For everyday human experiences, such as those encountered during the Apollo missions, the effects of time dilation are negligible and can be ignored.