The phenomenon of time dilation occurs when the passage of time is experienced differently by observers in different gravitational fields or relative speeds. The specific time dilation experienced in space relative to Earth depends on the specific conditions of the scenario.
If we consider a scenario where an observer is traveling at a significant fraction of the speed of light relative to Earth, special relativity predicts that time dilation will occur. In this case, as observed from Earth, time would appear to pass more slowly for the moving observer.
To calculate the time dilation in such a scenario, we can use the Lorentz factor, γ (gamma), which is defined as:
γ = 1 / sqrt(1 - v^2/c^2),
where v is the velocity of the moving observer and c is the speed of light.
Let's assume the observer is traveling at 0.99 times the speed of light (v = 0.99c). Plugging this value into the equation, we can calculate the corresponding γ factor:
γ = 1 / sqrt(1 - (0.99)^2) ≈ 7.0888.
This means that time would appear to pass approximately 7.0888 times slower for the moving observer compared to an observer at rest on Earth. In other words, for every 1 day experienced by the observer in space, approximately 7.0888 days would have passed on Earth.
It's important to note that this calculation assumes constant velocity and does not take into account other factors like acceleration, gravitational fields, or the effects of general relativity. These factors can introduce additional complexities and influence the observed time dilation.