Time can indeed work differently between Earth and Mars due to their relative velocities and the distances between them. This phenomenon is known as time dilation and is a consequence of Einstein's theory of relativity.
Time dilation occurs when an observer's perception of time is affected by their relative motion compared to another observer. There are two types of time dilation: gravitational time dilation and velocity time dilation.
Gravitational Time Dilation: This effect is due to the gravitational fields of massive objects. According to general relativity, time passes more slowly in stronger gravitational fields. Since Mars has less mass than Earth, its gravitational field is weaker. Therefore, time would pass slightly faster on Mars compared to Earth.
Velocity Time Dilation: This effect is caused by differences in relative velocity. According to special relativity, as an object moves closer to the speed of light, time appears to slow down from the perspective of a stationary observer. However, the difference in velocity between Earth and Mars is not significant enough for noticeable time dilation effects.
The most significant factor influencing the difference in time between Earth and Mars is the distance between them. Mars is, on average, about 225 million kilometers away from Earth. This distance introduces a delay in communication and travel time between the two planets. For example, the time it takes for a spacecraft to travel from Earth to Mars can range from several months to over a year, depending on the specific trajectory chosen.
To summarize, while gravitational time dilation has a minimal effect due to the weaker gravitational field on Mars, the main factor affecting time between Earth and Mars is the distance and the associated communication and travel times.